The gates of an amusement park are closely monitored to determine whether the number of people in the amusement park ever poses a safety hazard. On a certain day, the rate at which people enter amusement park is modeled by the function e(x)=0.03x^3+2, where the rate is measured in hundreds of people per hour since the gates opened. The rate at which people leave the amusement park is modeled by the function l(x)=0.5x+1, where the rate is measured in hundreds of people per hour since the gates opened. What does (e−l)(4) mean in this situation?

Answer:

D. 60

Step-by-step explanation:

60 is the only number that 3 and 4 and 5 all go into.



4 does not go into 15, so not answer A.



5 does not go into 12, so not answer B

3 does not go into 20, so not answer C

D is correct. 4 and 5 and 3 all go into 60.

Answer:

21. x = 18.1

22. x =28.7

Step-by-step explanation:

SOH = sin(theta) = opp/hyp

CAH = cos(theta) = adj/hyp

TOA = sin(theta) = opp/adj

21. You would be using tangent.

tan(theta) = Opp/Adj

tan(32°) = x/29

x = 29 * tan(32°)

x = 18.1

22. You would be using cosine

cos(theta) = Adj/Hyp

cos(43°) = 21/x

x * cos(43°) = 21

x = 21 / cos(43°)

x = 28.7

Use a Calculator to help you solve for those side lengths or degrees.

If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using

I am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.

The given function is f(z)=3z-8.

We need to find the value of f(-4), f(2), f(z-7).

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Now to find f(-4), replace z from -4.

f(-4)=3(-4)-8=-12-8=-20

Now to find f(2), replace z from 2.

f(2)=3(2)-8=6-8=-2

Now to find f(z-7), replace z from z-7.

f(z-7)=3(z-7)-8=3z-21-8=3z-29.

Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.

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[tex]Hello[/tex] [tex]There![/tex]

We need to find what number, if 6 is divided by it, gives us 12.

This isn't hard, I promise! I am going to take you through a few steps, and we'll find the answer.

Are you ready? Then let's begin...:)

[tex]Procedure:[/tex]

  ✦ We can think about it as: 6 divided by what number gives us 12?

(let the number be z)

[tex]^6/_z=12[/tex]

Multiply both sides by z

[tex]6=12z[/tex]

Divide both sides by z

[tex]z=^6/_{12}[/tex]

Which is the same as

[tex]z=^1/_2[/tex]

[tex]Greetings![/tex]

--

The perimeter and area of the basketball court is 18x + 6 and 8x² + 24x respectively.

Perimeter of basketball court = 2(length + width)

= 2(8x + x + 3)

= 2(9x + 3)

= 18x + 6

Perimeter of basketball court = 18x + 6

Area of basketball court = length × width

= 8x × (x + 3)

= 8x² + 24x

Area of basketball court = 8x² + 24x

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Answer:

  (c)  5.00×10^-5 kg

Step-by-step explanation:

The mass and energy are related by Einstein's formula E = mc².

__

Solving for mass in kg, we find it to be ...

  m = E/c² . . . . . . . . where E is in joules, and c is in meters/second

  m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg

The lost mass was about 5.00×10^-5 kg.

Answer:

5.00×10^−5 kg

Step-by-step explanation:

I took the test and it was correct! PLEASE LIKE  and have a wonderful day!

The student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.

We are told that the author of the article is making a claim that a playground will benefit a particular community.

Now, when trying to verify a claim by someone it is very important to try to get facts and figures about that fact to start with before asking for opinions.

Thus, what the student do is that he should look for opinions, the student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.

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Try: Re-reading the question.

Answer: The student should check if the author's article provides more facts or evidence than opinions.

What is the difference between facts and opinions? Facts provide real statements that have been proved with solid evidence by experts. Meanwhile, on the other hand, opinions are what people think. It is more like thinking than something with evidence. It hasn't or can't be proved. If it includes more facts then the author's claims are strong with solid evidence. If it includes more opinions then the author's claims are not strong, they are weak. Since it's only the author's point of view.

Answer:

[tex]\mathsf {SA = 112 in.^{2} }[/tex]

Step-by-step explanation:

[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]

[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]

[tex]\textsf {Solving :}[/tex]

[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]

[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]

[tex]\implies \mathsf {SA = 2 (56)}[/tex]

[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[tex]\textsc{heya!}[/tex]

[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:

[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:

[tex]\textsc{solution:}[/tex]

[tex]\textsc{explanation:}[/tex]

divide both sides by 9; after performing this operation, we obtain:

[tex]\bold{x=\frac{6}{9}}[/tex]

divide top & bottom by 3; we obtain the solution

[tex]\bold{x=\frac{2}{3}}[/tex]

[tex]\textsc{hopefully\;helpful!}[/tex]

by: [tex]^da_n^cIn_g}[/tex]

have a great rest of your day ahead ~ = )

~

Answer:

In order for each child to receive a book, first distribute one book to each.

This can be done in [math] 5\times 4\times 3 = 60 [/math] ways.

The remaining two books can be distributed in [math] 3^2 [/math] ways.

Total number of ways[math] = 60 \ times 9 = 540 [/ math]

The half life of the substance is 6.92 days.

