Answer:
105
Step-by-step explanation:
5 ÷ 35 = 7
140 ÷ 20 = 7
15 · 7 = 105
I hope this helps!
Answer:
x=3
y=5
Step-by-step explanation:
3x+2y=19
- 2x+2y=16
_____________
x=3
3(3)=9
19-9=10
10÷2=5
y=5
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
This is the diference of 2 perfect squares. 4 is a perfect square, x^2 is a perfect square, and 25 is a perfect square. The pattern for this is (ax + b)(ax - b). Our a is 2 since 2*2 = 4, and our b is 5 since 5*5 = 25. So your factors are (2a+5)(2a-5), choice C.
Step-by-step explanation:
3 + 3(k + 3) = 6(k - 2) + 9
3 + 3k + 9 = 6k - 12 + 9
12 + 12 - 9 = 6k - 3k
15 = 3k
k = 15/3
k = 5
