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
Fist, in the equation y=mx+b, b is the y-intercept. The y-intercept is the poin on the line that crosses the x-axis; the y-intercept is the value of yThese equations follow that format.
Y=mx+b
y

3x-4. <-----In this equation, the slope(m)=3 b= -4.
On the graph, we can see that the line crosses the x-axis at y=-4. Knowing that, we can eliminate the answer choices with +4 in the inequality.
The next step, is to pick an (x,y) coordinate that is in the shaded region and plug it into the remaining 2 inequalities. Which ever inequality is true after you solve it, that is the correct answer.
For example, I'll choose to plug in (-4,4) into the y

3x-4.
y

3x-4.
(4)

(3(-4))-4.
(4)

(-12)-4.
(4)

-16
So, this statement is true becasue -16 is less than positive 4. Therefore, the correct answer would be
y
3x-4. Hope that helped! Comment back with any further questions!
Answer:

Step-by-step explanation:
remember: tan(theta) = opposite/adjacent
Answer:
a=-0.5
Step-by-step explanation:
Distributive property for left side, difference of squares for right side.
8a-9a^2=-40+36-9a^2
-9a^2 cancels out
8a=-4
a=-0.5
L×w=64 ft^2...(1)
2w+8= l...(2)
l=64-w...(1a)
2w+8= 64-w
2w+w+8=64
3w=64-8
3w÷3= 56÷3
w=18.6'
l×w= 64
l×18.6= 64
l= 64÷18.6
l= 3.44 to the nearest hundredths.