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Fiesta28 [93]
2 years ago
9

What is the length of the missing leg? If necessary, round to the nearest tenth.

Mathematics
2 answers:
kap26 [50]2 years ago
5 0

Applying Pythagorean theorem

\\ \sf\longmapsto a^2=13^2-12^2

\\ \sf\longmapsto a^2=169-144

\\ \sf\longmapsto a^2=25

\\ \sf\longmapsto a=\sqrt{25}

\\ \sf\longmapsto a=5cm

zhannawk [14.2K]2 years ago
3 0

Answer:

5cm

Step-by-step explanation:

To find the missing side we use the hypotenuse theorem.

a^2 + b^2 = c^2

The longest side of the triangle would be c. So substitute the numbers into the variables.

a^2 + 12^2 = 13^2

a^2 = 13^2 - 12^2

a^2 = 169 - 144

a^2= 25

a = √25

a=5

The missing leg's length is 5cm

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Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and standard deviation of 1.00deg
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Answer:

Step-by-step explanation:

Hello!

The variable of interest is the readings on thermometers. This variable is normally distributed with mean μ= 0 degrees C and standard deviation σ= 1.00 degrees C.

The objective is to find the readings that are in the top 3.3% of the distribution and the lowest 3.3% of the distribution.

Symbolically:

The lower value P(X≤a)=0.033

Top value P(X≥b)=0.033

(see attachment)

Lower value:

The accumulated probability until "a" is 0.03, since the variable has a normal distribution, to reach the value of temperature that has the lowest 3.3%, you have to work under the standard normal distribution.

First we look the Z value corresponding to 0.033 of probability:

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Now you reverste the standardization using the formula Z= (a-μ)/δ

a= (Z*δ)+μ

a= (-1.838*1)+0

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Top value:

P(X≥b)=0.033

This value has 0.033 of the distribution above it then 1 - 0.033= 0.967

is below it.

You can rewrite the expression as:

P(X≤b)=0.967

Now you have to look the value of Z that corresponds to 0.967 of accumulated probability:

b= (Z*δ)+μ

b= (1.838*1)+0

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The cutoff values that separates rejected thermometers from the others are -1.838 and 1.838 degrees C.

I hope it helps!

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