Question 1

Solve the problem.
-A quality-control inspector examined 300 calculators and found 7 of them to be defective. At this rate, how many defective calculators will there be in a batch of 6000 calculators?

Accepted Answer

The rate of defective calculators is 7 out of 300. To find the number of defective calculators in a batch of 6000, use the proportion 7/300 = x/6000, solving for x gives x = (7/300)*6000 = 140.

Question 2

For the pair of similar triangles, find the length of the indicated side.
-
 In the upper triangle, the shortest side has length 12, and the middle side has length 18. In the lower triangle, the shortest side has length 8, the middle side has length 12, and the longest side has length 16. Find the length, x, of
The longest side of the upper triangle.

Accepted Answer

The answer of For the pair of similar triangles, find...

Question 3

Solve the problem.
-The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. How much will a 160-pound astronaut weigh on Mars?

Accepted Answer

The astronaut will weigh 0.4 times their Earth weight on Mars, so 160 pounds * 0.4 = 64 pounds.

Question 4

Find the equation of variation if the following is true.
-Suppose m varies directly as p and m = 42 when p = 6.

Accepted Answer

The answer of Find the equation of variation if the...

Question 5

Find the ratio. Simplify, if possible.
-A machine can fill 5691 boxes of cereal in 0.7 hour. How many boxes of cereal can it fill per hour?

Accepted Answer

The answer of Find the ratio. Simplify, if possible.
-A machine...

Question 6

Solve the problem.
-A machine can fill 1682 cartons of milk in 0.2 hour. How many cartons of milk can it fill per hour?

Accepted Answer

To find the number of cartons filled per hour, divide the total cartons filled in 0.2 hours by 0.2. 1682 / 0.2 = 8410 cartons.

Question 7

Solve.
-According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 18 volts are applied, the current is 4 amperes. What is the current when 13 volts are applied?

Accepted Answer

Ohm's law states that I = V/R, where I is the current, V is the voltage, and R is the resistance. Given that 18 volts produce 4 amperes, we can find the resistance (R = V/I = 18/4 = 4.5 ohms). Using this resistance, the current for 13 volts is I = V/R = 13/4.5 ≈ 2.89 amperes.

Question 8

For the pair of similar triangles, find the length of the indicated side.
- In the outer triangle, the shortest side has length 8, and the middle side has length 10. In the inner triangle, the shortest side has length 4, the middle side has length 5, and the longest side has length 6. Find the length, x, of
The longest side of the outer triangle.

Accepted Answer

The answer of For the pair of similar triangles, find...

Question 9

Solve the problem.
-Dr. Wong can see 9 patients in 2 hours. At this rate, how long would it take her to see 90 patients?

Accepted Answer

The answer of Solve the problem.
-Dr. Wong can see 9...

Question 10

Solve the problem.
-To determine the number of fish in a lake, a park ranger catches 200 fish, tags them, and returns them to the lake. Later, 108 fish are caught, and it is found that 48 of them are tagged. Estimate the number of fish in the
Lake.

Accepted Answer

This problem can be solved using the capture-recapture method. The formula to estimate the total population (N) is N = (number of fish in the first catch * total number of fish in the second catch) / number of tagged fish in the second catch. Plugging in the numbers: N = (200 * 108) / 48 = 450.

Question 11

Solve the problem.
-In a cake recipe, the ratio of milk to flour is  If 4 cups of milk are used, how many cups of flour are used?

Accepted Answer

The answer of Solve the problem.
-In a cake recipe, the...

Question 12

Solve the problem.
-Maria and Charlie can deliver 88 papers in 4 hours. How long would it take them to deliver 55 papers?

Accepted Answer

Maria and Charlie deliver 88 papers in 4 hours, so their rate is 88 papers / 4 hours = 22 papers per hour. To deliver 55 papers at this rate, it would take 55 papers / 22 papers per hour = 2.5 hours.

Question 13

Find the equation of variation if the following is true.
-Suppose r varies directly as s and r = 0.3333 when s = 1.

Accepted Answer

Direct variation means r = ks, where k is the constant of variation. Given r = 0.3333 when s = 1, substituting these values gives k = 0.3333, so the equation is r = 0.3333s.

