The answer is x=9 I’ve just did this problem once you take 4x+5 you’ll get 8
Answer:
Problem: ![\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-8%7D%7Bx%2B11%7D%20%5Ccdot%20%5Cfrac%7Bx%2B8%7D%7Bx-11%7D)
Answer: ![\frac{x^2-64}{x^2-121}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-64%7D%7Bx%5E2-121%7D)
Step-by-step explanation:
![\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-8%7D%7Bx%2B11%7D%20%5Ccdot%20%5Cfrac%7Bx%2B8%7D%7Bx-11%7D)
Writing as one fraction:
![\frac{(x-8)(x+8)}{(x+11)(x-11)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-8%29%28x%2B8%29%7D%7B%28x%2B11%29%28x-11%29%7D)
Now before we continue, notice both of your bottom and top are in the form of (a-b)(a+b) or (a+b)(a-b) which is the same format.
That is, we are multiplying conjugates on top and bottom.
When multiplying conjugates, all you have to do it first and last.
For example:
.
So your problem becomes this after the multiplication of conjugates:
![\frac{x^2-64}{x^2-121}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-64%7D%7Bx%5E2-121%7D)
Answer:
i)
ii)
And replacing we got:
![P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.00317%2B0.0211%2B0.0669%5D%3D%200.90883)
iii) ![P(X](https://tex.z-dn.net/?f=P%28X%20%3C2%29%3D%200.00317%2B%200.0211%3D%200.02427)
Step-by-step explanation:
Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part i
We want this probability:
Part ii
We want this probability:
And we can use the complement rule and we have:
![P(X\geq 3) = 1-P(X](https://tex.z-dn.net/?f=P%28X%5Cgeq%203%29%20%3D%201-P%28X%3C3%29%3D%201-P%28X%20%5Cleq%202%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%20%2BP%28X%3D2%29%5D)
And if we find the individual probabilites we got:
And replacing we got:
![P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.00317%2B0.0211%2B0.0669%5D%3D%200.90883)
Part iii
We want this probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%20%3C2%29%3D%20P%28X%3D0%29%20%2BP%28X%3D1%29)
And replacing we got:
![P(X](https://tex.z-dn.net/?f=P%28X%20%3C2%29%3D%200.00317%2B%200.0211%3D%200.02427)
Every hour is 60 minutes, there is 43 minutes before 12:00, and 155 minutes after 12:00
43 + 155 = 198
He was at the museum for 198 minutes, or 3 hour and 18 minutes.
Step-by-step explanation:
Write a proportion:
2½ cups / 1 batch = x cups / 3¾ batches
Cross multiply:
x × 1 = 2½ × 3¾
To multiply the fractions, first write them in improper form:
x = (5/2) × (15/4)
x = 75/8
Now write in proper form:
x = 9⅜
Your answer is correct! Well done!