Question 1

Determine whether the proportion is true or false. $\frac { 20 \text { miles } } { 12 \text { minutes } } = \frac { 10 \text { miles } } { 6 \text { minutes } }$

Accepted Answer

Both fractions simplify to $\frac{5 \text{ miles}}{3 \text{ minutes}}$, indicating the proportions are equal.

Question 2

According to the National Sample Survey of Registered Nurses, approximately one in five American Registered Nurses is male. If there are a total of 300 nurses working at a local hospital, how many of them would you expect to be male?

Accepted Answer

Given that approximately one in five nurses is male, you would expect 20% of the nurses to be male. 20% of 300 is 60, so the expected number of male nurses is 60.

Question 3

Using the data given below and a figure of 350 million for the number of Americans, determine the number of morbidly obese Americans.

Accepted Answer

The answer of Using the data given below and a...

Question 4

Solve. Round to the nearest hundredth. $\frac { n } { 10 } = \frac { 11 } { 23 }$

Accepted Answer

To solve for $n$, multiply both sides of the equation by 10: $n = 10 \times \frac{11}{23}$. Calculating this gives $n = \frac{110}{23}$, which is approximately 4.78 when rounded to the nearest hundredth.

Question 5

Solve. $\frac { 12 } { n } = \frac { 60 } { 35 }$

Accepted Answer

Cross-multiply to solve for $ n $: $ 12 \times 35 = 60 \times n $. Simplifying gives $ 420 = 60n $. Dividing both sides by 60 gives $ n = 7 $.

Question 6

For landscape maintenance, Gretchen Green uses 3 pounds of fertilizer for every 150 square feet of lawn. At this rate, how many pounds of fertilizer did she use on a lawn that measures 6750 square feet? Round to the nearest whole number.

Accepted Answer

Gretchen uses 3 pounds of fertilizer for every 150 square feet. For 6750 square feet, the amount of fertilizer used is (6750 / 150) * 3 = 45 * 3 = 135 pounds.

Question 7

Determine whether the proportion is true or false. $\frac { 3 \text { miles } } { 12 \text { hours } } = \frac { 6 \text { miles } } { 19 \text { hours } }$

Accepted Answer

The proportions are not equal because when both fractions are simplified, $\frac{3}{12}$ simplifies to $\frac{1}{4}$, while $\frac{6}{19}$ cannot be simplified to the same ratio.

Question 8

Solve. $\frac { 6 } { 20 } = \frac { n } { 50 }$

Accepted Answer

To solve for $n$, cross-multiply: $6 \times 50 = 20 \times n$, which simplifies to $300 = 20n$. Dividing both sides by 20 gives $n = 15$.

Question 9

Determine whether the proportion is true or false. $\frac { 1 } { 3 } = \frac { 4 } { 8 }$

Accepted Answer

$\frac{1}{3}$ is not equal to $\frac{4}{8}$ because when simplified, $\frac{4}{8}$ equals $\frac{1}{2}$.

Question 10

Solve. $\frac { 6 } { 42 } = \frac { 2 } { n }$

Accepted Answer

To solve the equation $\frac{6}{42} = \frac{2}{n}$, simplify the left side to $\frac{1}{7}$ by dividing both numerator and denominator by 6. Then, set the simplified fraction equal to the fraction on the right side: $\frac{1}{7} = \frac{2}{n}$. To find $n$, cross-multiply to get $1 \cdot n = 2 \cdot 7$, which simplifies to $n = 14$.

Question 11

Solve. $\frac { n } { 25 } = \frac { 6 } { 10 }$

Accepted Answer

Cross-multiply to solve for $ n $: $ n = \frac{6 \times 25}{10} = 15 $.

Question 12

Solve. Round to the nearest hundredth. $\frac { 2.6 } { 6 } = \frac { n } { 29 }$

Accepted Answer

To solve for $ n $, cross-multiply to get $ 2.6 \times 29 = 6 \times n $. This simplifies to $ 75.4 = 6n $. Dividing both sides by 6 gives $ n = 12.5667 $, which rounds to 12.57.

Question 13

In many medical offices, a 10% bleach solution is used as a disinfectant for cleaning the exam rooms. If $\frac { 1 } { 2 }$ cup of bleach is mixed with $3 \frac { 1 } { 2 }$ cups of water, how much bleach should be mixed with 7 cups of water in order to make a larger volume of this bleach solution?

Accepted Answer

The original solution has a ratio of 0.5 cups of bleach to 3.5 cups of water, which is 1:7. To maintain this ratio with 7 cups of water, 1 cup of bleach is needed.

Question 14

Determine whether the proportion is true or false. $\frac { 12 \text { feet } } { 8 \text { cups } } = \frac { 9 \text { feet } } { 6 \text { cups } }$

Accepted Answer

Both fractions simplify to $\frac{3}{2}$ when divided by their greatest common divisor, indicating they are equivalent proportions.

Question 15

Solve. Round to the nearest hundredth. $\frac { 28 } { n } = \frac { 8 } { 9 }$

Accepted Answer

To solve the equation $\frac{28}{n} = \frac{8}{9}$, cross-multiply to get $28 \times 9 = 8 \times n$. This simplifies to $252 = 8n$. Dividing both sides by 8 gives $n = 31.5$.

