Which of the following shapes could be formed by taking a longitudinal section perpendicular to the base of a rectangular prism?

Answer:

C

Step-by-step explanation:

C

Answer:

Step-by-step explanation:

its c

The probability that a randomly selected adult has an IQ less than 130 is 0.9332

For given question,

We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.

We need to find the probability that a randomly selected adult has an IQ less than 130

Sketch the curve.

The probability that X < 130 is equal to the area under the curve which is less than X = 130

Since μ = 100 and σ = 15 we have:

⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )

⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )

Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:

P (X < 130) = P (Z < 1.5)

Now, we use the standard normal table to conclude that:

P (Z < 1.5) = 0.9332

Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332

Learn more about the probability here:

https://brainly.com/question/23548526

#SPJ4

Step-by-step explanation:

a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.

So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.

Here we have

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

We must find cos.

Using the Pythagorean theorem

[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]

It is mostly notated as this,

[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]

But they mean the same thing, we know

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

So we plug that in for sin a.

[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]

Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.

[tex] \cos( \alpha ) = \frac{1}{10} [/tex]

2. We would get the same work for the second part, the only difference is that cosine is negative over the interval

(π/2, π)

So the answer for 2 is

[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]

Disclaimer: Your work you did was correct, just remember for fractions like

[tex]1 - \frac{99}{100} [/tex]

Convert 1 into a fraction that has a denominator of 100.

[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]

To acquire 90000000 views on his channel, he has to upload 20 videos every month.

Every month, he  posts 3 videos to his  channel. An average number of people watch each video. = 1500000

In search of:

How many months must pass before he begins to receive 90,000,000 views on his channel?

Step 1

On his channel, he posts three videos each month.

The average number of views per video is.

3 Videos Receive Views

= 3 * 1500000

= 4,500,000 Views

Number of 4,500,000 views each month

Complete 90000000 Views

Step 2

Total Views/Months = Total Views/Total Views

Days in a month = 90000000/4500000

                             = 20

20 Monthly months in the number

To acquire 90000000 views on his channel, he has to upload 20 videos every month.

20  Months is the right response, so.

To know more about Average number's visit:

https://brainly.com/question/16956746

#SPJ4

Answer:
the answer to the question is answer C

Answer:

Step-by-step explanation:

B is your answer

The height of the flag pole which is described as in the task content is; 8.2m.

The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;

tan 22° = 6/x

x = 6/tan 22 = 14.9m.

Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;

tan 9° = y/14.9

y = 14.9 tan 9° = 2.2m

Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.

Read more on trigonometric identities;

https://brainly.com/question/24349828

#SPJ1

The value of angle x of the given cyclic segment is; 49.5°

We are given the measure of the angle of  arc QS as (4x – 18)°

Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;

Thus;

(4x – 18)° = 180°

4x - 18 = 180

4x = 180 + 18

4x = 198

x = 198/4

x = 49.5°

The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.

The formula to measure the length of the arc is;

Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)

Arc Length Formula (if θ is in radians) s = ϴ × r.

Thus, the value of x of the given cyclic segment is; 49.5°

Read more about arc angle at; brainly.com/question/2005046

#SPJ1

The probability that a student chose football given that they like watching sports is: c. 0.27.

Using this formula

P[Like (Football)/Like (Sport)]

Where:

P=Probability

Like (Football)=0.23

Like (Sport)=0.23+0.18+0.26+0.17=0.84

Let plug in the formula

P[Like (Football)/Like (Sport)]=0.23/0.84

P[Like (Football)/Like (Sport)]=0.27

Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.

Learn more about Conditional Probability here:

https://brainly.com/question/10739997

https://brainly.com/question/10739947

#SPJ1

Answer:

C.

Step-by-step explanation:

30 full cylindrical containers are required to completely fill the fish tank.

To find what is the least number of full cylindrical containers needed to completely fill the fish tank:

We know the volume of the cylinder is given by: [tex]V=\pi r^{2} h[/tex]

The volume of a cylinder:

[tex]V=\pi (\frac{6}{2} )^{2} (8)\\V=75\pi inches^{3}[/tex]

The volume of cube V = 24 × 24 × 12 = 6912 cubic inches

A number of full cylindrical containers are needed to completely fill the fish tank:

Therefore, 30 full cylindrical containers are required to completely fill the fish tank.

