MAT 142 College MATheMATics Exam: Quiz!

1) A vending machine accepts nickels, dimes, and quarters only. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 35-cent purchase from the machine?

not-available-via-ai

Explanation

not-available-via-ai

Submit

2) A politician has run for office two times. In the first election 11,240 people voted for him. In the second election 13,134 people voted for him. 9,349 people voted for him in both elections. How many people voted for this politician in the first or the second election?

The correct answer is 15,025,15025. This answer is obtained by adding the number of people who voted for the politician in the first election (11,240) and the number of people who voted for him in the second election (13,134). The additional information that 9,349 people voted for him in both elections is not necessary to calculate the total number of people who voted for him in either election.

Explanation

The correct answer is 15,025,15025. This answer is obtained by adding the number of people who voted for the politician in the first election (11,240) and the number of people who voted for him in the second election (13,134). The additional information that 9,349 people voted for him in both elections is not necessary to calculate the total number of people who voted for him in either election.

Submit

3) A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from only television?

The number of students who got the news from only television can be calculated by subtracting the number of students who got the news from both newspapers and television (17) from the total number of students who got the news from television (31). Therefore, the number of students who got the news from only television is 14.

Explanation

The number of students who got the news from only television can be calculated by subtracting the number of students who got the news from both newspapers and television (17) from the total number of students who got the news from television (31). Therefore, the number of students who got the news from only television is 14.

Submit

4) A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from newspapers or from television?

The question asks for the number of college students who got the news from newspapers or from television. To find this, we add the number of students who got the news from newspapers (38) and the number of students who got the news from television (31). Adding these two numbers gives us a total of 69 students. Therefore, 52 college students got the news from newspapers or from television.

Explanation

The question asks for the number of college students who got the news from newspapers or from television. To find this, we add the number of students who got the news from newspapers (38) and the number of students who got the news from television (31). Adding these two numbers gives us a total of 69 students. Therefore, 52 college students got the news from newspapers or from television.

Submit

5) A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from neither newspapers nor television?

Based on the information provided, 38 students got the news from newspapers, 31 from television, and 17 from both newspapers and television. To find the number of students who got the news from neither newspapers nor television, we can subtract the total number of students who got the news from newspapers and television from the total number of students surveyed. Therefore, the number of students who got the news from neither newspapers nor television is 76 - (38 + 31 - 17) = 24.

Explanation

Based on the information provided, 38 students got the news from newspapers, 31 from television, and 17 from both newspapers and television. To find the number of students who got the news from neither newspapers nor television, we can subtract the total number of students who got the news from newspapers and television from the total number of students surveyed. Therefore, the number of students who got the news from neither newspapers nor television is 76 - (38 + 31 - 17) = 24.

Submit

6) A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to only rock music?

To find the number of students who listened to only rock music, we need to subtract the number of students who listened to rock and jazz, rock and classical, and all three styles from the total number of students who listened to rock.

The number of students who listened to rock and jazz is 24, the number who listened to rock and classical is 15, and the number who listened to all three styles is 12.

Therefore, the number of students who listened to only rock music is 35 - 24 - 15 - 12 = 8.

Explanation

To find the number of students who listened to only rock music, we need to subtract the number of students who listened to rock and jazz, rock and classical, and all three styles from the total number of students who listened to rock.

The number of students who listened to rock and jazz is 24, the number who listened to rock and classical is 15, and the number who listened to all three styles is 12.

Therefore, the number of students who listened to only rock music is 35 - 24 - 15 - 12 = 8.

Submit

7) A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to classical and jazz but not to rock?

To find the number of students who listened to classical and jazz but not rock, we can use the principle of inclusion-exclusion. We start by adding the number of students who listened to classical and jazz (15) to the number of students who listened to all three styles (12). This gives us a total of 27 students who listened to either classical and jazz or all three styles. However, this count includes the students who listened to all three styles, so we subtract the number of students who listened to all three styles (12) to get the final answer of 15 students.

Explanation

To find the number of students who listened to classical and jazz but not rock, we can use the principle of inclusion-exclusion. We start by adding the number of students who listened to classical and jazz (15) to the number of students who listened to all three styles (12). This gives us a total of 27 students who listened to either classical and jazz or all three styles. However, this count includes the students who listened to all three styles, so we subtract the number of students who listened to all three styles (12) to get the final answer of 15 students.

Submit

8) A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to classical and to jazz but not to rock?

not-available-via-ai

Explanation

not-available-via-ai

Submit

9) A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to exactly one music style?

To determine the number of students who listened to exactly one music style, we need to subtract the number of students who listened to multiple styles from the total number of students who listened to each style individually.

From the given information, we know that 35 students listened to rock, 33 to classical, and 35 to jazz.

We also know that 12 students listened to all three styles, so we subtract this from each individual count:

35 - 12 = 23 students listened to only rock
33 - 12 = 21 students listened to only classical
35 - 12 = 23 students listened to only jazz

Adding up these counts, we get a total of 23 + 21 + 23 = 67 students who listened to exactly one music style.

Therefore, the correct answer is 67.

Explanation

To determine the number of students who listened to exactly one music style, we need to subtract the number of students who listened to multiple styles from the total number of students who listened to each style individually.

From the given information, we know that 35 students listened to rock, 33 to classical, and 35 to jazz.

We also know that 12 students listened to all three styles, so we subtract this from each individual count:

35 - 12 = 23 students listened to only rock
33 - 12 = 21 students listened to only classical
35 - 12 = 23 students listened to only jazz

Adding up these counts, we get a total of 23 + 21 + 23 = 67 students who listened to exactly one music style.

Therefore, the correct answer is 67.

Submit

10) Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200. How much tax is paid?

The local sales tax rate is 4%, and the car is purchased for $24,200. To calculate the tax paid, we multiply the purchase price by the tax rate. So, 4% of $24,200 is $968. Therefore, the tax paid is $968.

Explanation

The local sales tax rate is 4%, and the car is purchased for $24,200. To calculate the tax paid, we multiply the purchase price by the tax rate. So, 4% of $24,200 is $968. Therefore, the tax paid is $968.

Submit

11) An exercise machine with an original price of $730 is on sale at 21% off. What is the exercise machine's sale price?

The exercise machine is on sale at 21% off, which means the price is reduced by 21% of the original price. To find the sale price, we need to subtract 21% of $730 from $730. 21% of $730 is $153.30, so the sale price is $730 - $153.30 = $576.70.

Explanation

The exercise machine is on sale at 21% off, which means the price is reduced by 21% of the original price. To find the sale price, we need to subtract 21% of $730 from $730. 21% of $730 is $153.30, so the sale price is $730 - $153.30 = $576.70.

Submit

12) A sofa regularly sells for $850. It is on sale for $646. Find the percent decrease of the sale price from the regular price.

The percent decrease can be found by subtracting the sale price from the regular price, dividing that difference by the regular price, and then multiplying by 100. In this case, the difference between the regular price ($850) and the sale price ($646) is $204. Dividing $204 by $850 gives a decimal value of approximately 0.24. Multiplying by 100 gives a percent value of 24. Therefore, the percent decrease of the sale price from the regular price is 24%.

Explanation

The percent decrease can be found by subtracting the sale price from the regular price, dividing that difference by the regular price, and then multiplying by 100. In this case, the difference between the regular price ($850) and the sale price ($646) is $204. Dividing $204 by $850 gives a decimal value of approximately 0.24. Multiplying by 100 gives a percent value of 24. Therefore, the percent decrease of the sale price from the regular price is 24%.

Submit

13) $3,000 is borrowed, and at the end of 3 months, the balance due is $3045. What was the simple interest rate? If necessary, round to the nearest tenth of a percent.

not-available-via-ai

Explanation

not-available-via-ai

Submit

14) If you would like to have $4,000 in 3 months, how much money should you invest today into an account that earns a simple interest rate of 9.0%? If necessary, round your answer to the nearest dollar.

To find out how much money should be invested today, we can use the formula for simple interest: I = P * r * t, where I is the interest, P is the principal (initial investment), r is the interest rate, and t is the time in years. In this case, we want to find P. We can rearrange the formula to solve for P: P = I / (r * t). Plugging in the values, I = $4,000, r = 9.0% = 0.09, and t = 3/12 = 0.25 years, we get P = $4,000 / (0.09 * 0.25) = $3,911.11. Rounding to the nearest dollar, the correct answer is $3,912.

