College Algebra Final Exam

The number 21 can be divided evenly by 7, which means that 7 is a factor of 21.

When y is equal to 3, we can substitute it into the expression y3(y3-y) to get 33(33-3). Simplifying this further, we have 27(30), which is equal to 810. Therefore, the correct answer is C. 648.

To solve the equation 2A/3 = 8 + 4A, we can start by multiplying both sides of the equation by 3 to eliminate the fraction. This gives us 2A = 24 + 12A. Next, we can subtract 12A from both sides to isolate the variable A. This gives us -10A = 24. Finally, we divide both sides by -10 to solve for A, which gives us A = -2.4. Therefore, the correct answer is A. -2.4.

To find the original cost of the statue, we need to find the cost price before the 35% profit was added. Let's assume the original cost was x. The selling price is 35% higher than the original cost, so it can be expressed as 1.35x. We know that the selling price is $670, so we can set up the equation 1.35x = 670. Solving for x, we find that the original cost was $496.30, which is option A.

After calculating the sales tax on the book, which is 8.25% of $80.00, we find that the tax amount is $6.60. To find out how much change the person will receive back, we need to subtract the total cost of the book and the tax from the amount of money they have. Therefore, $100 - $80 - $6.60 equals $13.40.

The cost of purchasing pens can be calculated by dividing the total number of pens needed (240) by the number of pens in each set (6), which equals 40 sets of pens. Each set of pens costs $2.35, so the total cost of pens is 40 sets multiplied by $2.35, which equals $94. The cost of purchasing staplers can be calculated by dividing the total number of staplers needed (6) by the number of staplers in each set (2), which equals 3 sets of staplers. Each set of staplers costs $12.95, so the total cost of staplers is 3 sets multiplied by $12.95, which equals $38.85. Adding the cost of pens ($94) and staplers ($38.85) together gives a total cost of $132.85. Therefore, the correct answer is A. $132.85.

To solve the addition problem 0.25 + 0.65, we add the decimal numbers together. Adding the tenths place, we get 0.2. Adding the hundredths place, we get 0.05. Therefore, the sum is 0.9, which is equivalent to 9/10.

The percent increase in sales can be calculated by taking the difference between the number of cars sold in the first week of the next month (19) and the number of cars sold in the last week of the previous month (12), dividing that difference by the number of cars sold in the last week of the previous month (12), and then multiplying by 100. In this case, the percent increase is (19-12)/12 * 100 = 58%. Therefore, the correct answer is A. 58%.

Sally can paint 1/4 of the house in 1 hour, while John can paint 1/6 of the house in 1 hour. To find out how long it will take for both of them to paint the house together, we need to find the combined rate at which they can paint. The combined rate is found by adding their individual rates, so Sally and John can paint 1/4 + 1/6 = 5/12 of the house in 1 hour. To find the time it takes to paint the entire house, we can divide 1 by the combined rate: 1 / (5/12) = 12/5 = 2.4 hours. Converting 0.4 hours to minutes gives us 0.4 * 60 = 24 minutes. Therefore, it will take them 2 hours and 24 minutes to paint the house together.

The original price of the car can be found by dividing the sales price by 0.8, since the sales price is 80% of the original price. Therefore, $12,590 divided by 0.8 equals $15,737.50.

The ten thousandths place is actually located 4 places to the right of the decimal.

The city council has decided to add a 0.3% tax on motel and hotel rooms. To calculate the tax amount, we multiply the cost of the motel room ($55) by the tax rate (0.3%). 0.3% of $55 is equal to $0.165, which rounds to 17 cents. Therefore, the city will receive 17 cents in taxes from the traveler.

To solve the equation 8x + 5x + 2x + 4x = 114, we can combine like terms on the left side of the equation. This gives us 19x = 114. To isolate x, we divide both sides of the equation by 19, which gives us x = 6.

Now, we can substitute this value of x into the expression 5x + 3 to find the value of 5x + 3. Plugging in x = 6, we get 5(6) + 3 = 30 + 3 = 33.

Therefore, the value of 5x + 3 is 33.

The down payment of $3,000 is made upfront. Then, there are 6 monthly payments of $225 each. To calculate the total amount paid so far, we add the down payment to the total of the monthly payments. Therefore, $3,000 + ($225 x 6) = $3,000 + $1,350 = $4,350. Therefore, the correct answer is B. $4,350.

Leah is 6 years older than Sue, and John is 5 years older than Leah. This means that Sue's age plus 6 (to account for the age difference between Leah and Sue) plus 5 (to account for the age difference between John and Leah) must equal 41. Therefore, Sue's age must be 41 - 6 - 5 = 30. Therefore, Sue is 8 years old.

If Lee worked 22 hours and made $132, we can find her hourly rate by dividing her total earnings by the number of hours worked. $132 divided by 22 hours equals $6 per hour. If she works 15 hours next week at the same rate, she will make $6 per hour multiplied by 15 hours, which equals $90. Therefore, the correct answer is B. $90.

