Consider the geometric sequence below
( shown in picture )
select all functions that define the given sequence
asap

The Option 1 and Option 4 are correct.

Step-by-step explanation:

The geometric sequence is:

-4,-6,-9,-27/2,-81/2,

The Option 1 and Option 4 are correct.

f(1) = -4.

f(n) = 3/2 f(n-1)

Put n=2

f(2) = 3/2(f(1)

f(2) = 3/2(-4)

f(2) = -6

So, we get the series using this formula

Option 1 is correct.

Option 4 has formula

f(n) = -4 (3/2)^n-1

Put n= 1

f(1) = -4(3/2)^0

f(1) = -4

Put n = 2

f(2) = -4(3/2)^2-1

f(2) = -4(3/2)

f(2) = -6

Put n=3

f(3) = -4(3/2)^3-1

f(3) = -4(3/2)^2

f(3) = -4(9/4)

f(3)=-9

So we get the series, Hence Option 4 is correct.

We conclude that the car have mileage rating less than 30 miles per gallon.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 30 miles/gallon

Sample:

26, 24, 20, 25, 27, 25, 28, 30, 26, 33

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 110.4

Sample size, n = 10

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

We use one-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                  

We fail to accept the null hypothesis and reject it.

We conclude that the car have mileage rating less than 30 miles per gallon.

b) We assumed that the level of significance is 0.05 that is 5%.