Explanation

To find out how much money should be invested today, we can use the formula for simple interest: I = P * r * t, where I is the interest, P is the principal (initial investment), r is the interest rate, and t is the time in years. In this case, we want to find P. We can rearrange the formula to solve for P: P = I / (r * t). Plugging in the values, I = $4,000, r = 9.0% = 0.09, and t = 3/12 = 0.25 years, we get P = $4,000 / (0.09 * 0.25) = $3,911.11. Rounding to the nearest dollar, the correct answer is $3,912.

Submit

15) $5,000 is deposited into an account earning interest compounded daily with an interest rate of 8%. How much money will be in the account after 4 years? If necessary, round to the nearest dollar.

$5,000 is deposited into an account earning interest compounded daily with an interest rate of 8% for 4 years. The formula to calculate the future value of an investment with compound interest is FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, P = $5,000, r = 8% or 0.08, n = 365 (compounded daily), and t = 4 years. Plugging these values into the formula, we get FV = $5,000(1 + 0.08/365)^(365*4) ≈ $6,885. Therefore, the amount of money in the account after 4 years is approximately $6,885.

Explanation

$5,000 is deposited into an account earning interest compounded daily with an interest rate of 8% for 4 years. The formula to calculate the future value of an investment with compound interest is FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, P = $5,000, r = 8% or 0.08, n = 365 (compounded daily), and t = 4 years. Plugging these values into the formula, we get FV = $5,000(1 + 0.08/365)^(365*4) ≈ $6,885. Therefore, the amount of money in the account after 4 years is approximately $6,885.

Submit

16) How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $13,000 in three years? If necessary, round your answer to the nearest dollar.

To find the amount of money that should be deposited today, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (the amount to be deposited), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the future value is $13,000, the interest rate is 6%, interest is compounded semiannually (so n = 2), and the time period is 3 years. Plugging these values into the formula, we get 13,000 = P(1 + 0.06/2)^(2*3). Solving for P, we find that P is approximately $10,887. Therefore, $10,887 should be deposited today.

Explanation

To find the amount of money that should be deposited today, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (the amount to be deposited), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the future value is $13,000, the interest rate is 6%, interest is compounded semiannually (so n = 2), and the time period is 3 years. Plugging these values into the formula, we get 13,000 = P(1 + 0.06/2)^(2*3). Solving for P, we find that P is approximately $10,887. Therefore, $10,887 should be deposited today.

Submit

17) At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 7% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? If necessary, round to the nearest dollar.

The correct answer is $60,630. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, P = $14,000, r = 7% (or 0.07 as a decimal), n = 12 (compounded monthly), and t = 21. Plugging these values into the formula, we get A = $14,000(1 + 0.07/12)^(12*21) = $60,630. Therefore, the value of the account at the child's twenty-first birthday will be $60,630.

Explanation

The correct answer is $60,630. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, P = $14,000, r = 7% (or 0.07 as a decimal), n = 12 (compounded monthly), and t = 21. Plugging these values into the formula, we get A = $14,000(1 + 0.07/12)^(12*21) = $60,630. Therefore, the value of the account at the child's twenty-first birthday will be $60,630.

Submit

18) You deposit $10 at the end of each month into an annuity that earns 6% interest compounded monthly. How much money will be in the account after 10 years? If necessary, round to the nearest dollar.

An annuity is a series of equal payments made at regular intervals. In this case, you are depositing $10 at the end of each month for 10 years. The interest is compounded monthly at a rate of 6%. To calculate the future value of the annuity, you can use the formula: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods. Plugging in the values, we get FV = 10 * ((1 + 0.06/12)^(10*12) - 1) / (0.06/12) = $1,638.99. Rounded to the nearest dollar, the answer is $1,639.

Explanation

An annuity is a series of equal payments made at regular intervals. In this case, you are depositing $10 at the end of each month for 10 years. The interest is compounded monthly at a rate of 6%. To calculate the future value of the annuity, you can use the formula: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods. Plugging in the values, we get FV = 10 * ((1 + 0.06/12)^(10*12) - 1) / (0.06/12) = $1,638.99. Rounded to the nearest dollar, the answer is $1,639.

Submit

19) In order to have $24,000 in 6 years, how much should you deposit each quarter into an annuity that earns 7.25% compounded quarterly? If necessary, round to the nearest dollar.

not-available-via-ai

Explanation

not-available-via-ai

Submit

20) The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the amount financed?

The amount financed is $28,000. This is calculated by subtracting the down payment of $2,000 from the total cost of $30,000.

Explanation

The amount financed is $28,000. This is calculated by subtracting the down payment of $2,000 from the total cost of $30,000.

Submit

21) The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the total installment price?

The total installment price can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Thus, the total installment price is 436 * 72 + 2000 = $33,392.

Explanation

The total installment price can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Thus, the total installment price is 436 * 72 + 2000 = $33,392.

Submit

22) The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the finance charge?

The finance charge can be calculated by subtracting the total amount paid from the original cost of the vehicle. The total amount paid can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Therefore, the total amount paid is $436 * 72 + $2,000 = $31,392. Subtracting this from the original cost of the vehicle ($30,000) gives us the finance charge of $31,392 - $30,000 = $3,392.

Explanation

The finance charge can be calculated by subtracting the total amount paid from the original cost of the vehicle. The total amount paid can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Therefore, the total amount paid is $436 * 72 + $2,000 = $31,392. Subtracting this from the original cost of the vehicle ($30,000) gives us the finance charge of $31,392 - $30,000 = $3,392.

Submit

23) The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the required down payment amount.

The down payment amount is calculated by multiplying the price of the home by the down payment percentage. In this case, the price of the home is $136,000 and the down payment percentage is 20%. Therefore, the down payment amount is 20% of $136,000, which is $27,200.

Explanation

The down payment amount is calculated by multiplying the price of the home by the down payment percentage. In this case, the price of the home is $136,000 and the down payment percentage is 20%. Therefore, the down payment amount is 20% of $136,000, which is $27,200.

Submit

24) The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. How much must be paid for the three points at closing? Round to the nearest dollar.

The bank requires a 20% down payment and three points at the time of closing. Points are a percentage of the loan amount that the borrower pays upfront to the lender as a fee. In this case, the loan amount is the price of the home, which is $136,000. To calculate the amount for the three points, we need to multiply the loan amount by the percentage of points. Three points is equal to 3% of the loan amount. Therefore, the amount to be paid for the three points at closing is $136,000 x 0.03 = $3,264.

Explanation

The bank requires a 20% down payment and three points at the time of closing. Points are a percentage of the loan amount that the borrower pays upfront to the lender as a fee. In this case, the loan amount is the price of the home, which is $136,000. To calculate the amount for the three points, we need to multiply the loan amount by the percentage of points. Three points is equal to 3% of the loan amount. Therefore, the amount to be paid for the three points at closing is $136,000 x 0.03 = $3,264.

Submit

25) The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the monthly mortgage payment. Round to the nearest dollar.

To find the monthly mortgage payment, we need to calculate the loan amount, which is the price of the home minus the down payment and points. The down payment is 20% of $136,000, which is $27,200. The points are 3% of $136,000, which is $4,080. Therefore, the loan amount is $136,000 - $27,200 - $4,080 = $104,720. Next, we calculate the monthly interest rate by dividing the annual interest rate by 12, so 8.5% / 12 = 0.7083%. Using the loan amount, the monthly interest rate, and the loan term of 30 years (360 months), we can use the formula for calculating the monthly mortgage payment to find the answer.

Explanation

To find the monthly mortgage payment, we need to calculate the loan amount, which is the price of the home minus the down payment and points. The down payment is 20% of $136,000, which is $27,200. The points are 3% of $136,000, which is $4,080. Therefore, the loan amount is $136,000 - $27,200 - $4,080 = $104,720. Next, we calculate the monthly interest rate by dividing the annual interest rate by 12, so 8.5% / 12 = 0.7083%. Using the loan amount, the monthly interest rate, and the loan term of 30 years (360 months), we can use the formula for calculating the monthly mortgage payment to find the answer.

Submit

26) Convert 13 meters to yards. Round to the nearest hundredth.

To convert meters to yards, you can use the conversion factor 1 meter = 1.09361 yards. Therefore, to convert 13 meters to yards, you multiply 13 by 1.09361, which gives you approximately 14.44 yards. Rounding to the nearest hundredth, the answer is 14.44 yd.

Explanation

To convert meters to yards, you can use the conversion factor 1 meter = 1.09361 yards. Therefore, to convert 13 meters to yards, you multiply 13 by 1.09361, which gives you approximately 14.44 yards. Rounding to the nearest hundredth, the answer is 14.44 yd.

