Question

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)
Answer
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)
Answer
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:

(−4)×(75)×(−34)÷(715)
Answer
Solve the following word problem. A fish is swimming at −10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of −37.8 meters? Show your work and write a sentence to explain what your answer means.(4 points)
Answer
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
negative 15

15
15

−50
negative 50

50
Answered by GPT 3.5
The quotient is the rate of change in the plane's altitude. To find it, we divide the change in altitude (4,000 feet) by the time it takes to make the adjustment (3.5 minutes):

Rate of change = Change in altitude / Time taken

Rate of change = 4000 feet / 3.5 minutes

Calculating this, we find:

Rate of change = 1142.86 feet per minute

Therefore, the rate of change in the plane's altitude is approximately 1142.86 feet per minute.
Answered by GPT 3.5
To find the change in the amount of water in 1 minute, we need to divide the change in water (250 gallons) by the time taken (5 minutes):

Change in water in 1 minute = Change in water / Time taken

Change in water in 1 minute = 250 gallons / 5 minutes

Calculating this, we find:

Change in water in 1 minute = 50 gallons

Therefore, the change in the amount of water in 1 minute is 50 gallons.
Answered by GPT 3.5
Using the properties of operations and rules for multiplying and dividing signed numbers, we can solve the expression:

(−4)×(75)×(−34)÷(715)

First, we can start by multiplying the numbers:

(−4)×(75)×(−34) = 10,200

Next, we divide by 715:

10,200 ÷ 715 = 14.29 (rounded to the nearest hundredth)

Therefore, the value of the expression (−4)×(75)×(−34)÷(715) is approximately 14.29.
Answered by GPT 3.5
To find how long it will take for the fish to reach a depth of −37.8 meters, we can use the equation:

Time = (Final depth - Initial depth) / Rate of change

The initial depth is −10.8 meters, the final depth is −37.8 meters, and the rate of change is 1.5 meters every 2 minutes.

Time = (−37.8 - (−10.8)) / 1.5

Simplifying this expression, we get:

Time = −27 / 1.5

Time = −18

Therefore, it will take the fish −18 minutes to reach a depth of −37.8 meters.

The negative sign indicates that the fish is swimming deeper into the water and the time given is in reference to reaching a depth below sea level. So, the fish will take 18 minutes to descend 37.8 meters deeper into the water beyond its current position of 10.8 meters below sea level.