Answer:
Angle CGB is an acute angle because it's less than 90°
You can write three equations in the numbers of nickels (n), dime (d), and quarters (q).
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
_____
I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
Given :
Diameter of pizza ,
.
To Find :
Is square box of size equal to diameter big enough to fit pizza inside it .
Solution :
Area of pizza :
![A_p=\pi(\dfrac{D}{2})^2\\\\A_p=\pi\times (\dfrac{31}{3\times 2})^2\\\\A_p=83.86\ inch^2](https://tex.z-dn.net/?f=A_p%3D%5Cpi%28%5Cdfrac%7BD%7D%7B2%7D%29%5E2%5C%5C%5C%5CA_p%3D%5Cpi%5Ctimes%20%28%5Cdfrac%7B31%7D%7B3%5Ctimes%202%7D%29%5E2%5C%5C%5C%5CA_p%3D83.86%5C%20inch%5E2)
Area of square with side equal to diameter :
![A_s=D^2\\\\A_s=(\dfrac{31}{3})^2\\\\A_s=106.78\ inch^2](https://tex.z-dn.net/?f=A_s%3DD%5E2%5C%5C%5C%5CA_s%3D%28%5Cdfrac%7B31%7D%7B3%7D%29%5E2%5C%5C%5C%5CA_s%3D106.78%5C%20inch%5E2)
Since , the area of square is more than area of pizza .
Therefore , pizza can easily be fitted .
Hence , this is the required solution .
Answer: 0.2119
Step-by-step explanation:
We assume that the random variable X is normally distributed.
Given : Population mean : ![\mu=100](https://tex.z-dn.net/?f=%5Cmu%3D100)
Standard deviation : ![\sigma=20](https://tex.z-dn.net/?f=%5Csigma%3D20)
Z-score : ![z=\dfrac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
Then, z-score corresponds to 116
![z=\dfrac{116-100}{20}=0.8](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B116-100%7D%7B20%7D%3D0.8)
By using the standard normal distribution table for z , we have
![P(x>116)=P(z>0.8)=1-P(z\leq0.8)](https://tex.z-dn.net/?f=P%28x%3E116%29%3DP%28z%3E0.8%29%3D1-P%28z%5Cleq0.8%29)
![=1-0.7881446\approx0.2119](https://tex.z-dn.net/?f=%3D1-0.7881446%5Capprox0.2119)
Hence, the required probability = 0.2119
Answer:
b
Step-by-step explanation:
edge 2021 -2020