Answer:
x = 7 and x = -1
Step-by-step explanation:
<u>Step 1: Factor</u>
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0
<u>Step 2: Solve for x</u>
(x - 7)(x + 1) = 0
x - 7 = 0 and x + 1 = 0
x - 7 + 7 = 0 + 7 and x + 1 - 1 = 0 - 1
x = 7 and x = -1
Answer: x = 7 and x = -1
Answer:
y = -6
Step-by-step explanation:
To simplify this equation as much as possible, we have to get the variable y by itself.
To do this, we would do the inverse operation of subtraction and add 7 to the left and right side of the equation.
-7 + 7 + 5y = -37 + 7
The 7s cancel out on the left side because -7+7 = 0 and so we are left with,
5y = -30
Then we would do the inverse operation of multiplication and divide by 5 on the left and right side of the equation.
5y/5 = -30/5
y = -6
Answer:
D. 30
Step-by-step explanation:
Having a population that doesn't follow normal distribution (skewed) can still have sampling distribution that is completely normal. This fact is presented in the Central Limit Theorem.
Central Limit Theorem: states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, we just need to take a large sample.
So how much sample size do we need?
There is no straight forward answer to this rather we have to analyse the situation closely!
1. If the population distribution is already normal then a smaller sample size would be enough to ensure normal distribution.
2. If the population distribution is very skewed than a larger number of sample size is needed to ensure normal distribution. The rule of thumb is to take sample size equal to or more than 30 to be on safer side. This is the case in this problem hence option D fits the best.
Answer:
Step-by-step explanation:
We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.
(x^2 +4x) +(y^2 -10y) = 7
(x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25
(x +2)^2 +(y -5)^2 = 6^2
Compare to ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle
We see that the center is ...
(h, k) = (-2, 5)
and the radius is ...
r = 6