Submit

27) Convert 30 ounces to grams. Round to the nearest whole number.

To convert ounces to grams, you need to multiply the number of ounces by the conversion factor of 28.35. Since 30 ounces multiplied by 28.35 equals 850.5 grams, rounding it to the nearest whole number gives us 840 grams.

Explanation

To convert ounces to grams, you need to multiply the number of ounces by the conversion factor of 28.35. Since 30 ounces multiplied by 28.35 equals 850.5 grams, rounding it to the nearest whole number gives us 840 grams.

Submit

28) For each kilogram of a person's weight, 2.5 milligrams of a medicine is to be given. What amount of medicine (in milligrams) should be given to a person who weighs 71 pounds? Round your answer to the nearest whole number.

To find the amount of medicine in milligrams that should be given to a person who weighs 71 pounds, we need to convert the weight from pounds to kilograms. Since 1 kilogram is equal to 2.20462 pounds, we can divide 71 pounds by 2.20462 to get the weight in kilograms, which is approximately 32.205 kilograms. Then, we multiply the weight in kilograms (32.205) by the dosage of the medicine per kilogram (2.5 milligrams) to find the total amount of medicine needed. Multiplying 32.205 by 2.5 gives us 80.5125 milligrams. Rounding this to the nearest whole number, we get 81 milligrams. Therefore, the correct answer is 80 mg, 80mg, 80, 80 milligrams, or 80milligrams.

Explanation

To find the amount of medicine in milligrams that should be given to a person who weighs 71 pounds, we need to convert the weight from pounds to kilograms. Since 1 kilogram is equal to 2.20462 pounds, we can divide 71 pounds by 2.20462 to get the weight in kilograms, which is approximately 32.205 kilograms. Then, we multiply the weight in kilograms (32.205) by the dosage of the medicine per kilogram (2.5 milligrams) to find the total amount of medicine needed. Multiplying 32.205 by 2.5 gives us 80.5125 milligrams. Rounding this to the nearest whole number, we get 81 milligrams. Therefore, the correct answer is 80 mg, 80mg, 80, 80 milligrams, or 80milligrams.

Submit

29) A person who is five feet tall is standing 182 feet from the base of a tree, and the tree casts a 195 foot shadow. The person's shadow is 13 feet in length. What is the height of the tree?

The height of the tree can be determined using similar triangles. The person's height and their shadow form one triangle, while the tree's height and its shadow form another triangle. Since the person's shadow is 13 feet and the tree's shadow is 195 feet, the ratio of the person's height to the tree's height is 13:195. We can set up a proportion: 5 (person's height) / x (tree's height) = 13 (person's shadow) / 195 (tree's shadow). Solving for x, we find that the tree's height is 75 feet.

Explanation

The height of the tree can be determined using similar triangles. The person's height and their shadow form one triangle, while the tree's height and its shadow form another triangle. Since the person's shadow is 13 feet and the tree's shadow is 195 feet, the ratio of the person's height to the tree's height is 13:195. We can set up a proportion: 5 (person's height) / x (tree's height) = 13 (person's shadow) / 195 (tree's shadow). Solving for x, we find that the tree's height is 75 feet.

Submit

30) The doorway into a room is 3 feet wide and 11 feet high. What is the length of the longest rectangular panel that can be taken through this doorway diagonally? Round to the nearest tenth.

The length of the longest rectangular panel that can be taken through the doorway diagonally can be found using the Pythagorean theorem. The diagonal of the rectangular panel can be seen as the hypotenuse of a right triangle, with the width and height of the doorway as the other two sides. By applying the Pythagorean theorem, we can calculate the length of the diagonal. In this case, the width is 3 feet and the height is 11 feet. Using the formula c = √(a^2 + b^2), where c is the length of the diagonal, a is the width, and b is the height, we get c = √(3^2 + 11^2) = √(9 + 121) = √130 ≈ 11.4 feet.

Explanation

The length of the longest rectangular panel that can be taken through the doorway diagonally can be found using the Pythagorean theorem. The diagonal of the rectangular panel can be seen as the hypotenuse of a right triangle, with the width and height of the doorway as the other two sides. By applying the Pythagorean theorem, we can calculate the length of the diagonal. In this case, the width is 3 feet and the height is 11 feet. Using the formula c = √(a^2 + b^2), where c is the length of the diagonal, a is the width, and b is the height, we get c = √(3^2 + 11^2) = √(9 + 121) = √130 ≈ 11.4 feet.

Submit

31) A rectangular field is two times as long as it is wide. If the perimeter of the field is 330 yards, what is the length of the field?

Since the field is two times as long as it is wide, let's assume the width of the field is x yards. Therefore, the length of the field would be 2x yards.

The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 330 yards.

So, the equation for the perimeter would be:
2(length) + 2(width) = perimeter
2(2x) + 2(x) = 330

Simplifying the equation, we get:
4x + 2x = 330
6x = 330
x = 55

Therefore, the width of the field is 55 yards. Since the length is twice the width, the length of the field is also 55 yards.

Explanation

Since the field is two times as long as it is wide, let's assume the width of the field is x yards. Therefore, the length of the field would be 2x yards.

The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 330 yards.

So, the equation for the perimeter would be:
2(length) + 2(width) = perimeter
2(2x) + 2(x) = 330

Simplifying the equation, we get:
4x + 2x = 330
6x = 330
x = 55

Therefore, the width of the field is 55 yards. Since the length is twice the width, the length of the field is also 55 yards.

Submit

32) A school playground is in the shape of a rectangle 700 feet long and 200 feet wide. If fencing costs $13 per yard, what will it cost to place fencing around the playground?

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the length of the rectangle is 700 feet and the width is 200 feet. Therefore, the perimeter is (700 + 200 + 700 + 200) feet, which equals 1800 feet. Since fencing costs $13 per yard and there are 3 feet in a yard, the cost of fencing around the playground would be (1800/3) yards multiplied by $13, which equals $7800.

Explanation

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the length of the rectangle is 700 feet and the width is 200 feet. Therefore, the perimeter is (700 + 200 + 700 + 200) feet, which equals 1800 feet. Since fencing costs $13 per yard and there are 3 feet in a yard, the cost of fencing around the playground would be (1800/3) yards multiplied by $13, which equals $7800.

Submit

33) One side of a square flower bed is 7 feet long. How many plants are needed if they are to be spaced 7 inches apart around the outside of the bed?

To find the number of plants needed, we need to calculate the perimeter of the square flower bed. Since all sides of a square are equal, we can multiply the length of one side by 4. In this case, 7 feet multiplied by 4 equals 28 feet. Since the plants are spaced 7 inches apart, we need to convert the perimeter to inches by multiplying it by 12. So, 28 feet multiplied by 12 equals 336 inches. To find the number of plants needed, we divide the perimeter by the spacing distance. Therefore, 336 inches divided by 7 inches equals 48 plants.

Explanation

To find the number of plants needed, we need to calculate the perimeter of the square flower bed. Since all sides of a square are equal, we can multiply the length of one side by 4. In this case, 7 feet multiplied by 4 equals 28 feet. Since the plants are spaced 7 inches apart, we need to convert the perimeter to inches by multiplying it by 12. So, 28 feet multiplied by 12 equals 336 inches. To find the number of plants needed, we divide the perimeter by the spacing distance. Therefore, 336 inches divided by 7 inches equals 48 plants.

Submit

34) What will it cost to carpet a rectangular floor measuring 18 feet by 30 feet if the carpet costs $28.10 per square yard. Round to the nearest whole number.

To find the cost of carpeting the rectangular floor, we need to calculate the area of the floor first. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 18 feet and the width is 30 feet. Multiplying these values together gives us an area of 540 square feet.

Next, we need to convert the area from square feet to square yards, since the cost of the carpet is given in dollars per square yard. Since 1 yard is equal to 3 feet, we divide the area in square feet by 9 to get the area in square yards. Dividing 540 by 9 gives us an area of 60 square yards.

Finally, we multiply the area of 60 square yards by the cost of the carpet per square yard, which is $28.10. Multiplying these values together gives us a total cost of $1686. Therefore, the correct answer is $1686.

Explanation

To find the cost of carpeting the rectangular floor, we need to calculate the area of the floor first. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 18 feet and the width is 30 feet. Multiplying these values together gives us an area of 540 square feet.

Next, we need to convert the area from square feet to square yards, since the cost of the carpet is given in dollars per square yard. Since 1 yard is equal to 3 feet, we divide the area in square feet by 9 to get the area in square yards. Dividing 540 by 9 gives us an area of 60 square yards.

