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(\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%
Answer:
(b) x ≤ -4
Step-by-step explanation:
There are a few things to note when reading an inequality on a number line.
The number line would contain the following:
i. <em>circles</em>: These can be closed or open. Closed circles are denoted by a shaded small circle showing that the point or number shown on the number line is included in the inequality. Open circles are denoted by an unshaded small circle showing that the point or number shown on the number line is not included in the range of inequality.
ii. <em>arrows</em>: An arrow can point to the right or left. When it points to the right, that means the values greater than the number specified on the number line are included in the range. When it points to the left, the values less than the number are included.
From the given number line,
The type of circle is a closed circle since it is shaded. This means that the number pointed at on the number line (-4 in this case) is included in the range.
Also, the arrow is pointing leftwards. This means that values less than the number pointed at (-4 in this case) are included in the range.
Therefore, the inequality should read,
x ≤ -4
This shows that all values of x less than or equal to -4 are included in the range.
The answer is you add 0.05 every time
The answer:
the valid proof is <span>Amanda's.
</span><span>Statement Justification ∠1 + ∠4 = 180°
Definition of Supplementary
Angles ∠3 + ∠4 = 180°
Definition of Supplementary Angles
∠1 + ∠4 = ∠3 + ∠4
Transitive Property of Equality ∠1 ≅ ∠3 </span>
Answer:
72
Step-by-step explanation:
