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svlad2 [7]
3 years ago
11

Please help me. (20 points)

Mathematics
1 answer:
alexandr402 [8]3 years ago
7 0

Hello from MrBillDoesMath!

Answer:

75

Discussion:


A plane triangle has 180 degrees. Using this in the diagram gives  

x + 81 + angle BAC = 180             (***)

(The diagram is a bit fuzzy but I think the above numbers are accurate)

The diagram also shows that  (156 + angle BAC )= 180 as a straight line has 180 degrees. So

angle BAC = 180 - 156 = 24

Substituting this in (***) above gives

x + 81 + 24 = 180 =>

x + 105 = 180   =>               (as 81 + 24 = 105)

x = 180  107 = 75


Check: Does

x + 81 + angle BAC = 180   ?

75 + 81 + 24 = 180.  Yes




Thank you,

MrB

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Answer:

978 in^2

Step-by-step explanation:

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7 0
3 years ago
What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean
Elena-2011 [213]

Answer:

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Step-by-step explanation:

The following information is missing:

The standard deviation of population is 100.

We are given the following information in the question:

Population mean, μ = 502

Standard Deviation, σ = 100

Sample size, n  = 90

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Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(test score within 10 points)

P(492 \leq x \leq 512) \\\\= P(\displaystyle\frac{492 - 502}{10.54} \leq z \leq \displaystyle\frac{512-502}{10.54}) \\\\= P(-0.9487 \leq z \leq 0.9487)\\= P(z \leq 0.9487) - P(z < -0.9487)\\= 0.829 -0.171 = 0.658 = 65.8\%

P(492 \leq x \leq 512) = 65.8\%

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3 years ago
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