Question 1

Write the ordered pair for each point shown in the xy plane.
-

Accepted Answer

The answer of Write the ordered pair for each point...

Question 2

Solve the problem.
-Two machines are turned on at 8:00 A.M. If one can produce 36 items each hour and the other can produce 33 items each hour, at what time will they produce a total of 138 items?

Accepted Answer

The two machines produce a total of 36 + 33 = 69 items per hour together. To produce 138 items, it will take 138 / 69 = 2 hours. Starting from 8:00 A.M., two hours later is 10:00 A.M.

Question 3

Solve the problem.
-How many liters of a 50% alcohol solution must be mixed with 40 liters of a 70% solution to get a 60% solution?

Accepted Answer

To solve this problem, let's denote the amount of 50% alcohol solution needed as x liters. The total amount of alcohol in the 50% solution is 0.5x liters, and in the 40 liters of 70% solution, it is 0.7*40 liters. The final mixture will have (x + 40) liters of solution, and we want this to be a 60% alcohol solution, so the total alcohol in the final mixture should be 0.6(x + 40) liters. Setting up the equation: 0.5x + 0.7*40 = 0.6(x + 40). Solving for x gives x = 40 liters.

Question 4

Write the ordered pair for each point shown in the xy plane.
-

Accepted Answer

The answer of Write the ordered pair for each point...

Question 5

Solve the problem.
-Two machines are turned on at 8:00 A.M. If one can produce 39 items each hour and the other can produce 43 items each hour, at what time will they produce a total of 574 items?

Accepted Answer

The total production per hour by both machines is 39 + 43 = 82 items. To produce 574 items, it would take 574 / 82 = 7 hours. Starting from 8:00 A.M., 7 hours later would be 3:00 P.M.

Question 6

Solve the problem.
-Bill needs an average of 75 on four tests in science to make the honor roll. What is the lowest score he can receive on the fourth test if his first three scores are 61, 82, and 60?

Accepted Answer

To achieve an average of 75 over four tests, Bill needs a total of 4 * 75 = 300 points. The sum of his first three scores is 61 + 82 + 60 = 203. Therefore, he needs 300 - 203 = 97 on the fourth test.

Question 7

Write the ordered pair for each point shown in the xy plane.
-

Accepted Answer

The answer of Write the ordered pair for each point...

Question 8

Solve the problem.
-Martha can rake the leaves in her yard in 5 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Accepted Answer

The answer of Solve the problem.
-Martha can rake the leaves...

Question 9

Solve the problem.
-A chemist makes a mixture of concentrated hydrochloric acid and distilled water so that the ratio of acid to water is 7 : 3. If he starts with 28 L of acid, how much water is mixed with the acid?

Accepted Answer

The ratio of acid to water is 7:3, meaning for every 7 parts of acid, there are 3 parts of water. If the chemist starts with 28 L of acid, which corresponds to 7 parts (since 28 divided by 7 equals 4), each part of the ratio represents 4 L (28 L / 7 parts = 4 L per part). Therefore, for the 3 parts of water, it would be 3 parts * 4 L/part = 12 L of water.

Question 10

Solve the problem.
-Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 19 pounds of feed worth $0.27 per pound by mixing one kind worth $0.22 per pound with another worth $0.41 per pound. How many pounds of
The cheaper kind should they use in the mix? (Round to the nearest pound.)

Accepted Answer

The answer of Solve the problem.
-Tim and Judy mix two...

Question 11

Solve the problem.
-Liz ran 30 mi, 34 mi, and 38 mi during three weeks. How many miles must she run the fourth week to give her an average of 30 miles per week?

Accepted Answer

To achieve an average of 30 miles per week over four weeks, Liz needs to run a total of 30 miles/week * 4 weeks = 120 miles. She has already run 30 + 34 + 38 = 102 miles. Therefore, she must run 120 - 102 = 18 miles in the fourth week.

Question 12

Solve the problem.
-An experienced accountant can prepare a tax return in 8 hours. A novice accountant can do the job in 11 hours. How long will it take them to do the job working together?

Accepted Answer

The answer of Solve the problem.
-An experienced accountant can prepare...

Question 13

Solve the problem.
-A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 7% cement should he mix with 3 bags of 37% cement to produce a mix containing 12% cement?

Accepted Answer

The answer of Solve the problem.
-A contractor mixes concrete from...

Question 14

Solve the problem.
-Anne and Nancy use a metal alloy that is 20.75% copper to make jewelry. How many ounces of a 19% alloy must be mixed with a 24% alloy to form 80 ounces of the desired alloy?

