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3 years ago

Solve the triangle.

Mathematics

1 answer:

vekshin13 years ago

8 0

9514 1404 393

Answer:

b = 757.7 m
A = 17.2°
C = 14.3°

Step-by-step explanation:

From the law of cosines, you can find the length of side b to be ...

b = √(a² +c² -2ac·cos(B))

b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36

b ≈ 757.7

From the law of sines, you can find the measure of angle C to be ...

C = arcsin(c/b·sin(B))

C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)

C ≈ 14.3°

A = 180° -148.5° -14.3°

A = 17.2°

_____

Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.

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A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century the mean number of t

Bas_tet [7]

Answer:

a) 0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) 0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) 0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

Step-by-step explanation:

We have the mean during an interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

During the 20th century the mean number of the major hurricanes to strike U.S mainland per year was 0.6.

This means that $\mu = 0.6$

Find the probability that the number of major hurricane to strike U.S mainland in any any give year is:

a) Exactly one

This is P(X = 1). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293$

0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) At most one

This is:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

Then

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.6}*0.6^{0}}{(0)!} = 0.5488$

$P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5488 + 0.3292 = 0.878$

0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) More than one

This is:

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.878 = 0.122$

0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

6 0

3 years ago

Find the solutions to the equation below.<br> Check all that apply.<br> 2x^2 + 1-1x + 5 = 0

Serggg [28]

Is -2 and option cause tbh that’s what i keep getting

7 0

3 years ago

Read 2 more answers

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Evgesh-ka [11]

Answer:

-2

Step-by-step explanation:

5 0

4 years ago

Which line best represents the line of best fit for this scatter plot? (5 points)

Bogdan [553]

Line Q, you always want the line that has as many dots on it as possible!! :)

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3 years ago

What is the surface area of the prism shown to the left?<br><br> (idk the answer i guessed)

scoundrel [369]

Answer:

828

Step-by-step explanation:

Missing leg of triangle:

√15²-12²= √225-144=√81=9

Triangle faces= 2*1/2*12*9= 108

Base= 20*9= 180

Front face= 20*15= 300

Back face= 20*12= 240

Total= 108+180+300+240= 828

Second choice

3 0

4 years ago