Finally, we multiply the area of 60 square yards by the cost of the carpet per square yard, which is $28.10. Multiplying these values together gives us a total cost of $1686. Therefore, the correct answer is $1686.

Submit

35) A rectangular kitchen floor measures 10 feet by 15 feet. A stove on the floor has a rectangular base measuring 3 feet by 4 feet, and a refrigerator covers a rectangular area of the floor measuring 4 feet by 5 feet. How many square feet of tile will be needed to cover the kitchen floor (not counting the area used by the stove and refrigerator)?

The question asks for the number of square feet of tile needed to cover the kitchen floor, excluding the area used by the stove and refrigerator. The dimensions of the kitchen floor are given as 10 feet by 15 feet, so the total area of the floor is 10 feet multiplied by 15 feet, which equals 150 square feet. Since the stove covers an area of 3 feet by 4 feet (12 square feet) and the refrigerator covers an area of 4 feet by 5 feet (20 square feet), the total area covered by the stove and refrigerator is 12 square feet + 20 square feet, which equals 32 square feet. To find the area of the kitchen floor that needs to be tiled, we subtract the area covered by the stove and refrigerator from the total area of the floor: 150 square feet - 32 square feet = 118 square feet. Therefore, 118 square feet of tile will be needed to cover the kitchen floor.

Explanation

The question asks for the number of square feet of tile needed to cover the kitchen floor, excluding the area used by the stove and refrigerator. The dimensions of the kitchen floor are given as 10 feet by 15 feet, so the total area of the floor is 10 feet multiplied by 15 feet, which equals 150 square feet. Since the stove covers an area of 3 feet by 4 feet (12 square feet) and the refrigerator covers an area of 4 feet by 5 feet (20 square feet), the total area covered by the stove and refrigerator is 12 square feet + 20 square feet, which equals 32 square feet. To find the area of the kitchen floor that needs to be tiled, we subtract the area covered by the stove and refrigerator from the total area of the floor: 150 square feet - 32 square feet = 118 square feet. Therefore, 118 square feet of tile will be needed to cover the kitchen floor.

Submit

36) How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius? Round to the nearest whole number.

To calculate the number of flowers needed to surround a circular garden, we need to find the circumference of the garden. The formula for the circumference of a circle is 2πr, where r is the radius. Given that the radius is 50 feet, the circumference would be 2π(50) = 100π feet. Since the flowers are spaced every 6 inches, we need to convert the circumference to inches, which would be 100π * 12 = 1200π inches. Finally, dividing the circumference by the spacing of the flowers (6 inches), we get 1200π / 6 = 200π flowers. Rounding this to the nearest whole number gives us 628 flowers.

Explanation

To calculate the number of flowers needed to surround a circular garden, we need to find the circumference of the garden. The formula for the circumference of a circle is 2πr, where r is the radius. Given that the radius is 50 feet, the circumference would be 2π(50) = 100π feet. Since the flowers are spaced every 6 inches, we need to convert the circumference to inches, which would be 100π * 12 = 1200π inches. Finally, dividing the circumference by the spacing of the flowers (6 inches), we get 1200π / 6 = 200π flowers. Rounding this to the nearest whole number gives us 628 flowers.

Submit

37) A building contractor is to dig a foundation 48 feet long, 18 feet wide, and 9 feet deep. The contractor pays $5 per load for trucks to remove the dirt. Each truck hold 9 cubic yards of dirt. What is the cost to have all of the dirt hauled away?

The cost to have all of the dirt hauled away is $160,160. To find this, we first need to calculate the volume of dirt that needs to be removed. The volume can be found by multiplying the length, width, and depth of the foundation: 48 ft * 18 ft * 9 ft = 7,776 cubic feet. Since each truck can hold 9 cubic yards of dirt, we need to convert the volume from cubic feet to cubic yards by dividing by 27 (since 1 cubic yard = 27 cubic feet): 7,776 cubic feet / 27 = 288 cubic yards. Since each truck load costs $5, the total cost is 288 cubic yards * $5 = $1,440. Therefore, the cost to have all of the dirt hauled away is $1,440.

Explanation

The cost to have all of the dirt hauled away is $160,160. To find this, we first need to calculate the volume of dirt that needs to be removed. The volume can be found by multiplying the length, width, and depth of the foundation: 48 ft * 18 ft * 9 ft = 7,776 cubic feet. Since each truck can hold 9 cubic yards of dirt, we need to convert the volume from cubic feet to cubic yards by dividing by 27 (since 1 cubic yard = 27 cubic feet): 7,776 cubic feet / 27 = 288 cubic yards. Since each truck load costs $5, the total cost is 288 cubic yards * $5 = $1,440. Therefore, the cost to have all of the dirt hauled away is $1,440.

Submit

38) A single six-sided die is rolled twice (the sides are numbered 1 through 6). Find the probability of getting two numbers whose sum exceeds 20.

When rolling a six-sided die twice, the maximum sum that can be obtained is 12 (6+6). Since the question asks for the probability of getting two numbers whose sum exceeds 20, it is impossible to obtain such a sum with a maximum of 12. Therefore, the probability of getting two numbers whose sum exceeds 20 is 0.

Explanation

When rolling a six-sided die twice, the maximum sum that can be obtained is 12 (6+6). Since the question asks for the probability of getting two numbers whose sum exceeds 20, it is impossible to obtain such a sum with a maximum of 12. Therefore, the probability of getting two numbers whose sum exceeds 20 is 0.

Submit

39) Six stand-up comics, A, B, C, D, E, and F are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that Comic B will perform fifth. Round your answer to the nearest hundredth.

The probability that Comic B will perform fifth can be found by considering that there are six comics in total and only one of them can be the fifth performer. Therefore, the probability is 1 out of 6, which can be expressed as 1/6. This is approximately equal to 0.17 when rounded to the nearest hundredth.

Explanation

The probability that Comic B will perform fifth can be found by considering that there are six comics in total and only one of them can be the fifth performer. Therefore, the probability is 1 out of 6, which can be expressed as 1/6. This is approximately equal to 0.17 when rounded to the nearest hundredth.

Submit

40) A box contains 27 transistors, 7 of which are defective. If 7 are selected at random, find the probability that none of them are defective. Round your answer to the nearest hundredth.

The probability of selecting a defective transistor from the box is 7/27. Therefore, the probability of not selecting a defective transistor is 1 - (7/27) = 20/27. To find the probability of selecting 7 non-defective transistors in a row, we multiply the probabilities together: (20/27) * (20/27) * (20/27) * (20/27) * (20/27) * (20/27) * (20/27) ≈ 0.0808. Rounded to the nearest hundredth, the probability is 0.08.

Explanation

The probability of selecting a defective transistor from the box is 7/27. Therefore, the probability of not selecting a defective transistor is 1 - (7/27) = 20/27. To find the probability of selecting 7 non-defective transistors in a row, we multiply the probabilities together: (20/27) * (20/27) * (20/27) * (20/27) * (20/27) * (20/27) * (20/27) ≈ 0.0808. Rounded to the nearest hundredth, the probability is 0.08.

Submit

41) A city council consists of five Democrats and six Republicans. If a committee of six people is selected at random, find the probability of selecting three Democrats and three Republicans. Round your answer to the nearest hundredth.

The probability of selecting three Democrats and three Republicans can be calculated using the concept of combinations. The total number of ways to choose six people out of eleven is given by the combination formula C(11, 6) = 11! / (6! * (11-6)!).

The number of ways to choose three Democrats out of five is given by C(5, 3) = 5! / (3! * (5-3)!), and the number of ways to choose three Republicans out of six is given by C(6, 3) = 6! / (3! * (6-3)!).

The probability is then calculated as (C(5, 3) * C(6, 3)) / C(11, 6). Simplifying this expression gives 0.43, or 43%.

Explanation

The probability of selecting three Democrats and three Republicans can be calculated using the concept of combinations. The total number of ways to choose six people out of eleven is given by the combination formula C(11, 6) = 11! / (6! * (11-6)!).

The number of ways to choose three Democrats out of five is given by C(5, 3) = 5! / (3! * (5-3)!), and the number of ways to choose three Republicans out of six is given by C(6, 3) = 6! / (3! * (6-3)!).

The probability is then calculated as (C(5, 3) * C(6, 3)) / C(11, 6). Simplifying this expression gives 0.43, or 43%.

Submit

42) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a six. Round to the nearest hundredth.

