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SVEN [57.7K]
3 years ago
7

4. Given: a + m = n, n= 4a; Prove: m = 3a

Mathematics
1 answer:
IrinaVladis [17]3 years ago
4 0

Answer:

<em>Proof below</em>

Step-by-step explanation:

<u>Algebraic Manipulation</u>

It refers to the process of modifying algebraic expressions, often into a simpler form or more easily handled and dealt with.

It also helps us to prove some identities.

We are given the relations:

a + m = n

n = 4a

Substituting the last equation in the first, we have:

a + m = 4a

Subtracting a on both sides of the equation:

m = 4a - a

Simplifying:

m = 3a

Hence proved

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4 years ago
The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. a. Find the probabi
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a. 0.443

b. 0.023

Step-by-step explanation:

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

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds.

This means that \mu = 22, \sigma = 5

a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds.

This is the pvalue of Z when X = 26 subtracted by the pvalue of Z when X = 20. So

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

Z = \frac{26 - 22}{5}

Z = 0.8

Z = 0.8 has a pvalue of 0.788

X = 20

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

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Z = -0.4

Z = -0.4 has a pvalue of 0.345

0.788 - 0.345 = 0.443

The answer is 0.443

b. Find the probability that a randomly selected turkey weighs below 12 pounds.

This is the pvalue of Z when X = 12. So

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

Z = \frac{12 - 22}{5}

Z = -2

Z = -2 has a pvalue of 0.023

The answer is 0.023.

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