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 (rate of change) can be calculated by dividing the change in elevation (50 feet) by the time it took to climb (22 minutes).
Rate of change = Change in elevation / Time taken
Rate of change = 50 feet / 22 minutes
Calculating this quotient, we find that the rate of change is 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
The quotient that best represents the rate of change in the bird's altitude is calculated by dividing the change in altitude (10 meters - 3 meters = 7 meters) by the time taken (3 seconds).
Rate of change = Change in altitude / Time taken
Rate of change = 7 meters / 3 seconds
Calculating this quotient, we find that the rate of change is approximately 2.33 meters per second.
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 describes the rate of change in the whale's depth is calculated by dividing the change in depth (0 meters - (-15 meters) = 15 meters) by the time taken (9.5 seconds).
Rate of change = Change in depth / Time taken
Rate of change = 15 meters / 9.5 seconds
Calculating this quotient, we find that the rate of change 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 the value decrease per month, we divide the decrease in value ($2,500) by the time taken (6 months) using division of rational numbers.
Value decrease per month = Decrease in value / Time taken
Value decrease per month = $2,500 / 6 months
Calculating this division, we find that the value decreases approximately by $416.67 per month (rounded to the nearest hundredth).
A restaurant uses a 15-pound bag of flour in 4 days. Each day, the bag of flour gets lighter as more flour is used. How much does the average amount of flour in the bag change each day? (Round to the nearest hundredth.)(1 point)
To find the average amount of flour in the bag that changes each day, we divide the total weight of flour used (15 pounds) by the number of days (4 days) using division of rational numbers.
Average change per day = Total weight of flour used / Number of days
Average change per day = 15 pounds / 4 days
Calculating this division, we find that the average amount of flour in the bag changes by approximately 3.75 pounds per day (rounded to the nearest hundredth).
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)
The quotient that describes the rate of change in the squirrel's height above the ground can be calculated by dividing the change in height (100 feet - 45 feet = 55 feet) by the time taken (5.25 seconds).
Rate of change = Change in height / Time taken
Rate of change = 55 feet / 5.25 seconds
Calculating this quotient, we find that the rate of change is approximately 10.48 feet per second (rounded to the nearest hundredth).
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)
The quotient that describes the average rate of change in the dolphin's position can be calculated by dividing the change in position (3.5 meters + 10 meters = 13.5 meters) by the time taken (12.5 seconds).
Average rate of change = Change in position / Time taken
Average rate of change = 13.5 meters / 12.5 seconds
Calculating this quotient, we find that the average rate of change in the dolphin's position is approximately 1.08 meters per second (rounded to the nearest hundredth).
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)
The quotient that describes the rate of change in the diver's depth can be calculated by dividing the change in depth (10 meters) by the time taken (10.1 seconds).
Rate of change = Change in depth / Time taken
Rate of change = 10 meters / 10.1 seconds
Calculating this quotient, we find that the rate of change in the diver's depth is approximately 0.99 meters per second (rounded to the nearest hundredth).
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)
To find the value decrease per month, we divide the decrease in value ($4,000) by the time taken (12 months) using division of rational numbers.
Value decrease per month = Decrease in value / Time taken
Value decrease per month = $4,000 / 12 months
Calculating this division, we find that the value decreases approximately by $333.33 per month (rounded to the nearest hundredth).
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)
To find the amount of water the canteen should change every 10 minutes, we need to divide the recommended amount of water per hour (24 ounces) by the number of 10-minute intervals in an hour (6).
Amount of water to change every 10 minutes = Recommended amount of water per hour / Number of 10-minute intervals in an hour
Amount of water to change every 10 minutes = 24 ounces / 6 intervals
Calculating this division, we find that the amount of water in the canteen should change by approximately 4 ounces every 10 minutes.
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)
To find the rate of change in the bird's altitude, we need to calculate the change in altitude and divide it by the time taken.
Change in altitude = Starting altitude (10 meters) - Ending altitude (3 meters) = 7 meters
Time taken = 3 seconds
Rate of change = Change in altitude / Time taken
Rate of Change = 7 meters / 3 seconds
Calculating this quotient, we find that the rate of change in the bird's altitude is approximately 2.33 meters per second (rounded to the nearest hundredth). Since the bird is descending, the negative sign is implied, indicating that the bird is descending at a rate of 2.33 meters per second.
It says it's the wrong answer.
Apologies for the confusion. As the bird is descending, the change in altitude would be negative. Let's recalculate:
Change in altitude = Starting altitude (10 meters) - Ending altitude (3 meters) = 10 meters - 3 meters = 7 meters (negative)
Time taken = 3 seconds
Rate of change = Change in altitude / Time taken = -7 meters / 3 seconds = -2.33 meters per second
The correct interpretation of the quotient is that the bird's altitude is decreasing at a rate of approximately 2.33 meters per second.