3/8 = 9 blueberry muffins so 15 (or 5/8) of the muffins should be strawberry if that's the only other kind of muffins in this equation.
Answer:
B. 15"
Step-by-step explanation:
![a^{2}+b^2=c^2\\9^2+12^2=c^2\\81+144=c^2\\225=c^2\\\sqrt{225} = 15](https://tex.z-dn.net/?f=a%5E%7B2%7D%2Bb%5E2%3Dc%5E2%5C%5C9%5E2%2B12%5E2%3Dc%5E2%5C%5C81%2B144%3Dc%5E2%5C%5C225%3Dc%5E2%5C%5C%5Csqrt%7B225%7D%20%3D%2015)
X - the score he must get
![\frac{70+75+83+80+x}{5} \geq 80 \\ \frac{308+x}{5} \geq 80 \\ 308+x \geq 400 \\ x \geq 92](https://tex.z-dn.net/?f=%5Cfrac%7B70%2B75%2B83%2B80%2Bx%7D%7B5%7D%20%5Cgeq%2080%20%5C%5C%0A%5Cfrac%7B308%2Bx%7D%7B5%7D%20%5Cgeq%2080%20%5C%5C%0A308%2Bx%20%5Cgeq%20400%20%5C%5C%0Ax%20%5Cgeq%2092)
He must get at least 92 points.
Answer:
A) 34.13%
B) 15.87%
C) 95.44%
D) 97.72%
E) 49.87%
F) 0.13%
Step-by-step explanation:
To find the percent of scores that are between 90 and 100, we need to standardize 90 and 100 using the following equation:
![z=\frac{x-m}{s}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-m%7D%7Bs%7D)
Where m is the mean and s is the standard deviation. Then, 90 and 100 are equal to:
![z=\frac{90-100}{10}=-1\\ z=\frac{100-100}{10}=0](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B90-100%7D%7B10%7D%3D-1%5C%5C%20z%3D%5Cfrac%7B100-100%7D%7B10%7D%3D0)
So, the percent of scores that are between 90 and 100 can be calculated using the normal standard table as:
P( 90 < x < 100) = P(-1 < z < 0) = P(z < 0) - P(z < -1)
= 0.5 - 0.1587 = 0.3413
It means that the PERCENT of scores that are between 90 and 100 is 34.13%
At the same way, we can calculated the percentages of B, C, D, E and F as:
B) Over 110
![P( x > 110 ) = P( z>\frac{110-100}{10})=P(z>1) = 0.1587](https://tex.z-dn.net/?f=P%28%20x%20%3E%20110%20%29%20%3D%20P%28%20z%3E%5Cfrac%7B110-100%7D%7B10%7D%29%3DP%28z%3E1%29%20%3D%200.1587)
C) Between 80 and 120
![P( 80](https://tex.z-dn.net/?f=P%28%2080%3Cx%3C%20110%20%29%20%3D%20P%28%20%5Cfrac%7B80-100%7D%7B10%7D%20%3Cz%3E%5Cfrac%7B120-100%7D%7B10%7D%29%3DP%28-2%3Cz%3C2%29%5C%5CP%28-2%3Cz%3C2%29%3DP%28z%3C2%29%20-%20P%28z%3C-2%29%20%3D%200.9772%20-%200.0228%20%3D%200.9544)
D) less than 80
![P( x < 80 ) = P( z](https://tex.z-dn.net/?f=P%28%20x%20%3C%2080%20%29%20%3D%20P%28%20z%3C%5Cfrac%7B80-100%7D%7B10%7D%29%3DP%28z%3C-2%29%20%3D%200.9772)
E) Between 70 and 100
![P( 70](https://tex.z-dn.net/?f=P%28%2070%3Cx%3C%20100%20%29%20%3D%20P%28%20%5Cfrac%7B70-100%7D%7B10%7D%20%3Cz%3E%5Cfrac%7B100-100%7D%7B10%7D%29%3DP%28-3%3Cz%3C0%29%5C%5CP%28-3%3Cz%3C0%29%3DP%28z%3C0%29%20-%20P%28z%3C-3%29%20%3D%200.5%20-%200.0013%20%3D%200.4987)
F) More than 130
![P( x > 130 ) = P( z>\frac{130-100}{10})=P(z>3) = 0.0013](https://tex.z-dn.net/?f=P%28%20x%20%3E%20130%20%29%20%3D%20P%28%20z%3E%5Cfrac%7B130-100%7D%7B10%7D%29%3DP%28z%3E3%29%20%3D%200.0013)