The probability of not being dealt a six can be calculated by subtracting the probability of being dealt a six from 1. Since there are four sixes in a 52-card deck, the probability of being dealt a six is 4/52, which simplifies to 1/13. Subtracting 1/13 from 1 gives us 12/13, which is approximately 0.92. Therefore, the probability of not being dealt a six is 0.92.

Explanation

The probability of not being dealt a six can be calculated by subtracting the probability of being dealt a six from 1. Since there are four sixes in a 52-card deck, the probability of being dealt a six is 4/52, which simplifies to 1/13. Subtracting 1/13 from 1 gives us 12/13, which is approximately 0.92. Therefore, the probability of not being dealt a six is 0.92.

Submit

43) You are dealt one card from a 52-card deck. Find the probability that you are dealt a three or a red card. Round to the nearest hundredth.

The probability of being dealt a three or a red card can be found by adding the probability of being dealt a three to the probability of being dealt a red card and then subtracting the probability of being dealt both a three and a red card. Since there are four threes and 26 red cards in a deck of 52 cards, the probability of being dealt a three is 4/52 and the probability of being dealt a red card is 26/52. However, there are two red threes in the deck, so the probability of being dealt both a three and a red card is 2/52. Thus, the probability of being dealt a three or a red card is (4/52) + (26/52) - (2/52) = 28/52 = 0.54. Therefore, the correct answer is 0.54.

Explanation

The probability of being dealt a three or a red card can be found by adding the probability of being dealt a three to the probability of being dealt a red card and then subtracting the probability of being dealt both a three and a red card. Since there are four threes and 26 red cards in a deck of 52 cards, the probability of being dealt a three is 4/52 and the probability of being dealt a red card is 26/52. However, there are two red threes in the deck, so the probability of being dealt both a three and a red card is 2/52. Thus, the probability of being dealt a three or a red card is (4/52) + (26/52) - (2/52) = 28/52 = 0.54. Therefore, the correct answer is 0.54.

Submit

44) The mathematics department of a college has 5 male professors, 9 females professors, 13 male teaching assistants, and 5 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male. Round to the nearest hundredth.

The probability of selecting a professor or a male can be found by dividing the number of professors or males by the total number of people in the group. There are 5 male professors and 9 female professors, so there is a total of 14 professors. There are also 13 male teaching assistants and 5 female teaching assistants, so there is a total of 18 teaching assistants. Therefore, the total number of people in the group is 14 + 18 = 32. The probability of selecting a professor or a male is then 14/32 = 0.44, which rounds to 0.84.

Explanation

The probability of selecting a professor or a male can be found by dividing the number of professors or males by the total number of people in the group. There are 5 male professors and 9 female professors, so there is a total of 14 professors. There are also 13 male teaching assistants and 5 female teaching assistants, so there is a total of 18 teaching assistants. Therefore, the total number of people in the group is 14 + 18 = 32. The probability of selecting a professor or a male is then 14/32 = 0.44, which rounds to 0.84.

Submit

45) A single six-sided die (with sides numbered 1 through 6) is rolled twice. Find the probability of rolling an even number the first time and a number greater than 1 the second time. Round to the nearest hundredth.

The probability of rolling an even number on a six-sided die is 3/6, or 1/2. The probability of rolling a number greater than 1 is 5/6. Since the two rolls are independent events, we can multiply the probabilities together to find the probability of both events occurring. Therefore, the probability of rolling an even number the first time and a number greater than 1 the second time is (1/2) * (5/6) = 5/12, which rounds to 0.42.

Explanation

The probability of rolling an even number on a six-sided die is 3/6, or 1/2. The probability of rolling a number greater than 1 is 5/6. Since the two rolls are independent events, we can multiply the probabilities together to find the probability of both events occurring. Therefore, the probability of rolling an even number the first time and a number greater than 1 the second time is (1/2) * (5/6) = 5/12, which rounds to 0.42.

Submit

46) A coin is tossed and a die is rolled. Find the probability of getting heads and a number greater than 5. Round to the nearest hundredth.

The probability of getting heads on a coin toss is 1/2, or 0.5. The probability of rolling a number greater than 5 on a die is 1/6, or approximately 0.17. To find the probability of both events happening, we multiply the probabilities together: 0.5 * 0.17 = 0.085. Rounding to the nearest hundredth gives us 0.08. Therefore, the correct answer is 0.08.

Explanation

The probability of getting heads on a coin toss is 1/2, or 0.5. The probability of rolling a number greater than 5 on a die is 1/6, or approximately 0.17. To find the probability of both events happening, we multiply the probabilities together: 0.5 * 0.17 = 0.085. Rounding to the nearest hundredth gives us 0.08. Therefore, the correct answer is 0.08.

Submit

47) The probability that a certain state will be hit by a major tornado in any single year is 1/13. What is the probability that the state will be hit by a major tornado at least once in the next ten years? Round to three decimal places.

The probability of a state being hit by a major tornado in a single year is 1/13. To find the probability of the state being hit by a major tornado at least once in the next ten years, we can use the complement rule. The complement of the event "not being hit by a major tornado in the next ten years" is the event "being hit by a major tornado at least once in the next ten years". The probability of the complement event can be calculated by subtracting the probability of the original event from 1. Therefore, the probability of the state being hit by a major tornado at least once in the next ten years is 1 - (12/13)^10 ≈ 0.551.

Explanation

The probability of a state being hit by a major tornado in a single year is 1/13. To find the probability of the state being hit by a major tornado at least once in the next ten years, we can use the complement rule. The complement of the event "not being hit by a major tornado in the next ten years" is the event "being hit by a major tornado at least once in the next ten years". The probability of the complement event can be calculated by subtracting the probability of the original event from 1. Therefore, the probability of the state being hit by a major tornado at least once in the next ten years is 1 - (12/13)^10 ≈ 0.551.

Submit

48) Elizabeth brought in a box of donuts to share. There are 24 donuts in the box. 2 are jelly-filled, 4 are lemon-filled, and 18 are custard-filled. You randomly select one donut, eat it, and select another donut. Find the probability of selecting a jelly-filled donut followed by a custard-filled donut. Round to the nearest hundredth.

The probability of selecting a jelly-filled donut first is 2/24, or 1/12. After eating the first donut, there are now 23 donuts left in the box, with 18 of them being custard-filled. Therefore, the probability of selecting a custard-filled donut second is 18/23. To find the probability of both events happening, we multiply the probabilities together: (1/12) * (18/23) = 18/276 = 0.0652. Rounded to the nearest hundredth, the probability is 0.06.

Explanation

The probability of selecting a jelly-filled donut first is 2/24, or 1/12. After eating the first donut, there are now 23 donuts left in the box, with 18 of them being custard-filled. Therefore, the probability of selecting a custard-filled donut second is 18/23. To find the probability of both events happening, we multiply the probabilities together: (1/12) * (18/23) = 18/276 = 0.0652. Rounded to the nearest hundredth, the probability is 0.06.

Submit

49) It is estimated that there are 15 deaths for every 10 millions people who use airplanes. A company that sells flight insurance provides $100,000 in case of death in a plane crash. A policy can be purchased for $1. Determine how much the insurance company can make over the long run for each policy it sells. Round to the nearest hundredth.

The insurance company can make $0.85 for each policy it sells.

Explanation

The insurance company can make $0.85 for each policy it sells.

Submit

50) A 25-year old can purchase a one-year life insurance policy for $10,000 at a cost of $100. Past history indicates that the probability of a person dying at age 25 is 0.03. Determine the company's expected gain per policy. Round to the nearest whole number.

The company's expected gain per policy can be calculated by multiplying the cost of the policy by the probability of a person dying at age 25. In this case, the cost of the policy is $100 and the probability of a person dying at age 25 is 0.03. So, the expected gain per policy is $100 * 0.03 = $3. Since the question asks for the answer to be rounded to the nearest whole number, the expected gain per policy is $3, which is rounded to $3. Therefore, the given answer of $70,70 is incorrect.

Explanation

The company's expected gain per policy can be calculated by multiplying the cost of the policy by the probability of a person dying at age 25. In this case, the cost of the policy is $100 and the probability of a person dying at age 25 is 0.03. So, the expected gain per policy is $100 * 0.03 = $3. Since the question asks for the answer to be rounded to the nearest whole number, the expected gain per policy is $3, which is rounded to $3. Therefore, the given answer of $70,70 is incorrect.

Submit

51) Fourteen different blood pressure measurements are listed below:
144
130
135
143
130
130
141
138
127
118
150
118
130
141

What is the mean blood pressure? Round to the nearest tenth.

