For some number to be divisible by 12 it has to be divisible by 6 and by 2.
we can write number n as:
n = 6 + 12*k where k is positive integer.
If we divide n by 12 we will get remainder 6 because 12*k part is divisible by 12.
The part 12*k is as said divisible by 12 which means it is divisible by 6 (as first stated) and it has remainder 0. That leaves us with 6/6 which again has 0 as remainder. That means that number n is divisible by 6
The answer is 0
If you use the equation for Rachel it would be
y=3x and for oliver it would be y=2x+5
Answer: 

Step-by-step explanation:
Given :

re - writing the equation , we have

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.
The formula for finding the quadratic equation when the roots are known is :
- sum of roots(x) + product of root = 0
sum of roots = -2 + 4 = 2
product of roots = -2 x 4 = -8
substituting into the formula , we have:
, which could be written in inequality form as

comparing with
, it means that :


Answer:
The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).
Step-by-step explanation:
We have to calculate a 96% confidence interval for the proportion.
We consider the sample size to be the customers that responded the survey (n=800), as we can not assume the answer for the ones that did not answer.
The sample proportion is p=0.8.

The standard error of the proportion is:

The critical z-value for a 96% confidence interval is z=2.054.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 96% confidence interval for the population proportion is (0.77, 0.83).