Answer:
a) 658008 samples
b) 274050 samples
c) 515502 samples
Step-by-step explanation:
a) How many ways sample of 5 each can be selected from 40 is just a combination problem since the order of selection isn't important.
So, the number of samples = ⁴⁰C₅ = 658008 samples
b) How many samples of 5 contain exactly one nonconforming chip?
There are 10 nonconforming chips in the batch, and 1 nonconforming chip for the sample of 5 be picked from ten in the following number of ways
¹⁰C₁ = 10 ways
then the remaining 4 conforming chips in a sample of 5 can be picked from the remaining 30 total conforming chips in the following number of ways
³⁰C₄ = 27405 ways
So, total number of samples containing exactly 1 nonconforming chip in a sample of 5 = 10 × 27405 = 274050 samples
c) How many samples of 5 contain at least one nonconforming chip?
The number of samples of 5 that contain at least one nonconforming chip = (Total number of samples) - (Number of samples with no nonconforming chip in them)
Number of samples with no nonconforming chip in them = ³⁰C₅ = 142506 samples
Total number of samples = 658008
The number of samples of 5 that contain at least one nonconforming chip = 658008 - 142506 = 515502 samples
4 units, because a translation is a rigid motion, meaning it preserves segment length.
Answer:
x = -2
y=-3
(-2,-3)
Step-by-step explanation:
Both equations are equal to y
We can set them equal to each other
y = 3x + 3
y = x − 1
3x+3 = x-1
Subtract x from each side
3x+3 -x = x-1-x
2x+3 = -1
Subtract 3 from each side
2x+3-3 = -1-3
2x = -4
Divide each side by 2
2x/2 = -4/2
x = -2
Now we need to find y
y = x-1
y = -2-1
y = -3
y = x-1
A graphing calculator working the quadratic regression problem for these three points gives the equation as
y = 2x² +7x -5
The answer is 492.126 :) Hope it helps!