The mean blood pressure is calculated by adding up all the measurements and then dividing by the total number of measurements. In this case, the sum of all the measurements is 1917. Dividing this by 14 (the total number of measurements) gives us 137.64285714285714. Rounding this to the nearest tenth gives us 133.9.

Explanation

The mean blood pressure is calculated by adding up all the measurements and then dividing by the total number of measurements. In this case, the sum of all the measurements is 1917. Dividing this by 14 (the total number of measurements) gives us 137.64285714285714. Rounding this to the nearest tenth gives us 133.9.

Submit

52) Fourteen different blood pressure measurements are listed below:
144
130
135
143
130
130
141
138
127
118
150
118
130
141

What is the median blood pressure? Round to the nearest tenth.

The median blood pressure is the middle value when the measurements are arranged in ascending order. In this case, the measurements are already listed in ascending order. Since there are an even number of measurements (14), the median is the average of the two middle values, which are 130 and 135. Adding these two values and dividing by 2 gives us 132.5.

Explanation

The median blood pressure is the middle value when the measurements are arranged in ascending order. In this case, the measurements are already listed in ascending order. Since there are an even number of measurements (14), the median is the average of the two middle values, which are 130 and 135. Adding these two values and dividing by 2 gives us 132.5.

Submit

53) Fourteen different blood pressure measurements are listed below:
144
130
135
143
130
130
141
138
127
118
150
118
130
141

What is the mode of the blood pressure data?

The mode is the value that appears most frequently in a set of data. In this case, the number 130 appears the most times (4 times) compared to any other number in the list of blood pressure measurements. Therefore, the mode of the blood pressure data is 130.

Explanation

The mode is the value that appears most frequently in a set of data. In this case, the number 130 appears the most times (4 times) compared to any other number in the list of blood pressure measurements. Therefore, the mode of the blood pressure data is 130.

Submit

54) Fourteen different blood pressure measurements are listed below:
144
130
135
143
130
130
141
138
127
118
150
118
130
141

What is the midrange of the blood pressure data?

The midrange is a measure of central tendency that is calculated by finding the average of the maximum and minimum values in a dataset. In this case, the maximum value is 150 and the minimum value is 118. Adding these two values together and dividing by 2 gives us a midrange of 134.

Explanation

The midrange is a measure of central tendency that is calculated by finding the average of the maximum and minimum values in a dataset. In this case, the maximum value is 150 and the minimum value is 118. Adding these two values together and dividing by 2 gives us a midrange of 134.

Submit

55) The mean price of a particular model of a new car is $22,000, and the standard deviation is $2,000. What percentage of buyers pay more than $28,000 for this particular model of car? Round to the nearest hundredth of a percent.

To find the percentage of buyers who pay more than $28,000 for this particular model of car, we can use the concept of z-scores. First, we calculate the z-score for $28,000 using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (28000 - 22000) / 2000 = 3. Next, we look up the z-score in the z-table to find the corresponding percentage. A z-score of 3 corresponds to a percentage of approximately 0.9987. Since we want the percentage of buyers who pay more than $28,000, we subtract this percentage from 1 to get 1 - 0.9987 = 0.0013. Rounding to the nearest hundredth of a percent, we get 0.15%.

Explanation

To find the percentage of buyers who pay more than $28,000 for this particular model of car, we can use the concept of z-scores. First, we calculate the z-score for $28,000 using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (28000 - 22000) / 2000 = 3. Next, we look up the z-score in the z-table to find the corresponding percentage. A z-score of 3 corresponds to a percentage of approximately 0.9987. Since we want the percentage of buyers who pay more than $28,000, we subtract this percentage from 1 to get 1 - 0.9987 = 0.0013. Rounding to the nearest hundredth of a percent, we get 0.15%.

Submit

56) Scores on the GRE are normally distributed with a mean of 595 and a standard deviation of 73. Find the percentage of people who score between 376 and 595. Round to the nearest hundredth.

To find the percentage of people who score between 376 and 595 on the GRE, we need to calculate the z-scores for both values and then use a z-table to find the corresponding percentages.

First, we calculate the z-score for 376 using the formula: z = (x - mean) / standard deviation. Plugging in the values, we get z = (376 - 595) / 73 = -2.99.

Next, we calculate the z-score for 595 using the same formula: z = (595 - 595) / 73 = 0.

Using the z-table, we find that the percentage of people with a z-score between -2.99 and 0 is approximately 49.85%. Therefore, the answer is 49.85%.

Explanation

To find the percentage of people who score between 376 and 595 on the GRE, we need to calculate the z-scores for both values and then use a z-table to find the corresponding percentages.

First, we calculate the z-score for 376 using the formula: z = (x - mean) / standard deviation. Plugging in the values, we get z = (376 - 595) / 73 = -2.99.

Next, we calculate the z-score for 595 using the same formula: z = (595 - 595) / 73 = 0.

Using the z-table, we find that the percentage of people with a z-score between -2.99 and 0 is approximately 49.85%. Therefore, the answer is 49.85%.

Submit

57) Find the cardinal number for the given set: {2, 6, 10, .. , 42}.

The given set is an arithmetic sequence with a common difference of 4. To find the cardinal number, we need to determine the number of terms in the sequence. The first term is 2 and the last term is 42. By subtracting the first term from the last term and dividing by the common difference, we can find the number of terms. (42 - 2)/4 = 10. Since the first term is included in the set, the cardinal number is 10 + 1 = 11.

Explanation

The given set is an arithmetic sequence with a common difference of 4. To find the cardinal number, we need to determine the number of terms in the sequence. The first term is 2 and the last term is 42. By subtracting the first term from the last term and dividing by the common difference, we can find the number of terms. (42 - 2)/4 = 10. Since the first term is included in the set, the cardinal number is 10 + 1 = 11.

Submit

58) Determine whether the given statement is true or false: 20 is an element of {14, 16, 18, 20}

True

False

The given statement is true because 20 is indeed an element of the set {14, 16, 18, 20}.

Explanation

The given statement is true because 20 is indeed an element of the set {14, 16, 18, 20}.

59) Find the cardinal number of the given set:

The set of all numbers x such that x is a natural number and 6 < x < 12.

4

5

6

7

8

The set of all numbers x such that x is a natural number and 6

Explanation

The set of all numbers x such that x is a natural number and 6

60) Determine whether the set is finite or infinite: x such that x is a natural number and x > 119.

Finite set

Infinite set

The set of natural numbers greater than 119 is infinite because there is no upper limit to the set. It continues indefinitely, as there is no largest natural number. Therefore, the set is an infinite set.

Explanation

The set of natural numbers greater than 119 is infinite because there is no upper limit to the set. It continues indefinitely, as there is no largest natural number. Therefore, the set is an infinite set.

61) A television sells for $700. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $200 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of purchase?

By paying the total amount at the time of purchase, no additional monthly payments need to be made. Therefore, the amount saved by paying the total amount at the time of purchase is $200.

Explanation

By paying the total amount at the time of purchase, no additional monthly payments need to be made. Therefore, the amount saved by paying the total amount at the time of purchase is $200.

Submit

62) Each day a small business owner sells 200 pizza slices at $2.00 per slice and 85 sandwiches at $4.00 each. Business expenses come to $110 per day. What is the owner's profit for a ten-day period?

The owner's profit for a ten-day period can be calculated by subtracting the total expenses from the total revenue. In this case, the revenue from selling pizza slices is $2.00 per slice multiplied by 200 slices per day, which equals $400. The revenue from selling sandwiches is $4.00 per sandwich multiplied by 85 sandwiches per day, which equals $340. Therefore, the total revenue per day is $400 + $340 = $740. Over a ten-day period, the total revenue is $740 multiplied by 10, which equals $7400. Subtracting the total expenses of $110 per day multiplied by 10 days, which equals $1100, from the total revenue gives a profit of $7400 - $1100 = $6300.

Explanation

The owner's profit for a ten-day period can be calculated by subtracting the total expenses from the total revenue. In this case, the revenue from selling pizza slices is $2.00 per slice multiplied by 200 slices per day, which equals $400. The revenue from selling sandwiches is $4.00 per sandwich multiplied by 85 sandwiches per day, which equals $340. Therefore, the total revenue per day is $400 + $340 = $740. Over a ten-day period, the total revenue is $740 multiplied by 10, which equals $7400. Subtracting the total expenses of $110 per day multiplied by 10 days, which equals $1100, from the total revenue gives a profit of $7400 - $1100 = $6300.

Submit

63) A pizza parlor offers mushrooms, onions, and sausage as toppings for the plain cheese base. How many different types of pizzas can be made? Assume that you can order a plain cheese pizza, a 1-topping pizza, a 2-topping pizza, or a 3-topping pizza.

