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.
To interpret the quotient that describes the rate of change in the squirrel's height above the ground, we divide the change in height by the time it takes to make the change.
The change in height is from a perch 100 feet above the ground to a hole that is 45 feet from the ground, so the change in height is 100 - 45 = 55 feet.
The time it takes for the squirrel to make the change in height is 5.25 seconds.
Now, we can calculate the quotient:
Rate of change = Change in height / Time taken
Rate of change = 55 feet / 5.25 seconds
Rate of change ≈ 10.48 feet per second
Therefore, the quotient represents that the squirrel is descending at a rate of approximately 10.48 feet per second.
The correct quotient that describes the rate of change in the squirrel's height above the ground is 10.48 feet/second.
To interpret the quotient that describes the average rate of change in the dolphin's position, we divide the change in position by the time it takes to make the change.
The change in position is from an altitude of 3.5 meters above the surface of the water to a depth of 10 meters below the surface of the water, so the change in position is 3.5 + (-10) = -6.5 meters.
The time it takes for the dolphin to make the change in position is 12.5 seconds.
Now, we can calculate the quotient:
Rate of change = Change in position / Time taken
Rate of change = -6.5 meters / 12.5 seconds
Rate of change ≈ -0.52 meters per second
Therefore, the quotient represents that the dolphin's position is changing at an average rate of approximately -0.52 meters per second.
To interpret the quotient that describes the average rate of change in the diver's depth, we divide the change in depth by the time it takes to make the change.
The change in depth is a descent of 10 meters.
The time it takes for the diver to make the descent is 10.1 seconds.
Now, we can calculate the quotient:
Rate of change = Change in depth / Time taken
Rate of change = -10 meters / 10.1 seconds
Rate of change ≈ -0.99 meters per second
Therefore, the quotient represents that the diver's depth is changing at an average rate of approximately -0.99 meters per second.
To find out how much the car's value decreases per month, we divide the total decrease in value by the number of months.
The car's value decreases by $4000 in the first 12 months.
We divide $4000 by 12 to find the decrease per month:
Decrease per month = -$4000 / 12
Decrease per month ≈ -$333.33
Therefore, the value of the car decreases by approximately -$333.33 per month.
To find out how much the amount of water in the canteen should change every 10 minutes, we need to determine the proportion of water that should be consumed in a 10-minute period.
A hiker is recommended to drink 24 ounces of water per hour. To find out how much should be consumed in 10 minutes, we divide 24 by 60 (minutes per hour) and multiply the result by 10 (minutes):
Amount of water per 10 minutes = (24 ounces / 60 minutes) * 10 minutes
Amount of water per 10 minutes = 4 ounces
Therefore, the amount of water in the canteen should decrease by 4 ounces every 10 minutes.
question 1: 1/2
question 2: 8
question 3: -5/12
question 4: 1 ounce(s)
question 5: $100
only for connexus these are the right answers is promis.
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.
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 -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 1.08 meters/second.
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 -0.49 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 -0.99 meters/second.
The quotient that scribes 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 $4000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)(1 point)
Responses
-$333.33
-$0.003
$0.003
$333.33
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
-0.4 ounces
-0.4 ounces
0.4 ounces
0.4 ounces
4 ounces
Joshua is sharing half of a pizza with three friends. Which expression can be used to find the fraction of a whole pizza each person will get, if they sprint what they have evenly?(1 point)
Responses
2⋅14
2 times 1 fourth
2⋅4
2 times 4
12⋅14
1 half times 1 fourth
12⋅4
To find the fraction of a whole pizza each person will get when Joshua shares half of a pizza with three friends, we can divide the half pizza into equal parts.
Since Joshua is sharing the half pizza with three friends, the total number of people sharing the pizza is 4 (Joshua + 3 friends). Thus, we need to divide the half pizza among 4 people, which results in:
1 divided by 4, or 1/4
Therefore, the correct expression to find the fraction of a whole pizza each person gets is 1/4.
Joshua is sharing half of a pizza with three friends. Which expression can be used to find the fraction of a whole pizza each person will get, if they sprint what they have evenly?(1 point)
Responses
a. 2⋅14
2 times 1 fourth
b. 2⋅4
2 times 4
c. 12⋅14
1 half times 1 fourth
d. 12⋅4
To find the fraction of a whole pizza each person will get if Joshua shares half of a pizza with three friends, we need to divide the half pizza evenly among the four people (Joshua and his three friends).
If each person gets an equal portion, we divide the half pizza into four equal parts. This can be represented by the expression 1/4.
Therefore, the correct choice is:
a. 2⋅14
2 times 1 fourth
7. Which quotient is between -4 and -5?
Hint: Use your calculator for this problem.
(1 point)
Responses
a.−5 1/2÷(−1 1/2)
negative 5 and 1 half divided by open paren negative 1 and 1 half close paren
b.1 2/3÷(−1/2)
1 and 2 thirds divided by open paren negative 1 half close paren
c. −9 1/3÷2
negative 9 and 1 third divided by 2
d. 2 5/6÷(−1/2)
To determine which quotient is between -4 and -5, we can use a calculator to find the decimal equivalent of each quotient and compare them.
a. −5 1/2 ÷ (−1 1/2)
This quotient can be written as -11/2 ÷ (-3/2).
