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MAVERICK [17]
3 years ago
7

Geometry...................

Mathematics
1 answer:
m_a_m_a [10]3 years ago
8 0

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Number of employees = 192

See the table

Process

a) To solve this question, consider only the employees that prefer a jacket

          Male        77

          Female  +35

                         112 employees prefer a jacket

- Calculate the probability

            P = 112 / 192

            P = 0.58

b) Female and prefers a jacket

            P = (54 /192)(35/192)

            P = (0.28)(0.18)

            P = 0.05

 

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The base of a solid is the region in the first quadrant bounded above by the line y = 5, below by y = sin−1(x), and to the right
Arturiano [62]

Each cross section is a square with side length equal to the vertical distance between the curves y=5 and y=\sin^{-1}x, with 0\le x\le1, or 5-\sin^{-1}x. Then each section has an area of (5-\sin^{-1}x)^2, so the volume of this solid is

\displaystyle\int_0^1(5-\sin^{-1}x)^2\,\mathrm dx=\boxed{33-5\pi+\frac{\pi^2}4}

For computing the integral, consider the substitution

u=5-\sin^{-1}x\implies x=\sin(5-u)\implies\mathrm dx=-\cos(5-u)\,\mathrm du

Then the integral becomes

\displaystyle\int_5^{5-\pi/2}u^2(-\cos(5-u))\,\mathrm du

=\displaystyle\int_{5-\pi/2}^5u^2\cos(u-5)\,\mathrm du

Integrate by parts twice; for the first round, take

f=u^2\implies\mathrm df=2u\,\mathrm du

\mathrm dg=\cos(u-5)\,\mathrm du\implies g=\sin(u-5)

\implies\displaystyle u^2\sin(u-5)\bigg|_{5-\pi/2}^5-2\int_{5-\pi/2}^5u\sin(u-5)\,\mathrm du

For the second round, take

f=u\implies\mathrm df=\mathrm du

\mathrm dg=-\sin(u-5)\,\mathrm du\implies g=\cos(u-5)

\implies\displaystyle\bigg(u^2\sin(u-5)+u\cos(u-5)\bigg)\bigg|_{5-\pi/2}^5-\int_{5-\pi/2}^5\cos(u-5)\,\mathrm du

and the rest is trivial.

8 0
3 years ago
Ayden earned a grade of 89% on his multiple choice history final that had a total of
Genrish500 [490]

Answer:

178

Step-by-step explanation:

Method 1: Set up a proportion

Set up an equation of the form:

\frac{\color{red}{\text{part}}}{\color{orange}{\text{whole}}}=

whole

part

​  

=

\,\,\frac{\color{blue}{\text{percent}}}{100}

100

percent

​  

 

Assign the variable xx to the unknown value:

\color{red}{x}=

x=

\,\,\color{red}{\text{part}}

part

The question asks what \textit{part}part of the total questions is 89%

Substitute the known values with the numbers given in the problem, and the unknown value with xx:

\frac{\color{red}{x}}{\color{orange}{200}}=

200

x

​  

=

\,\,\frac{\color{blue}{89}}{100}

100

89

​  

 

Solve for xx:

100\cdot\color{red}{x}=

100⋅x=

\,\,\color{orange}{200}\cdot\color{blue}{89}

200⋅89

Cross multiply

\frac{100x}{100}=

100

100x

​  

=

\,\,\frac{17800}{100}

100

17800

​  

 

Divide both sides by 100

178

Simplify

Method 2: Convert to decimal and multiply

{89}{100}=0.89

89%=  

100

89

​  

=0.89

Move decimal 2 places to the left

{Multiply result by the total:}

Multiply result by the total:

0.89{200}=

0.89⋅200=

178

number

percent

178

89%

200

100%

4 0
3 years ago
Read 2 more answers
The Split Ends Salon orders 10 cases of hand-made hairbrushes.
r-ruslan [8.4K]

Answer:

it would take 65 hours to produce all of the order.

Step-by-step explanation:

1. you already would figure out that 26 hours=4 cases or 6.5 hours per case of hairbrushes.

2. You would figure out that 26+26 is 52 so 52 hours for 8 cases

3. Then you remember u have 8 cases of hairbrushes now. Set up a mental equation where you can solve in your mind: if I need 10 cases, but have figured out I only calculated 8, how much more would I still need to meet the order?

4. After mentally solving the hypothetical problem, you then would conclude you needed 2 more cases from 8 to equal 10.

5. you then divide 26 hours per 4 cases and you get 13 hours for 2 cases.

6. finally you multiply 26+26+13 which you would get 65 as the answer

7 0
2 years ago
Line AB is Perpendicular to line BC. A=(-3,2) and C=(2,7). Which of the following could be the coordinates of B? Select all that
Llana [10]

Answer:

The answer would be Choice F; (-3,7)

Step-by-step explanation:

  1. Plot the two guaranteed given points
  2. A, (-3,2) and C, (2,7)
  3. Find the point where the x and y would share and then form a right angle. This is called being Perpendicular.
  4. So, take the <em>x</em> of A, and the <em>y</em> of C and you have the coordinates of B.

(-3,7)

6 0
2 years ago
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Is this relation a function? justify you answer. ​
kenny6666 [7]

Answer:

Yes

Step-by-step explanation:

If you perform the vertical line test, each row where there is a point only gets hit once, if it got hit twice it would not be a function.

8 0
3 years ago
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