Answer: a) Mean = ![=37.80](https://tex.z-dn.net/?f=%3D37.80)
Standard deviation=![=1.9442](https://tex.z-dn.net/?f=%3D1.9442)
b) Mean = ![56.00](https://tex.z-dn.net/?f=56.00)
Standard deviation=![4.0988](https://tex.z-dn.net/?f=4.0988)
c) Mean = ![=24](https://tex.z-dn.net/?f=%3D24)
Standard deviation=![2.4495](https://tex.z-dn.net/?f=2.4495)
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = ![n\pi](https://tex.z-dn.net/?f=n%5Cpi)
Standard deviation=![\sqrt{n\pi(1-\pi)}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%5Cpi%281-%5Cpi%29%7D)
a. ![n=42,\ \pi=0.90](https://tex.z-dn.net/?f=n%3D42%2C%5C%20%5Cpi%3D0.90)
Mean = ![42\times0.90=37.80](https://tex.z-dn.net/?f=42%5Ctimes0.90%3D37.80)
Standard deviation=![\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442](https://tex.z-dn.net/?f=%5Csqrt%7B42%280.90%29%280.10%29%7D%3D%5Csqrt%7B3.78%7D%5Capprox1.9442)
b. ![n=80,\ \pi=0.70](https://tex.z-dn.net/?f=n%3D80%2C%5C%20%5Cpi%3D0.70)
Mean = ![80\times0.70=56.00](https://tex.z-dn.net/?f=80%5Ctimes0.70%3D56.00)
Standard deviation=![\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988](https://tex.z-dn.net/?f=%5Csqrt%7B80%280.70%29%280.30%29%7D%3D%5Csqrt%7B16.8%7D%5Capprox4.0988)
c. ![n=32,\ \pi=0.75](https://tex.z-dn.net/?f=n%3D32%2C%5C%20%5Cpi%3D0.75)
Mean = ![32\times0.75=24](https://tex.z-dn.net/?f=32%5Ctimes0.75%3D24)
Standard deviation=![\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495](https://tex.z-dn.net/?f=%5Csqrt%7B32%280.75%29%280.25%29%7D%3D%5Csqrt%7B6%7D%5Capprox2.4495)
Answer:
Option B. $231.13 is the correct answer.
Step-by-step explanation:
Given that
Listed price of furniture = P = $255
Discount = d = 12%
Sales tax = s = 3%
First of all, we have to find the discounted price by calculating the discount first
So,
![Discount = 12\%\ of\ P\\= 0.12*255\\= 30.6](https://tex.z-dn.net/?f=Discount%20%3D%2012%5C%25%5C%20of%5C%20P%5C%5C%3D%200.12%2A255%5C%5C%3D%2030.6)
Discounted Price:
![= Listed\ Price - Discount\\= 255 - 30.6\\= 224.4](https://tex.z-dn.net/?f=%3D%20Listed%5C%20Price%20-%20Discount%5C%5C%3D%20255%20-%2030.6%5C%5C%3D%20224.4)
The sales tax will be calculated on the discounted price
So,
![Sales\ tax = 3\%\ of\ Discounted\ price\\= 0.03 * 224.4\\= 6.732](https://tex.z-dn.net/?f=Sales%5C%20tax%20%3D%203%5C%25%5C%20of%5C%20Discounted%5C%20price%5C%5C%3D%200.03%20%2A%20224.4%5C%5C%3D%206.732)
Now,
![Final\ price\ of\ furniture = Discounted\ price + Sales\ tax\\= 224.4 + 6.732\\=231.132](https://tex.z-dn.net/?f=Final%5C%20price%5C%20of%5C%20furniture%20%3D%20Discounted%5C%20price%20%2B%20Sales%5C%20tax%5C%5C%3D%20224.4%20%2B%206.732%5C%5C%3D231.132)
He will actually pay $231.132 for the furniture.
Hence,
Option B. $231.13 is the correct answer.
Answer:
A
Step-by-step explanation:
We will use d for drama and y for yearbook.
d + y = 64
d = y + 10
Now that we have the system if equations we can use substitution where you plug y+10 in for d in the first equation.
(y + 10) + y = 64
2y + 10 = 64
2y = 54
y = 27
If 27 of the 64 are in the yearbook club, 37 are in drama.
Answer:
y = 4
Step-by-step explanation:
First we want to raise -1 to the power of 2
y = 2 * 1 - 5 * -1 - 3
Multiply
2 - 5 * -1 - 3
Multiply
y = 2 + 5 - 3
y = 7 - 3
y = 4