Know more about cylinders here:

https://brainly.com/question/24159177

#SPJ4

Answer:

Step-by-step explanation:

400*60% can be rewriten as 400×0.6 which is 240, so a is false.

the same steps can be repeated for b and c

b) 200*0.6=120, therefore is false

c) 120*0.6=72, therefore is false

2)

[tex]60 percent * x=87\\0.6x=87\\x=\frac{87}{0.6} \\\\x=145[/tex]

Now we check the answer by using the same steps in problems a,b,c

[tex]145*0.6=87\\87=87[/tex]

3)

[tex]0.6c=43.2\\c=\frac{43.2}{0.6} \\c=72[/tex]

and finally

[tex]0.38e=190\\e=\frac{190}{0.38} \\e=500[/tex]

Answer:

Step-by-step explanation:

Just multiply how much she waxes in 3/5 hour by 5/3.  Answer is 100/3 or 33.33 sq. meters per hour

Answer:

11/15 km

Step-by-step explanation:

Simply sum the areas:

2/5 + 1/3 = (6 + 5)/15 = 11/15

Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)

P(x) = -1.50x - (-0.75)x + 20,000

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).

Given:

C(x) = -0.75x+20,000 and R(x)= -1.50x

P(x) = R(x) - C(x)

= -1.50x - (-0.75)x + 20,000

= -1.50x + 0.75x + 20,000

Apply rule -(-a) = a

= -1.5x + 0.75x + 20000

Add similar elements:

-1.5 x + 0.75x = -0.75x

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

To learn more about profit function refer to:

https://brainly.com/question/16866047

#SPJ9

Answer:

C: 1 Quart

Step-by-step explanation:

2 pints are the equivalent of 1 quart

Answer:1 Quart

Step-by-step explanation: Because 2 pints equals=1 quart

Answer:

4 degrees ( to nearest degree).

Step-by-step explanation:

The trig ratio you want is the tangent.

tan x = 10,000 / 160,000    where x is the angle of depression.

tan x = 0.0625

x = 3.576 degrees.

The volume of the triangular prism as described is; 20 cubic foot.

A triangular pyramid refers to pyramid which has a triangular base

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism = (1/3) ×5 × 12

Volume = 20 cubic foot

Therefore, volume of the triangular prism as described is; 20 cubic foot.

Read more on triangular prism;

https://brainly.com/question/12807315

#SPJ1

Answer:  the average rate of change of the function is 23.

Step-by-step explanation:

[tex]h(x)=x^2-10x+21\ \ \ \ \ -1\leq x\leq 10 \ \ \ \ A(x)=?\\\displaystyle\\A(x)=\frac{\Delta y}{\Delta x}=\frac{h(x-g)-h(x)}{g} \\g=x_{max}-x_{min}\\g=10-(-1)\\g=10+1\\g=11.\ \ \ \ \ \Rightarrow\\A(x)=\frac{(x-11)^2-10*(x-11)+21-(x^2-10x+21)}{11} \\A(x)=\frac{x^2-22x+121-10x+110+21-x^2+10x-21}{11} \\A(x)=\frac{231-22x}{11}\\ A(x)=\frac{11*(21-2x)}{11}\\ A(x)=21-2x.\\x=x_{min}\ \ \ \ \ \Rightarrow\\A(x)=21-2*(-1)\\A(x)=21+2\\A(x)=23.[/tex]

Answer:

67

Step-by-step explanation:

All triangles have three angles. The sum of the three angles should equal up to 180 degrees.

108-104-37= 67

The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).

To find the function which has a phase shift to the right:

The function has a phase shift of pi/2 to the right.

By definition, you have the phase shift is:

When you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where  [tex]c=-\pi[/tex]  and [tex]b=2[/tex], you obtain:

Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).

Know more about trigonometric functions here:

https://brainly.com/question/1143565

#SPJ4

The complete question is given below:
Which function has a phase shift of pi/2 to the right?