Accepted Answer

Let x be the number of ounces of the 19% alloy. Then, the number of ounces of the 24% alloy is 80 - x.The total amount of copper in the desired alloy is 0.2075 * 80 = 16.6 ounces.The amount of copper in the 19% alloy is 0.19 * x ounces.The amount of copper in the 24% alloy is 0.24 * (80 - x) ounces.Therefore, we have the equation:0.19 * x + 0.24 * (80 - x) = 16.6Solving for x, we get:x = 52 ounces.Therefore, the correct answer is A) 52 oz.

Question 15

Solve the problem.
-A merchant has coffee worth $4 a pound that she wishes to mix with 90 pounds of coffee worth $16 a pound to get a mixture that can be sold for $12 a pound. How many pounds of the $4 coffee should be used?

Accepted Answer

The answer of Solve the problem.
-A merchant has coffee worth...

Question 16

Solve the problem.
-One maid can clean the house in 3 hours. Another maid can do the job in 5 hours. How long will it take them to do the job working together?

Accepted Answer

The answer of Solve the problem.
-One maid can clean the...

Question 17

Solve the problem.
-Frank can type a report in 2 hours. James takes 4 hours to type it. How long will it take the two of them typing together?

Accepted Answer

The answer of Solve the problem.
-Frank can type a report...

Question 18

Solve the problem.
-In a chemistry class, 4 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

The problem can be solved using the equation for mixture: (amount of substance in first solution + amount of substance in second solution) / (total volume of solution) = desired concentration. For the 4% solution: 4 liters * 4% = 0.16 liters of silver iodide. Let x be the liters of the 10% solution needed, so x * 10% = 0.1x liters of silver iodide. The total volume of the solution will be 4 + x liters, and we want a 6% silver iodide solution: (0.16 + 0.1x) / (4 + x) = 6%. Solving for x gives x = 2 liters.

Question 19

Solve the problem.
-It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 40 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired
Strength?

Accepted Answer

To achieve a 40% antifreeze solution, we need to replace some of the 20% solution with 100% antifreeze. Let x be the amount to drain and replace. The equation is: (40 - x)(0.2) + x = 40(0.4). Solving gives x = 10 L.

Question 20

Solve the problem.
-A water tank can be filled in 5 minutes and emptied in 9 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Accepted Answer

The answer of Solve the problem.
-A water tank can be...

Quiz 1: Equations, Inequalities, and Modeling

Write the ordered pair for each point shown in the xy plane. -

Solve the problem. -Two machines are turned on at 8:00 A.M. If one can produce 36 items each hour and the other can produce 33 items each hour, at what time will they produce a total of 138 items?

Solve the problem. -How many liters of a 50% alcohol solution must be mixed with 40 liters of a 70% solution to get a 60% solution?

Write the ordered pair for each point shown in the xy plane. -

Solve the problem. -Two machines are turned on at 8:00 A.M. If one can produce 39 items each hour and the other can produce 43 items each hour, at what time will they produce a total of 574 items?

Solve the problem. -Bill needs an average of 75 on four tests in science to make the honor roll. What is the lowest score he can receive on the fourth test if his first three scores are 61, 82, and 60?

Write the ordered pair for each point shown in the xy plane. -

Solve the problem. -Martha can rake the leaves in her yard in 5 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Solve the problem. -A chemist makes a mixture of concentrated hydrochloric acid and distilled water so that the ratio of acid to water is 7 : 3. If he starts with 28 L of acid, how much water is mixed with the acid?

Solve the problem. -Liz ran 30 mi, 34 mi, and 38 mi during three weeks. How many miles must she run the fourth week to give her an average of 30 miles per week?

Solve the problem. -An experienced accountant can prepare a tax return in 8 hours. A novice accountant can do the job in 11 hours. How long will it take them to do the job working together?

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 7% cement should he mix with 3 bags of 37% cement to produce a mix containing 12% cement?

Solve the problem. -Anne and Nancy use a metal alloy that is 20.75% copper to make jewelry. How many ounces of a 19% alloy must be mixed with a 24% alloy to form 80 ounces of the desired alloy?

Solve the problem. -A merchant has coffee worth $4 a pound that she wishes to mix with 90 pounds of coffee worth $16 a pound to get a mixture that can be sold for $12 a pound. How many pounds of the $4 coffee should be used?

Solve the problem. -One maid can clean the house in 3 hours. Another maid can do the job in 5 hours. How long will it take them to do the job working together?

Solve the problem. -Frank can type a report in 2 hours. James takes 4 hours to type it. How long will it take the two of them typing together?

Solve the problem. -In a chemistry class, 4 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 40 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired Strength?

Solve the problem. -A water tank can be filled in 5 minutes and emptied in 9 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?