Based on the study results, 8 out of 100 women over the age of 35 were married 2 or more times. This means that the proportion of women in this age group who were married 2 or more times is 8/100 or 0.08. To estimate the number of women in a group of 5,000 women over the age of 35 who would likely be married 2 or more times, we can multiply the proportion by the total number of women in the group: 0.08 * 5,000 = 400. Therefore, it is likely that 400 women in a group of 5,000 women over the age of 35 would be married 2 or more times.

The two planes will be 500 miles apart at 3:00 PM. This can be determined by using the Pythagorean theorem. The plane traveling north will have traveled 300 miles (150 mph * 2 hours) and the plane traveling west will have traveled 400 miles (200 mph * 2 hours). The distance between the two planes can be calculated as the square root of (300^2 + 400^2), which equals 500 miles.

During the 15% off sale, the dishwasher will cost 85% of its original price. So, the price of the dishwasher during the sale is 0.85 * $450 = $382.50.
As an employee, the person will receive an additional 20% off the lowest price. So, the employee will pay 80% of the sale price, which is 0.80 * $382.50 = $306. Therefore, the employee will pay $306 for the dishwasher.

The fraction 12/18 can be simplified to 2/3 by dividing both the numerator and denominator by their greatest common divisor, which is 6. Therefore, 12/18 is equivalent to 2/3 and not equivalent to 3/4.

Sarah needs a total of 3/8 + 3/5 = 15/40 + 24/40 = 39/40 cups of sugar for the cake and cookies. Since she only has 15/16 cups of sugar, she needs 39/40 - 15/16 = 624/640 - 600/640 = 24/640 = 3/80 cups more sugar. Therefore, the correct answer is C. She needs 3/80 of a cup of sugar.

If Sam can do a job in 4 days, Lisa can do it in 6 days, and Tom can do it in 2 days, it means that Sam's rate of work is faster than Lisa's and Tom's. To find the time it would take for them to complete the job together, we can calculate their combined rate of work. Sam's rate is 1/4 of the job per day, Lisa's rate is 1/6 of the job per day, and Tom's rate is 1/2 of the job per day. Adding their rates together, we get 1/4 + 1/6 + 1/2 = 11/12 of the job per day. Taking the reciprocal of this rate, we find that it would take approximately 1.09 days for them to complete the job together. Therefore, the correct answer is B. 1.09 days.

Jim needs a piece of string that is at least 4 inches longer than his waist so he can tie a knot in it. His waist is 36 inches, so the minimum length of the string should be 36 + 4 = 40 inches. However, the string cannot be more than 6 inches longer than his waist, so the maximum length of the string should be 36 + 6 = 42 inches. Among the given options, the only string that falls within this range is 3 ½ feet, which is equal to 42 inches. Therefore, the best option is C. 3 ½ feet.

Alfred wants to invest $4,000 at a 6% simple interest rate for 5 years. To calculate the interest, we use the formula: Interest = Principal x Rate x Time. Plugging in the values, we get: Interest = $4,000 x 0.06 x 5 = $1,200. Therefore, Alfred will receive $1,200 in interest.

To find out how much more water needs to be added, we can subtract the amount of water that was accidentally put into the mixing bowl from the required amount of water.

The required amount of water is 4/5 cups.
The amount of water accidentally put into the mixing bowl is 1/3 cups.

To find the difference, we subtract 1/3 cups from 4/5 cups.

4/5 - 1/3 = 12/15 - 5/15 = 7/15 cups.

Therefore, the amount of water that needs to be added is 7/15 cups, which is option D.

To calculate simple interest, we use the formula: Interest = Principal * Rate * Time. In this case, Susan wants to earn $2,500 in interest on a $10,000 principal over 5 years. Plugging in these values into the formula, we get: 2,500 = 10,000 * Rate * 5. Solving for the rate, we find that Rate = 2,500 / (10,000 * 5) = 0.05 = 5%. Therefore, Susan needs a simple interest rate of 5% to make $2,500 in interest.

John needs to travel 28 miles in 30 minutes. To find the speed, we divide the distance by the time. Therefore, John needs to travel at a speed of 56 mph to make it to the meeting on time.

Simon worked for a total of 14 hours and 15 minutes, which is 14.25 hours. He worked 8 hours at a rate of $10 per hour, earning $80. For the remaining 6.25 hours, he worked at a rate of $15 per hour (time and a half), earning $93.75. Adding the two amounts together, Simon got paid a total of $173.75.

If r = 5z, then 15z = 3y. We can solve for z by dividing both sides of the equation 15z = 3y by 15, which gives us z = y/5. Since r = 5z, we can substitute z with y/5 in the equation r = 5z, which gives us r = 5(y/5). Simplifying this expression, we get r = y. Therefore, the value of r is equal to y.

If 300 jellybeans cost x dollars, then the cost of each jellybean is x/300 dollars. To find out how many jellybeans can be purchased for 50 cents (0.50 dollars), we divide 0.50 by the cost of each jellybean (x/300). This gives us (0.50)/(x/300) = 150/x. Therefore, the correct answer is A. 150/x.

The fraction 1/200 is equivalent to 0.5%. To convert a percentage to a fraction, we divide the percentage by 100. So, 0.5% divided by 100 is equal to 0.005. To express 0.005 as a fraction, we write it as 1/200. Therefore, the fraction 1/200 is equivalent to 0.5%.

