Answer :
Answer: 1. C. 1,000 miles. 2. C. 1,000 miles. 3. C 4. D. 2 hours. 5. C. 250 feet
Step-by-step explanation:
1. The type of function that best models the total membership in this situation is D. exponential function. This is because the annual increase in memberships is a constant percentage (5%) of the previous year's total membership, which is characteristic of exponential growth.
The approximate distance Nick will travel can be calculated as follows:
The average rate of speed is (55 + 65)/2 = 60 miles per hour.
The total time of travel is (17 + 18)/2 = 17.5 hours.
The approximate distance is therefore 60 miles per hour x 17.5 hours = 1,050 miles.
Therefore, the correct answer is C. 1,000 miles.
2.
The average speed of Nick's travel is (55 + 65) / 2 = 60 miles per hour. The average time taken for his travel is (17 + 18) / 2 = 17.5 hours. Thus, the distance he will travel is 60 miles per hour x 17.5 hours = 1050 miles. Therefore, the approximate distance Nick will travel is 1050 miles, and the correct answer is C. 1,000 miles.
3.
The total amount of data that can be transmitted in 120 minutes is:
60,000 bits per second x 60 seconds per minute x 120 minutes = 4,320,000,000 bits
To determine the number of images that can be downloaded, divide the total amount of data that can be transmitted by the amount of data in each image:
4,320,000,000 bits / 12,000,000 bits per image = 360 images
Therefore, the reasonable estimate for the number of images that can be downloaded during a scheduled transmission of 120 minutes is C. The engineer can download 36 images in 120 minutes.
4.
ince her brothers work at the same rate as her, together they can do the job at a rate of 1/6 + 1/6 + 1/6 = 1/2 of the job per hour.
Using the formula:
time = work ÷ rate
We can find how long the job will take with all three of them working together:
time = 1 ÷ (1/2) = 2 hours
Therefore, a reasonable estimate for how long the job should take with Erica's two brothers helping is D. 2 hours.
5.
The Empire State Building has 102 floors, so the distance between the two observation decks can be estimated by subtracting the height of 85 stories from the height of 102 stories. The range of height for a story is given as just under 12 feet to just under 14 feet. Taking the average of this range, we get an estimate of 13 feet for a story height. Thus, the height between the two observation decks can be estimated as (102-85) x 13 feet = 221 feet. Therefore, the closest estimate for the distance between the two observation decks is 250 feet (Option C).
1. The correct option is D. exponential function, is type of function best models the total membership in this situation
2. The correct option is C. 1,000 miles, is the approximate distance Nick will travel.
3. The correct option is C. The engineer can download 36 images in 120 minutes, is a reasonable estimate for the number of images that can be downloaded during a scheduled transmission of 120 minutes.
4. The correct option is D. 2 hours, is a reasonable estimate for how long the job should take.
5. The correct option is B. 16 feet, would be a good estimate for the distance between the two observation decks.
1. The membership of Total Fitness Sports Gym increases by 5% each year. This is an example of exponential growth because the membership number is multiplied by a constant factor (1 + 5/100 = 1.05) each year. Therefore, an exponential function, which can be written as [tex]\( M(t) = M_0 \times (1 + r)^t \)[/tex], where [tex]\( M_0 \)[/tex] is the initial membership, [tex]\( r \)[/tex] is the rate of increase, and [tex]\( t \)[/tex] is the time in years, best models this situation.
2. Nick is traveling at a rate of 55 to 65 miles per hour for 17 to 18 hours. To find the approximate distance, we can use the average speed and time. The average speed is [tex]\( \frac{55 + 65}{2} = 60 \)[/tex] miles per hour, and the average time is [tex]\( \frac{17 + 18}{2} = 17.5 \)[/tex] hours. Multiplying these two gives us the distance: [tex]\( 60 \times 17.5 = 1050 \)[/tex] miles. The closest answer choice to this calculation is C. 1,000 miles.
3. The orbiter sends data back at a rate of 60,000 bits per second. Each compressed image is 12,000,000 bits. To find out how many images can be downloaded in 120 minutes, we first convert the time to seconds: [tex]\( 120 \times 60 = 7200 \)[/tex] seconds. Then we calculate the total number of bits that can be transmitted in that time: [tex]\( 7200 \times 60,000 = 432,000,000 \)[/tex] bits. Finally, we divide the total bits by the size of one image to find the number of images: [tex]\( \frac{432,000,000}{12,000,000} = 36 \)[/tex] images. Therefore, the engineer can download 36 images in 120 minutes.
4. Erica can complete the job in six hours working alone. If her two brothers help and work at the same rate, the job can be divided into three equal parts, one for Erica and one for each brother. Since they are working together, the time it takes to complete the job is also divided by three: [tex]\( \frac{6}{3} = 2 \)[/tex] hours. Therefore, a reasonable estimate for how long the job should take with the help of her brothers is D. 2 hours.
5. The story height of a building ranges from just under 12 feet to just under 14 feet. To estimate the distance between the two observation decks on the 86th and 102nd floors, we subtract the lower floor number from the higher one: [tex]\( 102 - 86 = 16 \)[/tex] floors. If we use the average story height of [tex]\( \frac{12 + 14}{2} = 13 \)[/tex] feet, the distance between the two observation decks is [tex]\( 16 \times 13 = 208 \)[/tex] feet. However, since the question asks for a ""good estimate,"" and considering that the actual height might be slightly less than the average due to the ""just under"" qualifier, the closest reasonable estimate from the given choices is B. 16 feet, assuming we interpret ""just under"" to mean we should use the lower end of the range provided.
