Question 11

Question

Question 11
A)Use long division to convert 6 7/15 to a decimal.(1 point)
Responses

≈0.46
approximately equals 0.46

≈6.47
approximately equals 6.47

≈6.14285
approximately equals 6.14285

6.715
6.715
Question 12
A)Kimberly ran 4/5 of the way around the track before getting tired and slowing her pace. What percentage of the track did she run at a slower pace?(1 point)
$$%
Question 13
A)What is 90.5% written as a decimal?(1 point)
$$
Question 14
A)A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth, and remember the plane is descending.(1 point)
The quotient that best represents the rate of change in the plane’s altitude is $$ feet/minute.
Question 15
A)A fire engine’s water tank holds 750 gallons of water. If the pump removes 250 gallons of water in 5 minutes, what is the change in the amount of water in gallons in 1 minute?(1 point)
Responses

15
15

−15
negative 15

−50
negative 50

50

GPT-4o mini · Answer

Sure, let's go through each of these questions one at a time.

Question 11 To convert $6 \frac{7}{15}$ to a decimal:

Convert $ \frac{7}{15} $ to decimal by performing long division of 7 by 15.
- 15 goes into 70 (7.00) four times, since $ 15 \times 4 = 60 $. This leaves a remainder of $ 70 - 60 = 10 $.
- Bring down a 0, making it 100. 15 goes into 100 six times, since $ 15 \times 6 = 90 $. This leaves a remainder of $ 100 - 90 = 10 $.
- It would repeat the process leading to $ 0.46666...$

Thus, $ \frac{7}{15} \approx 0.4666$.

So, $6 \frac{7}{15} \approx 6.4666$.

The closest answer is: ≈6.47.

Question 12 Kimberly ran $ \frac{4}{5} $ of the track. The remaining part of the track can be calculated as follows:

Calculate the remaining part: $ 1 - \frac{4}{5} = \frac{1}{5} $.
Convert $ \frac{1}{5} $ to a percentage: \[ \frac{1}{5} \times 100 = 20% \]

Thus, the percentage of the track she ran at a slower pace is: 20%.

Question 13 To express $90.5%$ as a decimal:

Divide the percentage by 100: \[ 90.5% = \frac{90.5}{100} = 0.905 \]

Thus, $90.5%$ written as a decimal is: 0.905.

Question 14 To find the rate of change in the plane's altitude:

The plane descended $4000$ feet in $3.5$ minutes.
Calculate the rate: \[ \text{Rate} = \frac{\text{change in altitude}}{\text{time}} = \frac{-4000\text{ feet}}{3.5\text{ minutes}} \approx -1142.8571428571429 \text{ feet/minute.} \]
Rounded to the nearest hundredth: \[ \approx -1142.86 \text{ feet/minute.} \]

Thus, the rate of change in the plane's altitude is: −1142.86 feet/minute.

Question 15 To find the change in the amount of water in gallons in $1$ minute:

The pump removes $250$ gallons in $5$ minutes.
Calculate the rate of change per minute: \[ \text{Rate} = \frac{-250 \text{ gallons}}{5 \text{ minutes}} = -50 \text{ gallons/minute.} \]

Thus, the change in the amount of water in gallons in $1$ minute is: −50.

If you have more questions or need further assistance with any of these, just let me know!