Jim can fill the pool in 30 minutes, which means he can fill 1/30 of the pool in 1 minute. Sue can fill the pool in 45 minutes, so she can fill 1/45 of the pool in 1 minute. Tony can fill the pool in 1 ½ hours, which is equal to 90 minutes, so he can fill 1/90 of the pool in 1 minute. To find out how quickly all three can fill the pool together, we add up their individual rates: 1/30 + 1/45 + 1/90 = 1/15. Therefore, all three can fill the pool together in 15 minutes.

To find the time it takes for all three of them to mix the 20 drinks, we need to calculate their combined rate of work. Steven can mix 20 drinks in 5 minutes, so his rate is 20 drinks/5 minutes = 4 drinks/minute. Sue can mix 20 drinks in 10 minutes, so her rate is 20 drinks/10 minutes = 2 drinks/minute. Jack can mix 20 drinks in 15 minutes, so his rate is 20 drinks/15 minutes = 4/3 drinks/minute. To find their combined rate, we add their individual rates: 4 drinks/minute + 2 drinks/minute + 4/3 drinks/minute = 14/3 drinks/minute. To find the time it takes for all 20 drinks to be mixed, we divide 20 drinks by the combined rate: 20 drinks / (14/3 drinks/minute) = 60/7 minutes. Converting this to minutes and seconds, we get 8 minutes and 34.29 seconds, which is closest to 2 minutes and 44 seconds.

Lynn can type a page in p minutes, so in 1 minute she can type 1/p of the page. Therefore, in 5 minutes she can type 5/p of the page, which is the same as option A.

The student received a "B" in the art class, which is equivalent to a 3.0 on a 4 point scale. He received an "A" in the history class, which is equivalent to a 4.0. He received a "C" in the science class, which is equivalent to a 2.0. He received a "B" in the mathematics class, which is equivalent to a 3.0. And he received an "A" in the science lab, which is equivalent to a 4.0. To calculate the GPA, we add up the grade points for each class and divide by the total number of credit hours. In this case, the student took a total of 13 credit hours (2 + 3 + 4 + 3 + 1). The total grade points is 16 (3 + 4 + 2 + 3 + 4). Dividing 16 by 13 gives us a GPA of 3.0.

Each day, the number of visitors tripled. Therefore, on Friday, there were 345 x 3 = 1,035 visitors. On Saturday, there were 1,035 x 3 = 3,105 visitors. Finally, on Sunday, there were 3,105 x 3 = 9,315 visitors. Therefore, the attendance on that Sunday was 9,315.

To find the number of ounces in 7 3/4 pounds, we can multiply the number of pounds by the number of ounces in 1 pound. Since there are 16 ounces in 1 pound, we can calculate 7 3/4 pounds as (7 + 3/4) * 16 = 124 ounces. Therefore, the correct answer is D. 124 ounces.

The second cyclist is traveling at a faster speed than the first cyclist, so they will eventually catch up. The first cyclist has a head start of 3 hours, during which they have traveled 6 * 3 = 18 miles. The second cyclist is traveling at a speed of 10 miles per hour, so it will take them 18 / 10 = 1.8 hours to cover the same distance. Therefore, the second cyclist will catch up with the first cyclist after 3 + 1.8 = 4.8 hours, which is equivalent to 4 ½ hours.

After a morning exercise session, the person drinks 12.8 oz of water. To determine what fraction of the daily average this represents, we need to divide 12.8 by the total amount of water consumed in a day (8 glasses x 8 oz per glass = 64 oz). 12.8/64 = 0.2, which can be simplified to 1/5. Therefore, the person has consumed 1/5 of the daily average.

The given expression is subtracting 1/2 from 3/4. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 4. So, we can rewrite 3/4 as 6/8. Now, subtracting 1/2 from 6/8 gives us 5/8. Simplifying 5/8 further, we get 1/4. Therefore, the correct answer is A. ¼.

The question states that the average of three numbers is V. To find the remaining number, we can use the formula for finding the average of three numbers, which is (X + Y + Z) / 3 = V. Rearranging this equation, we get X = 3V - Y - Z. Therefore, the remaining number is 3V - Z - Y, which matches option D.

To ensure that Grace has one of each color, she needs to take out the maximum number of jellybeans of the same color. Since she has 8 red jellybeans, she can take out all of them and still not have one of each color. Then, she can take out all 4 green jellybeans and still not have one of each color. Finally, she needs to take out one more jellybean to have one of each color. Therefore, the minimum number of jellybeans she must take out is 8 + 4 + 1 = 13.

When the value of x and y in the fraction is tripled, the numerator and denominator both increase by a factor of 3. Therefore, the ratio between the numerator and denominator remains the same, resulting in the value of the fraction remaining unchanged.

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To find the square of a fraction, we square both the numerator and the denominator separately. For 25/9, the numerator squared is 25^2 = 625, and the denominator squared is 9^2 = 81. Therefore, the square of 25/9 is 625/81. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1. So, the simplified fraction is 625/81.