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Sergeeva-Olga [200]
3 years ago
10

Please help!!! (Ignore the AD it’s actually supposed to be DC)

Mathematics
1 answer:
pashok25 [27]3 years ago
6 0

Answer:

BD = 22, DC = 11√3

Step-by-step explanation:

In triangle ABC, ∠B = 45°, ∠C = 90°. Hence:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

∠A + 45 + 90 = 180

∠A + 135 = 180

∠A = 45°

Using sine rule to find BC:

\frac{BC}{sinA}=\frac{AB}{sinC}  \\\\\frac{BC}{sin45}=\frac{11\sqrt{2} }{sin90}  \\\\BC=\frac{11\sqrt{2}*sin45 }{sin90}  \\BC=11

In triangle BCD, ∠D = 30°, ∠C = 90°. Hence:

∠D + ∠B + ∠C = 180° (sum of angles in a triangle)

∠B + 30 + 90 = 180

∠B + 120 = 180

∠B = 60°

Using sine rule to find BD:

\frac{BD}{sinC}=\frac{BC}{sinD}  \\\\\frac{BD}{sin90} =\frac{11}{sin30} \\\\BD=\frac{11*sin90}{sin30}\\\\BD=22

Using sin rule to find DC:

\frac{DC}{sinB}=\frac{BC}{sinD}  \\\\\frac{DC}{sin60} =\frac{11}{sin30} \\\\DC=\frac{11*sin60}{sin30}\\\\DC=11\sqrt{3}

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Answer:

a) 0.4121

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Step-by-step explanation:

Mean μ = $633

Standard deviation σ = $45.

Required:

a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?

We solve using z score formula

= z = (x-μ)/σ, where

x is the raw score

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σ is the population standard deviation.

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b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)

Converting 0.16 to percentage = 0.16 × 100% = 16%

The z score of 16%

= -0.994

We are to find x

Using z score formula

z = (x-μ)/σ

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Cross Multiply

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x = -44.73 + 633

x = $588.27

Approximately to the nearest dollar, the amount should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16

is $588

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