Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty one. Find the numbers

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

2x + 3y = 22

For the second equation

3x + 4y = 31

Multiply the first one by 3 and the second one by 2

That's

First equation

6x + 9y = 66

Second equation

6x + 8y = 62

Subtract the second equation from the first one

That's

6x - 6x + 9y - 8y = 66 - 62

Substitute y = 4 into 2x + 3y = 22

That's

2x + 3(4) = 22

2x = 22 - 12

2x = 10

Divide both sides by 2

Hope this helps you

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%.