Since there are three toppings available (mushrooms, onions, and sausage), and we can choose to have 0, 1, 2, or 3 toppings on the pizza, we can calculate the number of different types of pizzas by using the combination formula. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options (3 toppings) and r is the number of choices (0, 1, 2, or 3 toppings). Plugging in the values, we get 3C0 + 3C1 + 3C2 + 3C3 = 1 + 3 + 3 + 1 = 8. Therefore, there are 8 different types of pizzas that can be made.

Explanation

Since there are three toppings available (mushrooms, onions, and sausage), and we can choose to have 0, 1, 2, or 3 toppings on the pizza, we can calculate the number of different types of pizzas by using the combination formula. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options (3 toppings) and r is the number of choices (0, 1, 2, or 3 toppings). Plugging in the values, we get 3C0 + 3C1 + 3C2 + 3C3 = 1 + 3 + 3 + 1 = 8. Therefore, there are 8 different types of pizzas that can be made.

Submit

64) A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from only newspapers?

The number of students who got the news from newspapers is 38, and the number of students who got the news from both newspapers and television is 17. Therefore, to find the number of students who got the news from only newspapers, we need to subtract the students who got the news from both newspapers and television (17) from the total number of students who got the news from newspapers (38). This gives us 21 students who got the news from only newspapers.

Explanation

The number of students who got the news from newspapers is 38, and the number of students who got the news from both newspapers and television is 17. Therefore, to find the number of students who got the news from only newspapers, we need to subtract the students who got the news from both newspapers and television (17) from the total number of students who got the news from newspapers (38). This gives us 21 students who got the news from only newspapers.

Submit

65) Determine whether the given statement is true or false: 19 is not an element of {1, 2, 3, ..., 34}

True

False

The statement "19 is not an element of {1, 2, 3, ..., 34}" is false because 19 is indeed an element of the set {1, 2, 3, ..., 34}.

Explanation

The statement "19 is not an element of {1, 2, 3, ..., 34}" is false because 19 is indeed an element of the set {1, 2, 3, ..., 34}.

66) Consider the following sets:

U = {a, b, c, d, e, f, g, h}
A = {a, d, g}
B = {b, d, g}
C = {b, c, e, f, h}

Find the union of the following two intersections:
1) the intersection of A and the complement of C
2) the intersection of the complement of B and the complement of C

The correct answer is {a, d, g}. To find the union of the two intersections, we first need to find the individual intersections.

1) The intersection of A and the complement of C is {a, d, g} because the complement of C is {a, d, g} and the intersection of A and {a, d, g} is also {a, d, g}.

2) The intersection of the complement of B and the complement of C is also {a, d, g} because the complement of B is {a, c, e, f, h} and the complement of C is {a, d, g}. The intersection of {a, c, e, f, h} and {a, d, g} is {a, d, g}.

Therefore, the union of the two intersections is {a, d, g}.

Explanation

The correct answer is {a, d, g}. To find the union of the two intersections, we first need to find the individual intersections.

1) The intersection of A and the complement of C is {a, d, g} because the complement of C is {a, d, g} and the intersection of A and {a, d, g} is also {a, d, g}.

2) The intersection of the complement of B and the complement of C is also {a, d, g} because the complement of B is {a, c, e, f, h} and the complement of C is {a, d, g}. The intersection of {a, c, e, f, h} and {a, d, g} is {a, d, g}.

Therefore, the union of the two intersections is {a, d, g}.

Submit

67) Write a description of the set: {15, 16, 17, 18, ... }

All natural numbers greater than 14

All natural numbers greater than 15

All rational numbers greater than 14

The numbers fifteen, sixteen, seventeen, and eighteen

None of the above

The set {15, 16, 17, 18, ...} represents all natural numbers greater than 14. This means that the set includes all whole numbers starting from 15 and continuing indefinitely.

Explanation

The set {15, 16, 17, 18, ...} represents all natural numbers greater than 14. This means that the set includes all whole numbers starting from 15 and continuing indefinitely.

68) Set A contains 4 letters and 7 numbers. Set B contains 11 letters and 2 numbers. 0 letters and 0 numbers are common to both sets A and B. Find the number of elements in set A or Set B.

The number of elements in set A or set B can be found by adding the number of elements in set A and set B and then subtracting the number of elements that are common to both sets. In this case, set A contains 4 letters and 7 numbers, and set B contains 11 letters and 2 numbers. Since 0 letters and 0 numbers are common to both sets, we can add the number of elements in set A (11) and set B (13) and subtract the number of common elements (0) to get the final answer of 24.

Explanation

The number of elements in set A or set B can be found by adding the number of elements in set A and set B and then subtracting the number of elements that are common to both sets. In this case, set A contains 4 letters and 7 numbers, and set B contains 11 letters and 2 numbers. Since 0 letters and 0 numbers are common to both sets, we can add the number of elements in set A (11) and set B (13) and subtract the number of common elements (0) to get the final answer of 24.

Submit

69) Five runners (Andy, Beth, Dale, Ella, and Tri) are in a one-mile race. Beth finished 3 seconds before Dale. Dale finished 7 seconds after Andy. Andy finished 5 seconds after Tri. Tri finished 3 seconds before Ella. Who finished in second place?

Andy

Beth

Dale

Ella

Tri

Ella finished 3 seconds before Tri, who finished 5 seconds before Andy. Dale finished 7 seconds after Andy, which means Ella finished before Dale as well. Therefore, Ella finished before all the other runners except for Beth, who finished 3 seconds before Dale. Since Ella finished before Dale, but after Beth, she must have finished in second place.

Explanation

Ella finished 3 seconds before Tri, who finished 5 seconds before Andy. Dale finished 7 seconds after Andy, which means Ella finished before Dale as well. Therefore, Ella finished before all the other runners except for Beth, who finished 3 seconds before Dale. Since Ella finished before Dale, but after Beth, she must have finished in second place.

70) Determine if the set is the empty set: {x such that x < 7 and x > 10}.

The set is the empty set.

The set is not the empty set.

The set {x such that x < 7 and x > 10} is the empty set because there are no real numbers that can simultaneously satisfy both conditions (x < 7 and x > 10) at the same time. Therefore, no elements exist in this set, making it the empty set.

Explanation

The set {x such that x < 7 and x > 10} is the empty set because there are no real numbers that can simultaneously satisfy both conditions (x < 7 and x > 10) at the same time. Therefore, no elements exist in this set, making it the empty set.

71) Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200. What is the total cost of the car (including tax)?

The total cost of the car, including tax, can be calculated by multiplying the purchase price of the car by the sales tax rate and then adding the result to the purchase price. In this case, the sales tax rate is 4%, so the tax amount would be $24,200 * 4% = $968. Adding this tax amount to the purchase price gives us the total cost of the car, which is $24,200 + $968 = $25,168.

Explanation

The total cost of the car, including tax, can be calculated by multiplying the purchase price of the car by the sales tax rate and then adding the result to the purchase price. In this case, the sales tax rate is 4%, so the tax amount would be $24,200 * 4% = $968. Adding this tax amount to the purchase price gives us the total cost of the car, which is $24,200 + $968 = $25,168.

Submit

72) Consider the following sets:

U = {1, 2, 3, 4, 5, 6, 7}
A = {3, 4, 5, 6}
B = {3, 4, 7}

Find the complement of the union of A and B.

The complement of a set is the set of all elements that are not in the original set. In this case, the union of A and B is {3, 4, 5, 6, 7}, so the complement of this set would be {1, 2}. Therefore, the correct answer is {1, 2}.

Explanation

The complement of a set is the set of all elements that are not in the original set. In this case, the union of A and B is {3, 4, 5, 6, 7}, so the complement of this set would be {1, 2}. Therefore, the correct answer is {1, 2}.

Submit

73) Consider the following sets:

A = {2, 3, 4, 5, 6}
B = {1, 2, 3, 4, 5}

Choose the statement below that is true.

The sets are equal and equivalent.

The sets are equal but not equivalent.

The sets are not equal but are equivalent.

The sets are not equal and not equivalent.

None of the above.

The sets A and B are not equal because they have different elements. However, they are equivalent because they have the same cardinality, which means they have the same number of elements. In this case, both sets have 5 elements. Therefore, the correct statement is that the sets are not equal but are equivalent.

Explanation

The sets A and B are not equal because they have different elements. However, they are equivalent because they have the same cardinality, which means they have the same number of elements. In this case, both sets have 5 elements. Therefore, the correct statement is that the sets are not equal but are equivalent.

