After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. by the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. how many feet would the balloon rise in 8 minutes?

300 feet

Step-by-step explanation:

Note that:

.

Then the balloon rises at a constant rate of 30 meters per minute.

We can represent this situation through an arithmetic sequence as shown below

Where is the first term of the sequence and is the n-th term of the sequence and is the common difference between two consecutive terms.

In this case we look for the height of the balloon after 8 minutes.

Then we look for

Step-by-step explanation:

You have an arithmetic sequence in which

a₁ =  90

a₂ = 120

a₃ = 150

1. Calculate the explicit formula

This is an arithmetic sequence, because there is a constant difference of 30 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,  

aₙ = 90 + 30(n - 1) = 90 + 30n - 30

aₙ = 30n + 60

2. Calculate the eighth term

a₈ = 30 × 8 + 60 = 240 + 60 = 300

452,489 to the nearest thousand is 452,000

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;