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Stella [2.4K]
3 years ago
12

Billy is helping to make pizzas for a school function. He's made 25 pizzas so far. His principal asked him to make at least 30 p

izzas but no more than 75. Solve the compound inequality and interpret the solution.
30 ≤ x + 25 ≤ 75
Mathematics
1 answer:
Simora [160]3 years ago
7 0

Answer: Number of pizzas would be less than 5 but not more than 50.

Step-by-step explanation:

Since we have given that

Number of pizzas so far = 25

His principal asked him to make at least 30 pizzas but no more than 75.

According to question, we have

30 ≤ x + 25 ≤ 75

First we subtract 25 from both the sides:

30-25\leq x \leq 75-25\\\\=5\leq x\leq 50

Hence, number of pizzas would be less than 5 but not more than 50.

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8.52 The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches
sweet [91]

Answer:

Heights of 29.5 and below could be a problem.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.

This means that \mu = 32, \sigma = 1.5

There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.

Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus

Z = \frac{X - \mu}{\sigma}

-1.645 = \frac{X - 32}{1.5}

X - 32 = -1.645*1.5

X = 29.5

Heights of 29.5 and below could be a problem.

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2 years ago
Two hikers stopped for a snack. They shared 2/3 of a pound of trail mix. If the hikers shared the trail mix equally, how much tr
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each hiker gets 1 1/2

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artcher [175]

Answer:

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Step-by-step explanation:

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The measure of the two sides of a triangle. ​
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A.

Step-by-step explanation:

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Answer:

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