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.
The quotient that best represents the rate of change in the plane's altitude is 1142.86 feet/minute.
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)
To find the change in the amount of water in 1 minute, we need to find the amount of water removed in 1 minute. Since the pump removes 250 gallons of water in 5 minutes, the amount of water removed in 1 minute is 250 gallons divided by 5 minutes, which equals 50 gallons/minute. Therefore, the change in the amount of water in 1 minute is 50 gallons.
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(7/5)×(−3/4)÷(7/15)
(1 point)
Responses
−147/75
negative Start Fraction 147 over 75 End Fraction
9
9
−9
negative 9
147/75
To solve, we can simplify the expression step by step:
First, multiply the numbers:
(-4) × (7/5) × (-3/4) ÷ (7/15) = (-28/5) × (-3/4) ÷ (7/15)
Next, divide the numbers:
= (-28/5) × (-3/4) × (15/7)
Now, multiply the numbers:
= (-28 × -3 × 15) / (5 × 4 × 7)
Simplify the numerator:
= (84 × 15) / (5 × 4 × 7)
Simplify the denominator:
= 42 / (5 × 4 × 7)
Simplify further:
= 42 / (20 × 7)
= 42 / 140
Reduce the fraction:
= 3/10
So, the solution is 3/10.
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)
To solve this problem, we need to find out how many times the fish needs to descend 1.5 meters in order to reach a depth of -37.8 meters.
First, let's calculate the difference in depth between the fish's initial depth (-10.8 meters) and the desired depth (-37.8 meters):
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -47.6 meters
Now, let's divide the difference in depth by the descent rate of the fish (1.5 meters) to find out how many descents are needed:
-47.6 meters ÷ 1.5 meters = -31.73
Since the number of descents cannot be negative, we take the absolute value of the result:
|-31.73| = 31.73
Therefore, the fish will take approximately 31.73 descents, which will take 31.73 * 2 = 63.46 minutes.
In conclusion, it will take the fish approximately 63.46 minutes to reach a depth of -37.8 meters below sea level.