Question
A squirrel has stored its acorns in a hole that is 45 feet from the ground in a tall tree. The squirrel starts on a perch 100 feet above the ground. The squirrel moves from the perch down to its stored acorns in 5.25 seconds. Interpret the quotient to describe the rate of change in the squirrel’s height above the ground. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the rate of change in the squirrel’s height above the ground is −10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is negative 10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is −19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is negative 19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
The correct response is: The quotient that describes the rate of change in the squirrel’s height above the ground is -10.48 feet/second.
A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
The correct response is: The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second.
The correct response is: The quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.
Solve using division of rational numbers. If a car’s value decreases by $4,000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)(1 point)
Responses
$333.33
$333.33
0.003
0.003
−$333.33
negative 333.33 dollars
−0.003
To find the value decrease per month, we need to divide the total decrease in value ($4,000) by the number of months (12).
$4,000 ÷ 12 = $333.33
So, the value decreases by $333.33 per month.
It is recommended that hikers drink 24 ounces of water an hour. If a canteen has 24 ounces of water, how much should the amount of water in the canteen change every 10 minutes?(1 point)
Responses
0.4 ounces
0.4 ounces
4 ounces
4 ounces
−4 ounces
negative 4 ounces
−0.4 ounces
To find the amount by which the water in the canteen should change every 10 minutes, we need to divide the recommended water intake per hour (24 ounces) by 6. This is because there are 6 ten-minute intervals in an hour.
24 ounces ÷ 6 = 4 ounces
So, the amount of water in the canteen should change by 4 ounces every 10 minutes.
To find the rate of change in the squirrel's height above the ground, we need to determine the change in height (in feet) divided by the time it took for that change to occur (in seconds).
Given that the squirrel starts on a perch 100 feet above the ground and moves down to its stored acorns in 5.25 seconds, we can calculate the change in height by subtracting the height of the stored acorns (45 feet) from the height of the perch (100 feet): 100 ft - 45 ft = 55 ft.
Next, we divide the change in height (55 ft) by the time it took (5.25 seconds): 55 ft / 5.25 s = 10.48 ft/s.
Since the squirrel is moving downwards, the rate of change is negative. Therefore, the correct interpretation of the quotient is:
The quotient that describes the rate of change in the squirrel’s height above the ground is -10.48 feet/second.