Answer:
45
Step-by-step explanation:
Given
3z² - 6z ← substitute z = 5 into the expression
= 3(5)² - 6(5)
= 3(25) - 30
= 75 - 30
= 45
A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.
Answer: The correct option is B) about 34%
Proof:
We have to find 
To find
, we need to use z score formula:
When x = 4.2, we have:


When x = 5.1, we have:


Therefore, we have to find 
Using the standard normal table, we have:
= 

or 34.13%
= 34% approximately
Therefore, the percent of data between 4.2 and 5.1 is about 34%
1. Slope 3/4, through (4,-1)
y = 3/4 x + b
-1 = 3/4(4) + b
-1 = 3 + b
-1 - 3 = b
-4 = b
y = 3/4 x - 4
2. Slope = - 1/2, through (3,0)
y = -1/2 x + b
0 = -1/2(3) + b
0 = -1.5 + b
0 + 1.5 = b
1.5 = b
y = -1/2 x + 1.5
Take 1/2 of b and squaer it so
(b/2)^2 would complete the square
(sign doesn't matter becaus when squareing, sign goes positive)