Answer:
The answer is: y = 3x - 7
Step-by-step explanation:
Given point: (5, 8).
Slope m = 3
Use the point slope form and solve for y:
y - y1 = m(x - x1)
y - 8 = 3(x - 5)
y - 8 = 3x - 15
y = 3x - 15 + 8
y = 3x - 7
Proof:
f(x) = 3x - 7
f(5) = 3(5) - 7
= 15 - 7 = 8, giving (5, 8)
Answer:

Step-by-step explanation:
A direct variation equation has the following format:

Where k is a constant.
We know that y is 12 when x is -2. Thus, substitute:

Divide both sides by -2:

So, our direct variation equations is:

To find what x is when y equals -6, substitute in -6 for y:

Divide both sides by -6:

So, our answer is 1 :)
Answer:
Our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Step-by-step explanation:
The hypotheses would be;
Null hypothesis;H0: μ = 500
Alternative hypothesis;Ha: μ ≠ 500
Since it's two - tailed at 0.1 level of significance, then each tail will contain 5% or 0.05. From the z-table attached, the corresponding critical value of 0.05 is approximately 1.645 standard deviations from the mean.
Thus, our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Answer:
116
Step-by-step explanation:
13x-1 = 2(6x+4)
13x-1 = 12x+8
x=9