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3 years ago

I NEED HELP

Mathematics

1 answer:

Dmitrij [34]3 years ago

8 0

Answer:

-82, -83, -84

Step-by-step explanation:

Using a variable and corresponding expressions, we can set the sum of the consecutive integers equal to -249 and solve:

first integer: x

second integer: x + 1

third integer: x + 2

x + x + 1 + x + 2 = -249

Combine like terms: 3x + 3 = -249

Subtract 3 from both sides: 3x + 3 - 3 = -249 - 3 or 3x = -252

Divide both sides by 3: 3x/3 = -252/3

Solve for x: x = -84

first integer: -84

second integer: -84 + 1 = -83

third integer: -84 + 2 = -82

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3 years ago

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Answer:

There is a 97.585% probability that a fisherman catches a spotted seatrout within the legal limits.

Step-by-step explanation:

Problems of normally distributed samples 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

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

The lengths of the spotted seatrout that are caught, are normally distributed with a mean of 22 inches, and a standard deviation of 4 inches, so $\mu = 22, \sigma = 4$ .

What is the probability that a fisherman catches a spotted seatrout within the legal limits?

They must be between 10 and 30 inches.

So, this is the pvalue of the Z score of $X = 30$ subtracted by the pvalue of the Z score of $X = 10$

X = 30

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

$Z = \frac{30 - 22}{4}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

X = 10

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$Z = -3$

$Z = -3$ has a pvalue of 0.00135.

This means that there is a 0.9772-0.00135 = 0.97585 = 97.585% probability that a fisherman catches a spotted seatrout within the legal limits.

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