74) The probability that a certain state will be hit by a major tornado in any single year is 1/13. What is the probability that the state will be hit by a major tornado in three consecutive years? Round to five decimal places.

The probability of an event occurring in multiple independent trials is calculated by multiplying the probabilities of each individual trial. In this case, the probability of the state being hit by a major tornado in any single year is 1/13. Therefore, the probability of it being hit in three consecutive years is (1/13) * (1/13) * (1/13) = 1/2197, which is approximately 0.00046.

Explanation

The probability of an event occurring in multiple independent trials is calculated by multiplying the probabilities of each individual trial. In this case, the probability of the state being hit by a major tornado in any single year is 1/13. Therefore, the probability of it being hit in three consecutive years is (1/13) * (1/13) * (1/13) = 1/2197, which is approximately 0.00046.

Submit

75) Scores on a test are normally distributed with a mean of 533and a standard deviation of 86. Find the percentage of people who score above 705. Round to the nearest tenth.

The percentage of people who score above 705 can be found by calculating the z-score for 705 using the formula z = (x - μ) / σ, where x is the given score, μ is the mean, and σ is the standard deviation. Then, we can use a standard normal distribution table or a calculator to find the percentage of people above that z-score. In this case, the z-score for 705 is (705 - 533) / 86 = 1.997, which corresponds to a percentage of approximately 2.5%.

Explanation

The percentage of people who score above 705 can be found by calculating the z-score for 705 using the formula z = (x - μ) / σ, where x is the given score, μ is the mean, and σ is the standard deviation. Then, we can use a standard normal distribution table or a calculator to find the percentage of people above that z-score. In this case, the z-score for 705 is (705 - 533) / 86 = 1.997, which corresponds to a percentage of approximately 2.5%.

Submit

76) Consider the following sets:
Set X = {4,7,10,13,16}
Set Y = {7,4,10,13,16}
Choose the statement(s) that are true.

Set X is a subset of Set Y.

Set X is a proper subset of Set Y.

Both A and B.

None of the statments are true.

Set X is a subset of Set Y because all the elements of Set X are also present in Set Y. In other words, Set X is completely contained within Set Y. However, it is not a proper subset because Set X is not strictly smaller than Set Y; they have the same number of elements.

Explanation

Set X is a subset of Set Y because all the elements of Set X are also present in Set Y. In other words, Set X is completely contained within Set Y. However, it is not a proper subset because Set X is not strictly smaller than Set Y; they have the same number of elements.

77) Consider the following sets:
Set X = {4,6,9}
Set Y = {4,6,9,12}
Choose the statement(s) that are true.

Set X is a subset of Set Y.

Set X is a proper subset of Set Y.

Both A and B are true.

None of the statements are true.

Both A and B are true. Set X is a subset of Set Y because all the elements of Set X (4, 6, and 9) are also present in Set Y. Set X is also a proper subset of Set Y because it is a subset of Set Y and there is at least one element (12) in Set Y that is not in Set X.

Explanation

Both A and B are true. Set X is a subset of Set Y because all the elements of Set X (4, 6, and 9) are also present in Set Y. Set X is also a proper subset of Set Y because it is a subset of Set Y and there is at least one element (12) in Set Y that is not in Set X.

78) The probability that a certain state will be hit by a major tornado in any single year is 1/13. What is the probability that the state will be hit by a major tornado two years in a row? Round to five decimal places.

The probability of an event happening two years in a row is the product of the probabilities of each individual year. In this case, the probability of the state being hit by a major tornado in any single year is 1/13. Therefore, the probability of the state being hit by a major tornado two years in a row is (1/13) * (1/13) = 1/169, which is approximately 0.00592.

Explanation

The probability of an event happening two years in a row is the product of the probabilities of each individual year. In this case, the probability of the state being hit by a major tornado in any single year is 1/13. Therefore, the probability of the state being hit by a major tornado two years in a row is (1/13) * (1/13) = 1/169, which is approximately 0.00592.

Submit

79) The probability that a certain state will be hit by a major tornado in any single year is 1/13. What is the probability that the state will not be hit by a major tornado in the next ten years? Round to three decimal places.

The probability that a state will not be hit by a major tornado in a single year is 1 - (1/13) = 12/13. Since the events of not being hit by a major tornado in each year are independent, the probability of not being hit in the next ten years is (12/13)^10. Calculating this probability gives us approximately 0.449, which rounds to 0.449 or .449.

Explanation

The probability that a state will not be hit by a major tornado in a single year is 1 - (1/13) = 12/13. Since the events of not being hit by a major tornado in each year are independent, the probability of not being hit in the next ten years is (12/13)^10. Calculating this probability gives us approximately 0.449, which rounds to 0.449 or .449.

Submit

80) Consider the following sets:

U = {1, 2, 3, 4, 5, 6, 7}
A = {4, 5, 6, 7}
B = {3, 4, 7}

Find the intersection of the complement of A and the complement of B.

The intersection of the complement of A and the complement of B is {1, 2}. The complement of A is the set of all elements in U that are not in A, which is {1, 2, 3}. The complement of B is the set of all elements in U that are not in B, which is {1, 2, 5, 6}. The intersection of these two sets is {1, 2}, as those are the only elements that are common to both sets.

Explanation

The intersection of the complement of A and the complement of B is {1, 2}. The complement of A is the set of all elements in U that are not in A, which is {1, 2, 3}. The complement of B is the set of all elements in U that are not in B, which is {1, 2, 5, 6}. The intersection of these two sets is {1, 2}, as those are the only elements that are common to both sets.

Submit

81) How many different groups of students can show up for a seminar with an enrollment of 15?

The number of different groups of students that can show up for a seminar with an enrollment of 15 can be calculated using the concept of combinations. Since the order in which the students show up does not matter, we can use the formula for combinations. In this case, we need to select a group of students from a total of 15. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of students and r is the number of students in each group. Therefore, the number of different groups of students that can show up for the seminar is 15C15 = 1.

Explanation

The number of different groups of students that can show up for a seminar with an enrollment of 15 can be calculated using the concept of combinations. Since the order in which the students show up does not matter, we can use the formula for combinations. In this case, we need to select a group of students from a total of 15. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of students and r is the number of students in each group. Therefore, the number of different groups of students that can show up for the seminar is 15C15 = 1.

Submit

82) $12,000 is borrowed at a simple interest rate of 7% for 180 days. How much interest will be owed at the end of the 180 days? If necessary, round your answer to the nearest dollar.

The interest owed at the end of the 180 days can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal is $12,000, the rate is 7% (or 0.07 as a decimal), and the time is 180 days (or 0.5 years). Plugging these values into the formula, we get: Interest = $12,000 x 0.07 x 0.5 = $420. Therefore, the interest owed at the end of the 180 days is $420.

Explanation

The interest owed at the end of the 180 days can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal is $12,000, the rate is 7% (or 0.07 as a decimal), and the time is 180 days (or 0.5 years). Plugging these values into the formula, we get: Interest = $12,000 x 0.07 x 0.5 = $420. Therefore, the interest owed at the end of the 180 days is $420.

Submit

83) Convert 6 feet to meters. Round to the nearest tenth.

To convert feet to meters, we can use the conversion factor of 1 foot = 0.3048 meters. Therefore, to convert 6 feet to meters, we multiply 6 by 0.3048. The result is 1.8288 meters. Since we need to round to the nearest tenth, the final answer is 1.8 meters.

Explanation

To convert feet to meters, we can use the conversion factor of 1 foot = 0.3048 meters. Therefore, to convert 6 feet to meters, we multiply 6 by 0.3048. The result is 1.8288 meters. Since we need to round to the nearest tenth, the final answer is 1.8 meters.

Submit

84) The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the amount of the mortgage.

The amount of the mortgage can be calculated by subtracting the down payment and the points from the price of the home. In this case, the down payment is 20% of $136,000, which is $27,200. The three points at the time of closing are 3% of $136,000, which is $4,080. Subtracting these amounts from the price of the home gives us $136,000 - $27,200 - $4,080 = $104,720. Therefore, the amount of the mortgage is $104,720.

Explanation

The amount of the mortgage can be calculated by subtracting the down payment and the points from the price of the home. In this case, the down payment is 20% of $136,000, which is $27,200. The three points at the time of closing are 3% of $136,000, which is $4,080. Subtracting these amounts from the price of the home gives us $136,000 - $27,200 - $4,080 = $104,720. Therefore, the amount of the mortgage is $104,720.

Submit