Question 16

Determine whether the proportion is true or false. $\frac { 6 \text { minutes } } { 12 \text { cents } } = \frac { 5 \text { minutes } } { 10 \text { cents } }$

Accepted Answer

Both fractions simplify to $\frac{1}{2}$ minute per cent, indicating the proportions are equal.

Question 17

A saline solution has a concentration ratio of 3.5 milligrams of salt in 100 milliliters of solution. How many milligrams of salt will be needed to produce 500 milliliters of a saline solution having this same concentration?

Accepted Answer

To maintain the same concentration ratio of 3.5 milligrams of salt per 100 milliliters of solution, for 500 milliliters, you multiply the concentration ratio by 5 (since 500 ml is 5 times 100 ml). Thus, 3.5 mg * 5 = 17.5 milligrams of salt.

Question 18

Solve. Round to the nearest hundredth. $\frac { 3 } { 5 } = \frac { 7 } { n }$

Accepted Answer

To solve the equation $\frac{3}{5} = \frac{7}{n}$, cross multiply to get $3n = 5 \times 7$. Simplifying gives $3n = 35$, and dividing both sides by 3 gives $n = \frac{35}{3}$, which is approximately 11.67 when rounded to the nearest hundredth.

Question 19

Determine whether the proportion is true or false. $\frac { 11 \text { tiles } } { 3 \text { feet } } = \frac { 56 \text { tiles } } { 15 \text { feet } }$

Accepted Answer

To check if the proportions are equal, cross-multiply: $11 \times 15$ and $3 \times 56$. The results are 165 and 168, respectively, which are not equal.

Question 20

In his truck, Robert can drive 74.5 miles on 2 gallons of gas. Find the distance that Robert's truck can travel on 10 gallons of gas. Round to the nearest hundredth.

Accepted Answer

To find the distance Robert's truck can travel on 10 gallons of gas, we can use proportion.

Distance / Gas = Distance / Gas

We know that the distance Robert's truck can travel on 2 gallons of gas is 74.5 miles, so we can plug that in:

74.5 / 2 = Distance / 10

Solving for Distance:

Distance = 74.5 / 2 * 10 = 372.5

Therefore, the distance that Robert's truck can travel on 10 gallons of gas is 372.5 miles. Rounded to the nearest hundredth, the answer is C) 372.50 miles.

Quiz 4: Ratio and Proportion

Determine whether the proportion is true or false. 20 miles 12 minutes =10 miles 6 minutes \frac { 20 \text { miles } } { 12 \text { minutes } } = \frac { 10 \text { miles } } { 6 \text { minutes } }12 minutes 20 miles ​=6 minutes 10 miles ​

According to the National Sample Survey of Registered Nurses, approximately one in five American Registered Nurses is male. If there are a total of 300 nurses working at a local hospital, how many of them would you expect to be male?

Using the data given below and a figure of 350 million for the number of Americans, determine the number of morbidly obese Americans.

Solve. Round to the nearest hundredth. n10=1123\frac { n } { 10 } = \frac { 11 } { 23 }10n​=2311​

Solve. 12n=6035\frac { 12 } { n } = \frac { 60 } { 35 }n12​=3560​

For landscape maintenance, Gretchen Green uses 3 pounds of fertilizer for every 150 square feet of lawn. At this rate, how many pounds of fertilizer did she use on a lawn that measures 6750 square feet? Round to the nearest whole number.

Determine whether the proportion is true or false. 3 miles 12 hours =6 miles 19 hours \frac { 3 \text { miles } } { 12 \text { hours } } = \frac { 6 \text { miles } } { 19 \text { hours } }12 hours 3 miles ​=19 hours 6 miles ​

Solve. 620=n50\frac { 6 } { 20 } = \frac { n } { 50 }206​=50n​

Determine whether the proportion is true or false. 13=48\frac { 1 } { 3 } = \frac { 4 } { 8 }31​=84​

Solve. 642=2n\frac { 6 } { 42 } = \frac { 2 } { n }426​=n2​

Solve. n25=610\frac { n } { 25 } = \frac { 6 } { 10 }25n​=106​

Solve. Round to the nearest hundredth. 2.66=n29\frac { 2.6 } { 6 } = \frac { n } { 29 }62.6​=29n​

Determine whether the proportion is true or false. 12 feet 8 cups =9 feet 6 cups \frac { 12 \text { feet } } { 8 \text { cups } } = \frac { 9 \text { feet } } { 6 \text { cups } }8 cups 12 feet ​=6 cups 9 feet ​

Solve. Round to the nearest hundredth. 28n=89\frac { 28 } { n } = \frac { 8 } { 9 }n28​=98​

Determine whether the proportion is true or false. 6 minutes 12 cents =5 minutes 10 cents \frac { 6 \text { minutes } } { 12 \text { cents } } = \frac { 5 \text { minutes } } { 10 \text { cents } }12 cents 6 minutes ​=10 cents 5 minutes ​