The ratio of bananas to fruit is 13 : 21

The given parameters are

Banana = 13

Apple = 8

The total number of fruits is

Fruit = Banana + Apple

Substitute the known values in the above equation

Fruit = 13 + 8

Evaluate the sum

Fruit = 21

The ratio of bananas to fruit is then represented as:

Ratio = Banana : Fruit

Substitute the known values in the above equation

Ratio = 13 : 21

Hence, the ratio of bananas to fruit is 13 : 21

Read more about ratio at:

https://brainly.com/question/2328454

#SPJ1

Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

minus four x greater than 120

-4x > 120

x < 120/-4

There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4

x < -30

Check:

-4x > 120

-4(-30) > 120

120 > 120

Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1

Answer:

output = 9

Step-by-step explanation:

add 5 to the input to obtain output

output = 4 + 5 = 9

See below for the solution to the systems of equations

System of equations 1

Here, we have

y = -5x/3 + 3

y = x/3 -3

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (3, -2)

Hence, the solution to the system is (3, -2)

System of equations 2

Here, we have

y = 4x + 3

y = -x -2

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (-1, -1)

Hence, the solution to the system is (-1, -1)

Read more about system of equations at:

brainly.com/question/14323743

#SPJ1

The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x + 5

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = x + 5

The next step is to switch/swap the positions of x and y in the above equation y = x + 5

The equation becomes

x = y + 5

The next step is to make y the subject of the formula in the above equation x = y + 5

The equation becomes

y = x - 5

This is done by subtracting 5 from both sides of the equation.

So, we have:

y = x - 5

Express as an inverse function

f'1(x) = x - 5

Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

Read more about inverse equations at:

brainly.com/question/14391067

#SPJ1

Answer: x = 0 ; y = -7

Step-by-step explanation:

Given equation:

1) 3x + 8y = -56

2) 2x - y = 7

Subtract 2x on both sides of 2) equation to isolate y-value

2x - y - 2x = 7 -2x

-y = 7 - 2x

Divide -1 on both sides of 2) equation

-y / -1 = (7 - 2x) / -1

y = 2x - 7

Current system

1) 3x + 8y = -56

2) y = 2x - 7

Substitute 2) equation into the y-value of 1) equation

3x + 8 (2x - 7) = -56

Simplify by distributive property

3x + 8 × 2x - 8 × 7 = -56

3x + 16x - 56 = -56

Combine like terms

19x - 56 = -56

Add 56 on both sides

19x - 56 + 56 = -56 + 56

19x = 0

Divide 19 on both sides

19x / 19 = 0 / 19

[tex]\Large\boxed{x=0}[/tex]

Substitute the x-value into one of the equations to find the y-value

2x - y = 7

2 (0) - y = 7

0 - y = 7

-y = 7

[tex]\Large\boxed{y=-7}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

The product expression is given as:

(√6x² +4√8x³)(√9x-x√5x^5)

Evaluate the exponents

(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)

Expand the brackets

(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x

This gives

(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

Read more about simplified products at

https://brainly.com/question/20069182

#SPJ1

The equivalent expression of the radical expression ∛1080 is 6∛5

The radical expression is given as

∛1080

Express 1080 as 216 * 5

∛1080 = ∛(216 * 5)

Split the factors

∛1080 = ∛216 * ∛5

Evaluate the cube root of 216

∛1080 = 6 * ∛5

Evaluate the product

∛1080 = 6∛5

Hence, the equivalent expression of the radical expression ∛1080 is 6∛5

Read more about equivalent expression at

https://brainly.com/question/24734894

#SPJ1

Answer:

Step-by-step explanation:

To find:

Given:

[tex]\sf{7p+4=-p+9+2p+3p}[/tex]

Isolate the term of p, from one side of the equation.

Combine like terms.

[tex]\rightarrow \sf{7p+4=-p+2p+3p+9}[/tex]

Add the numbers from left to right.

-p+2p+3p=4p

7p+4=4p+9

Then, you subtract by 4 from both sides.

[tex]\sf{7p+4-4=4p+9-4}[/tex]

Solve.

7p=4p+5

Subtract by 4p from both sides.

7p-4p=4p+5-4p

Solve.

[tex]\boxed{\sf{3p=5}}[/tex]

Divide by 3 from both sides.

3p/3=5/3

Solve.

p=5/3

Divide is another option.

5/3=1.6666

So, the final answer is 3p=5.

I hope this helps, let me know if you have any questions.

[tex]denote \: by \: s \: the \: cost \: of \: a \: sweatshirt \\ denote \: by \: t \: the \: cost \: of \: a \: t \: shirt[/tex]

[tex]3t + 7s = 240.5 \\ 6t + 5s = 220[/tex]

[tex] - 6t - 14s = - 481 \\ 6t + 5s = 220[/tex]

[tex] - 9s = - 261 \\ s = \frac{ - 261}{ - 9} = 29 \: dollars[/tex]

[tex]3t + 7(29) = 240.5 \\ [/tex]

3t + 203 = 240.5

3t = 37.5

t = 12.5 dollars