MAT 142 College MATheMATics Exam: Quiz!

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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.

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.

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.

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.

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.

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.

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