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Iteru [2.4K]
3 years ago
13

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=83°, and DB= 1.3feet. What is the length of CD to the nearest tenth of a foot.

Mathematics
1 answer:
Lina20 [59]3 years ago
3 0

Answer:

CD\approx0.2

Step-by-step explanation:

By the tangent ratio, tanC=\frac{DB}{CD}. Substituting the given values into this equation gives us:

tan83° = \frac{1.3}{CD}

CD*tan83° =1.3 (Multiply both sides of the equation by CD)

CD=\frac{1.3}{tan83\textdegree} (Divide both sides of the equation by tan83\textdegree)

CD=0.15962\approx0.2

Hope this helps!

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The number of texts per day by students in a class is normally distributed with a 
kobusy [5.1K]

Answer:

1, 2, 6

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation

Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts

1) For x < 90:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{90-130}{20} =-2

From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%

Option 1 is correct

2) For x > 130:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0

From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%

Option 2 is correct

3) For x > 190:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{190-130}{20} =3

From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%

Option 3 is incorrect

4)  For x < 130:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0

For x > 100:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{100-130}{20} =-1.5

From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%

Option 4 is incorrect

5)  For x = 130:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0

Option 5 is incorrect

6)  For x = 130:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{160-130}{20} =1.5

Since 1.5 is between 1 and 2, option 6 is correct

5 0
3 years ago
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olasank [31]

<u>Answer:</u>

<h2>P = $100.80</h2>

<u>Steps:</u>

  • Price after clearance:

Pc = 120 - (120/100×20)

Pc = 120 - (1.2×20)

Pc = 120 - 24

Pc = 96

  • Price after sales tax:

P = Pc + (Pc/100×5)

P = 96 + (96/100×5)

P = 96 + (0.96×5)

P = 96 + 4.8

P = $100.80

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