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

[tex]\rm N = N_o e^{-kt}[/tex]

The concentration will reduce to half therefore

[tex]\rm N= \dfrac{N_o}{2}[/tex]

so,

[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]

ln 0.5 = - 0.1001 * t(1/2)

-0.693 = -.1001 * t(1/2)

t(1/2) = 6.92 days.

Therefore the half life of the substance is 6.92 days.

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Answer:

The minivan must keep a thrust of 496.79 pounds from rolling down the hill while the perpendicular force to the hill would be 5678.31 pounds. The picture illustrates the solutions to the problem.

The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.

The quantity which has magnitude, direction, and follows the law of vector addition is called a vector.

A minivan with a gross load of 5700 pounds is stopped on a road with a slant of 5°.

Balance the force along the hill. Then the value of the force is given as,

F = W sin θ

F = 5700 x sin 5°

F = 5700 x 0.087

F = 496.79 pounds

The magnitude of the force perpendicular to the hill will be given as,

N = W cos θ

N = 5700 x cos 5°

N = 5700 x 0.9962

N = 5678.31 pounds

The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.

The diagram is given below.

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Using proportions, it is found that the homeowner would have to pay $2,750 in property tax each year.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax at a rate of 25 mills means that for each $1,000 in value of the home, he pays $25 in taxes. Hence, for a home of value of $110,000, the amount he pays in taxes is given by:

A = 110 x 25 = $2,750.

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Two supplementary angles when addd together equal 180.

let one angle = x

The second angle is 5 times that so would be 5x

x + 5x = 180

Simplify:

6x = 180

Divide both sides by 6:

X = 30

One angle is 30, the second angle would be 150

The answer is 150

In order to determine your take home pay, multiply your gross income by the percent of taxes then subtract the amount to find your net pay.

Gross pay is the total income earned before any deductions. Net pay is the  gross income less any deductions.

Assume your net pay is $10000 and tax is 10%, net pay is:

$10,000 - (0.1 x 10,000) = $9,000

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Answer:

it is b

Step-by-step explanation:

The solution is Option A.

The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point A be A ( x , y )

Now , the vertex A is reflected over the line y = x

When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )

So , the coordinates of the point A' ( -2 , 10 )

Now , the coordinates of the point A will be

A ( x , y ) = A ( 10 , -2 )

Therefore , the value of A is A ( 10 , -2 )

Hence , the coordinates of the point before reflection is A ( 10 , -2 )

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Answer:

Mr. Garcia had 5 kilograms of blueberries at first

Step-by-step explanation:

to make this easiest, we can imagine that we're undoing mr. garcia's actions.

So, we can start by 'unpacking' mr garcia's bags

we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags

(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)

so,

1/4  x 9 = 9/4

(9 = 9/1 [if that is how you're used to multiplying a fraction])

Then, he also sold 2 3/4 kilograms

so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first

2 3/4 + 9/4 =  2 + 12/4

(12/4 = 3)

2 + 3 = 5

So, Mr. Garcia had 5 kilograms of blueberries at first

Answer:

The measure of a minor arc is less than 180° , and equal to the measure of the arc's central angle . A major arc is the longer arc connecting two endpoints on a circle. The measure of a major arc is greater than 180° , and equal to 360° minus the measure of the minor arc with the same endpoints.

The area of the prism is 12x² inches². Thus, the correct option is B.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

For a prism, the lateral sides of a prism are made up of rectangles which consist of the height and the length of the base. Therefore, a triangular prism has an equilateral base with a side length x inches. The height of the prism is four times as long as the side length. The lateral area will be,

Lateral Area = 3(x×4x) = 12x² inches²

Hence, the area of the prism is 12x² inches². Thus, the correct option is B.

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Answer:

the answer is $24.3

Step-by-step explanation:

Answer:

Train A = 466

Train B = 60

Step-by-step explanation:

Answer:

the solution is (7,-1)

Step-by-step explanation:

if you dont trust your boy look below

4x + 8(-2x+13)=20

4x -16x + 104 = 20

-12x + 104 *-104* = 20 -104

-12x/-12 = -84/-12

x = 7

y = -2(7) + 13

y = -14 + 13

y = -1

The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The values of the angels will be calculated by using the trigonometry property.

Sin A = Perpendicular / Hypotenuse

Sin A = 9 /41

Cos A = Base / Hypotenuse

Cos A =  40 / 41

Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

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The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Right triangle ABC is reflected over AC.

Then dilated by a scale factor of Two-thirds to form triangle DEC.

The triangle △ABC and △DEC are similar to each other.

△ABC ≅ △DEC

The dilation is 2/3. Then we have

DE / AB = 2 / 3

     3AB = 2DE

∠B ≅ ∠E = 90

There is no effect of dilation on angle.

Then the correct option is A, B, and D.

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Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

got it right on edge 23

Answer:

X= -3

Step-by-step explanation:

(4+5)-1/3(40-4)=X

X=9- 1/3(36)

X=9-12

La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%[/tex].

The question gives:

Then, you will have:

[tex]6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500[/tex]

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Based on the filing status and the taxable income, the tax for the following people are:

Based on the tax table, a single in the $80,600 - $80,650 bracket should pay $15,950.

A head of household in the $83,550 to $83,600 bracket would pay $15,216 and a married flling jointly in the $77,750 to $77,800 would pay $11,031.

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