Question 14

Solve.
-The number G of gears a machine can make varies directly as the time T it operates. If it can make 5155 gears in 19 hours, how many gears can it make in 3 hours?

Accepted Answer

The relationship between the number of gears and time is direct, so G = kT, where k is the constant of variation. From the given, 5155 = k*19, solving for k gives k = 271.32. For 3 hours, G = 271.32*3 = 813.96, which rounds to 813.95 gears.

Question 15

Find the equation of variation if the following is true.
-Suppose that y varies directly as z and y = 37 when z = 259.

Accepted Answer

The answer of Find the equation of variation if the...

Question 16

For the pair of similar triangles, find the length of the indicated side.
- In the left triangle, the hypotenuse has length 10, and the longer leg has length 8. In the right triangle, the hypotenuse has length 5, the longer leg has length 4, and the shorter leg has length 3. Find the length, x, of the
Shorter leg of the left triangle.

Accepted Answer

The answer of For the pair of similar triangles, find...

Question 17

Solve the problem.
-Sven can type 39 words per minute. How many words would he type in  hour (15 minutes)?

Accepted Answer

The answer of Solve the problem.
-Sven can type 39 words...

Question 18

Find the equation of variation if the following is true.
-Suppose p varies directly as q and p = 1 when q =

Accepted Answer

The answer of Find the equation of variation if the...

Question 19

Solve.
-The distance D that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 12-kg object stretches a spring 57 cm, find the distance when the weight is 9-kg. Round to the nearest
Hundredths when necessary.

Accepted Answer

The distance D varies directly with the weight W, so D = k*W, where k is the constant of proportionality. With a 12-kg object stretching the spring 57 cm, we find k = 57/12. For a 9-kg object, D = (57/12)*9 = 42.75 cm.

Question 20

Find the equation of variation if the following is true.
-Suppose y varies directly as x and y = 0.9 when x = 0.1.

Accepted Answer

The answer of Find the equation of variation if the...

Quiz 7: Rational Expressions and Equations

Solve the problem. -A quality-control inspector examined 300 calculators and found 7 of them to be defective. At this rate, how many defective calculators will there be in a batch of 6000 calculators?

Solve the problem. -The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. How much will a 160-pound astronaut weigh on Mars?

Find the equation of variation if the following is true. -Suppose m varies directly as p and m = 42 when p = 6.

Find the ratio. Simplify, if possible. -A machine can fill 5691 boxes of cereal in 0.7 hour. How many boxes of cereal can it fill per hour?

Solve the problem. -A machine can fill 1682 cartons of milk in 0.2 hour. How many cartons of milk can it fill per hour?

Solve. -According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 18 volts are applied, the current is 4 amperes. What is the current when 13 volts are applied?

Solve the problem. -Dr. Wong can see 9 patients in 2 hours. At this rate, how long would it take her to see 90 patients?

Solve the problem. -To determine the number of fish in a lake, a park ranger catches 200 fish, tags them, and returns them to the lake. Later, 108 fish are caught, and it is found that 48 of them are tagged. Estimate the number of fish in the Lake.

Solve the problem. -In a cake recipe, the ratio of milk to flour is If 4 cups of milk are used, how many cups of flour are used?

Solve the problem. -Maria and Charlie can deliver 88 papers in 4 hours. How long would it take them to deliver 55 papers?

Find the equation of variation if the following is true. -Suppose r varies directly as s and r = 0.3333 when s = 1.

Solve. -The number G of gears a machine can make varies directly as the time T it operates. If it can make 5155 gears in 19 hours, how many gears can it make in 3 hours?

Find the equation of variation if the following is true. -Suppose that y varies directly as z and y = 37 when z = 259.

Solve the problem. -Sven can type 39 words per minute. How many words would he type in hour (15 minutes) ?

Find the equation of variation if the following is true. -Suppose p varies directly as q and p = 1 when q =

Solve. -The distance D that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 12-kg object stretches a spring 57 cm, find the distance when the weight is 9-kg. Round to the nearest Hundredths when necessary.

Find the equation of variation if the following is true. -Suppose y varies directly as x and y = 0.9 when x = 0.1.