Find the numerical equivalent of 2^5 x 2 ^-2
To find the numerical equivalent of 2^5 x 2 ^-2, first calculate the value of each exponent separately.
2^5 = 2 x 2 x 2 x 2 x 2 = 32.
2^-2 = 1 / (2^2) = 1 / (2 x 2) = 1 / 4 = 0.25.
Then, multiply the two values together:
32 x 0.25 = 8.
Therefore, the numerical equivalent of 2^5 x 2 ^-2 is 8.
1. 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 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 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 -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 -19.05 feet/second.
Question 2
2. 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 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 -0.52 meters/second.
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 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
Question 3
3. The scuba diver was at a depth 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 scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -3.47 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -3.47 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
Question 4
4. Solve using division of rational numbers. If a car’s value decreases by $4000 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
$0.003
$0.003
$333.33
$333.33
Question 5
5. 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
-4 ounces
-4 ounces
4 ounces
4 ounces
answer all of the questions
1. The quotient that describes the rate of change in the squirrel's height above the ground is -19.05 feet/second.
2. The quotient that describes the rate of change in the dolphin's position is -0.52 meters/second.
3. The quotient that describes the average rate of change for the diver's depth is -0.99 meters/second.
4. The value of the car decreases by $333.33 per month.
5. The amount of water in the canteen should decrease by 4 ounces every 10 minutes.
To find the numerical equivalent of 2^5 x 2^-2, we can simplify the expression using the properties of exponents.
Step 1: Recall that a negative exponent indicates taking the reciprocal of the base. Therefore, 2^-2 can be rewritten as 1/2^2.
Step 2: Simplify each of the exponents separately. 2^5 is equal to 2 x 2 x 2 x 2 x 2, which equals 32.
Step 3: Similarly, 1/2^2 can be simplified as 1/(2 x 2), which equals 1/4.
Step 4: Multiply the simplified values together. 32 x 1/4 is equal to 32/4, which simplifies to 8.
Therefore, the numerical equivalent of 2^5 x 2^-2 is 8.
To find the numerical equivalent of 2^5 x 2^-2, we can simplify the expression by using the exponent rules:
When multiplying terms with the same base, we add the exponents. Hence, 2^5 x 2^-2 can be rewritten as 2^(5+(-2)).
To calculate 5 + (-2), we add the numbers together, which gives us 3. Therefore, the simplified expression is 2^3.
Finally, we can evaluate 2^3 by multiplying 2 three times:
2^3 = 2 x 2 x 2 = 8.
Thus, the numerical equivalent of 2^5 x 2^-2 is 8.