Using a calculator, we find that the decimal equivalent is approximately 3.67.
b. 1 2/3 ÷ (−1/2)
This quotient can be written as 5/3 ÷ (-1/2).
Using a calculator, we find that the decimal equivalent is approximately -3.33.
c. −9 1/3 ÷ 2
This quotient can be written as -28/3 ÷ 2.
Using a calculator, we find that the decimal equivalent is approximately -4.67.
d. 2 5/6 ÷ (−1/2)
This quotient can be written as 17/6 ÷ (-1/2).
Using a calculator, we find that the decimal equivalent is approximately -5.67.
Therefore, the quotient that is between -4 and -5 is:
c. −9 1/3 ÷ 2 (approximately -4.67)
convert 3 16/25 into a decimal
1.92
0.64
12.64
3.64
To convert 3 16/25 into a decimal, we first multiply the whole number (3) by the fraction denominator (25) and add the numerator (16). Then, we divide this sum by the denominator (25).
For 3 16/25:
3 x 25 = 75
75 + 16 = 91
91 ÷ 25 = 3.64
Therefore, 3 16/25 as a decimal is 3.64.
A mountain goat is climbing to the top of a large cliff. The cliff is 50 feet higher than its starting point. If it takes the goat 22 minutes to climb this cliff, interpret the quotient to describe the rate of change in the goat’s elevation. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the goat’s elevation is
To interpret the quotient that describes the rate of change in the goat's elevation, we divide the change in elevation by the time it takes to climb the cliff.
The change in elevation is 50 feet (since the cliff is 50 feet higher than the starting point).
The time it takes for the goat to climb the cliff is 22 minutes.
Now, we can calculate the quotient:
Rate of change = Change in elevation / Time taken
Rate of change = 50 feet / 22 minutes
Rate of change ≈ 2.27 feet per minute
Therefore, the quotient represents that the goat's elevation is changing at a rate of approximately 2.27 feet per minute.
A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth and remember that the bird is descending.(1 point)
The quotient that best represents the rate of change in the bird’s altitude is
meters/second.
To interpret the quotient that describes the rate of change in the bird's altitude, we divide the change in altitude by the time it takes for the bird to settle on the branch.
The change in altitude is from an average altitude of 10 meters above the ground to settling on a branch that is 3 meters above the ground, so the change is 10 - 3 = 7 meters.
The time it takes for the bird to settle on the branch is 3 seconds.
Now, we can calculate the quotient:
Rate of change = Change in altitude / Time taken
Rate of change = 7 meters / 3 seconds
Rate of change ≈ 2.33 meters per second
Therefore, the quotient represents that the bird's altitude is changing at a rate of approximately 2.33 meters per second as it descends to settle on the branch.
A whale is swimming at a current depth of 15 meters below the surface. It swims up toward the surface and arrives there 9.5 seconds later. Find the quotient that best describes the rate of change in the whale’s depth. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the whale’s depth is
meters/second.
To find the quotient that best describes the rate of change in the whale's depth, we need to divide the change in depth by the time it takes for the whale to reach the surface.
The change in depth is from a current depth of 15 meters below the surface to reaching the surface, which is a depth of 0 meters. So the change in depth is 15 - 0 = 15 meters.
The time it takes for the whale to reach the surface is given as 9.5 seconds.
Now, we can calculate the quotient:
Rate of change = Change in depth / Time taken
Rate of change = 15 meters / 9.5 seconds
Rate of change ≈ 1.58 meters per second
Therefore, the quotient that best represents the rate of change in the whale's depth is approximately 1.58 meters per second.
Solve using division of rational numbers. If a car’s value decreases by $2,500 in the first 6 months, how much does the value decrease per month? (Round to the nearest hundredth.) (1 point)
To find out how much the car's value decreases per month, we divide the total decrease in value by the number of months.
The car's value decreases by $2,500 in the first 6 months.
We divide $2,500 by 6 to find the decrease per month:
Decrease per month = $2,500 / 6
Decrease per month ≈ $416.67
Therefore, the value of the car decreases by approximately $416.67 per month.
-3 5/9 + 2 - 4 1/9
To simplify the expression -3 5/9 + 2 - 4 1/9, we need to first convert all the mixed numbers into improper fractions.
-3 5/9 can be rewritten as -(3*9 + 5)/9 = -32/9
4 1/9 can be rewritten as 4*9 + 1/9 = 37/9
Now we can substitute these values into the expression:
-3 5/9 + 2 - 4 1/9 = -32/9 + 2 - 37/9
Now let's find a common denominator, which is 9 in this case:
-32/9 + 2 - 37/9 = -32/9 + 18/9 - 37/9
Now we can simplify further:
-32/9 + 18/9 - 37/9 = (-32 + 18 - 37)/9 = -51/9
Finally, we can simplify the result by dividing both the numerator and denominator by their greatest common divisor, which is 3:
-51/9 = -17/3
Therefore, -3 5/9 + 2 - 4 1/9 simplifies to -17/3.