Y° = y₁° (opposite or Vertical angles), but y₁ = 45° corresponding angles,
then y = 45°
Answer: The percentage of legal quarters will be rejected by the vending machine = 2.275%
Step-by-step explanation:
Given: The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram.
Let x be the weights of legal U.S. quarters .
Required probability: ![P(x5.81)](https://tex.z-dn.net/?f=P%28x%3C5.53%29%2BP%28x%3E5.81%29)
![=P(\dfrac{x-\mu}{\sigma}\dfrac{5.81-5.67}{0.07})\\\\=P(z2)\approx0.02275 \ \ \ [By\ P-value\ calculator]](https://tex.z-dn.net/?f=%3DP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3C%5Cdfrac%7B5.33-5.67%7D%7B0.07%7D%29%2BP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3E%5Cdfrac%7B5.81-5.67%7D%7B0.07%7D%29%5C%5C%5C%5C%3DP%28z%3C-4.857%29%2BP%28z%3E2%29%5Capprox0.02275%20%20%20%20%5C%20%5C%20%5C%20%5BBy%5C%20%20P-value%5C%20calculator%5D)
The percentage of legal quarters will be rejected by the vending machine = 2.275%
The formula of an area of a square:
![A=a^2](https://tex.z-dn.net/?f=A%3Da%5E2)
a - a side
We have ![A=450\ in^2](https://tex.z-dn.net/?f=A%3D450%5C%20in%5E2)
substitute:
![a^2=450\to a=\sqrt{450}\\\\a=\sqrt{225\cdot2}\\\\a=\sqrt{225}\cdot\sqrt2\\\\\boxed{a=15\sqrt2\ in}](https://tex.z-dn.net/?f=a%5E2%3D450%5Cto%20a%3D%5Csqrt%7B450%7D%5C%5C%5C%5Ca%3D%5Csqrt%7B225%5Ccdot2%7D%5C%5C%5C%5Ca%3D%5Csqrt%7B225%7D%5Ccdot%5Csqrt2%5C%5C%5C%5C%5Cboxed%7Ba%3D15%5Csqrt2%5C%20in%7D)
Used:
![\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5Ccdot%20b%7D%3D%5Csqrt%7Ba%7D%5Ccdot%5Csqrt%7Bb%7D)
Answer:
E=1/2mv2, v/10./17
Step-by-step explanation:
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Answer:
Step-by-step explanation: