A school typically sells 500 yearbooks in a year for $50 each. The economics class does a project and discovers that they can sell 125 more yearbooks for every $5 decrease in price. The revenue for year book sales is r(x)+(500+125x)(50-5x). To maximize profit, what prices should the school charge for the yearbooks?

Answer:

There are 29760 possible ways

Step-by-step explanation:

Mrs. Pearson must elect a President, a Vice President and a Treasurer. Then you must choose 3 people. In this case the order matters, because there are three different positions (President, Vice President and Treasurer)

So this is a problem of perm

So this is a problem of permutations. The formula to calculate a permutation is:

[tex]P(n, r)=\frac{n!}{(n-r)!}[/tex]

Where n is the total number of people and you can choose r of them

So:

[tex]P(32, 3)=\frac{32!}{(32-3)!}[/tex]

[tex]P(32, 3)=\frac{32!}{29!}[/tex]

[tex]P(32, 3)=29760[/tex]

Final answer:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in a class. The total number of ways these roles can be assigned is 29760 ways.

Explanation:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in Mrs. Pearson's class.

To find the number of ways the roles can be assigned, we use the concept of permutations:

President can be selected from 32 students in 32 ways.

Vice President can be selected from the remaining 31 students in 31 ways.

Treasurer can be selected from the remaining 30 students in 30 ways.

Therefore, the total number of ways the roles can be assigned is 32 x 31 x 30 = 29760 ways.

Answer:

Two more people.

Step-by-step explanation:

If 4 people can mow a lawn in 6 hours, then 4 people can mow 1/6 of a lawn in 1 hour.

If 4 people can mow 1/6 of a lawn in 1 hour, then 1 person can mow 1/24 of a lawn in 1 hour.

If 1 person can mow 1/24 of a lawn in 1 hour, then 6 people can mow 1/4 of a lawn in 1 hour.

If 6 people can mow 1/4 of a lawn in 1 hour, then 6 people can mow a lawn in 4 hours.

6 people minus 4 people is 2 people.

There are two more people will be needed to mow the lawn in 4 hours, It is assuming that each person mows at the same rate

The rate of work is defined as the number of units of work completed per unit time.

Let the number of the person are x,

Condition 1;

4 people in 6 hours complete the work, work done in one hour;

1 hour =(1/6) of the total work

Condition 2;

If four individuals can do one-sixth of the total work, one person can do one-quarter of the work in an hour.

1 person do = (1/4) of the total work;

Condition 3;

If one person can do 1/24 of total work

Six persons can do 1/4 of total work in the same amount of time.

If six individuals can mow a quarter of a lawn in an hour, The number of  people will be needed to mow the lawn in 4 hours;

n=6-4

n=2

Hence, there are two more people will be needed to mow the lawn in 4 hours,

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Answer:

(x-3)^2

Step-by-step explanation:

Answer:

[tex]x<-2[/tex]

Step-by-step explanation:

Isolate the variable to find the solution set.

[tex]5>x+7 \\ \\ x<-2[/tex]

Answer:

see explanation

Step-by-step explanation:

Solve the inequality

5 > x + 7 ( subtract 7 from both sides )

- 2 > x ⇒ x < - 2

solution set {x | x ∈ R, x < - 2 }

Answer:

it would be a rectangle

Step-by-step explanation:

it would be a rectangle because when you cut it in the cross section there will be four parell sides, so therefore it would have to make a rectangle because the side lengths would not be even.

Answer: it would be a rectangle

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

Part 1) The length of DC is [tex]13\ units[/tex]

Part 2) The measures of the angles in the isosceles triangle are

The base angles are 67.4° and the vertex angle is 45.2°

Step-by-step explanation:

step 1

In the right triangle BDC Find the length of DC

Applying the Pythagoras Theorem

[tex]DC^{2}=BC^{2} +BD^{2}[/tex]

we have

[tex]BC=AB=10/2=5\ units[/tex]

[tex]BD=12\ units[/tex]

substitute

[tex]DC^{2}=5^{2} +12^{2}[/tex]

[tex]DC^{2}=169[/tex]

[tex]DC=13\ units[/tex]

step 2

Find the measures of internal angles in the isosceles triangle ABC

we know that

∠DAC=∠DCA ------> base angles

∠ADC ------> vertex angle

Find the measure of angle DCA

In the right triangle BDC

sin(∠DCA)=BD/DC

substitute the values

sin(∠DCA)=12/13

∠DCA=arcsin(12/13)=67.4°

so

∠DAC=∠DCA=67.4°

Find the measure of angle ∠ADC

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

∠DAC+∠DCA+∠ADC=180°

substitute

67.4°+67.4°+∠ADC=180°

∠ADC=180°-134.8°=45.2°

Answer:

1: Permutation

2: 3080

Step-by-step explanation:

As order matters, (first place as opposed to second place) this must be a permutation.

For first place, there are 56 different contestants that could win it, while once first place is selected, there are only 55 to get second. This means that

56*55=3080

Answer:

option C

x = 6

y = 4

z = 1

Step-by-step explanation:

Given in the question a matrix in the row echelon form of the augmented matrix.

[tex]\left[\begin{array}{ccc}1&0&+4=-1\\0&1&-1=+3\\0&0&+1=+1\end{array}\right][/tex]

First Equation

x0 + y0 + z(1) = 1

0 + 0 + z = 1

Second Equation

x0 + y(1) + z(-1) = 3

0 + y - z = 3

y -1 = 3

Third Equation

x(1) + y0 + z(4) = -1

x + 0 + 4z = -1

x + 4 = -1

Answer:

39° and 51°

Step-by-step explanation:

The angle formed by 1 and 2 is a right angle = 90°, thus

∠1 + ∠2 = 90 ← substitute values

x + 22 + 3x = 90

4x + 22 = 90 ( subtract 22 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Hence

∠1 = x + 22 = 17 + 22 = 39°

∠2 = 3x = 3 × 17 = 51°

Answer:

It's ÷ (divide)

Step-by-step explanation:

Because 48+27 is 75, and 750÷10 is also 75.

Hope I helped :)

Answer:

That number is 0.45

Step-by-step explanation:

3/5x = 2x - 63/100

0.63 = 2x - 3/5x

0.63 = 10/5x - 3/5x

0.63 = 7/5x

7x = 0.63*5 = 3.15

x = 3.15/7

Answer:

0.63Google

Step-by-step explanation:

Answer: 5 units down, 3 units up.

Step-by-step explanation: at the translation, the line is at 5, -3, putting the translation at 5 units right, 3 units up.

Answer:

the answer is d

Step-by-step explanation:

To solve 2y - x = 3/4 (-y + 1) for y, distribute 3/4, combine like terms, and isolate y. The solution is y = (4x - 3)/11, which is answer D.

The student has asked to solve for y in the equation: 2y - x = 3/4 (-y + 1). To solve for y, we can follow these steps:

First, distribute the 3/4 across the parentheses: 2y - x = 3/4 (-y) + 3/4 (1).

This simplifies to: 2y - x = -3/4y + 3/4.

Add 3/4y to both sides to get: 2y + 3/4y - x = 3/4.

Combine like terms on the left: (2 + 3/4)y - x = 3/4. This is equivalent to (11/4)y - x = 3/4.

Add x to both sides: (11/4)y = x + 3/4.

Finally, multiply both sides by 4/11 to solve for y: y = (4/11)x + 3/11.

Therefore, the correct answer is D) y = (4x - 3)/11.

Hey there! :)

Please keep in mind that slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

Using this, we can isolate y in our original given equation.

12x - y = 4

Start off by subtracting 12x from both sides.

-y = -12x + 4

Divide both sides by -1.

-y ÷ -1 = (-12x + 4) ÷ -1

Simplify!

y = 12x - 4

Therefore, using the slope-intercept form, we can come to the conclusion that because 12 is located in the "m" slot and "m=slope" then 12 is our slope. In addition, -4 is our y-intercept because it is located on the y position.

Slope = 12

Y-intercept = -4

Hope I helped! :)

Answer:

(x - 2)(x² + 2x + 4)

Step-by-step explanation:

A difference of cubes factors in general as

• a³ - b³ = (a - b)(a² + ab + b² )

note 8 = 2³ = 8 ⇒ b = 2 , with a = x

Hence

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)

Answer: The rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Step-by-step explanation:

Since we have given that

[tex]x^3-8[/tex]

We need to use the difference of cubes:

As we know the formula of "Difference of cubes":

[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

So, it can be written as

[tex](x)^3-(2)^3=(x-2)(x^2+2x+4)[/tex]

Hence, the rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Hello,

First we work out the equations:

x + y =62 will be the first equation.

2x= y +13 is the second equation.

We can first rewrite the second equation as 2x – y =13.

So we have:

x + y = 62

2x –y =13

KEEP IN MIND: With y being positive in one of the equations and negative in the other, we can combine the equations to quickly eliminate y and solve for x.

x + y = 62

+2x –y =13

3x = 75 divide both sides by 3 to get x.

x = 25

Now that we have x we can substitute the value for x, 25.

25 + y = 62 we can subtract 25 from both sides to get y.

y = 62- 25

y = 37

2(25) = 37 + 13

Therefore,

50 = 50

Have a amazing day.

The two numbers your friend has are 25 and 37. This solution is found by creating a system of equations based on the clues given and solving for the two variables.

Your friend essentially gave you a system of two equations to solve where the two numbers are x and y. The first equation from your friend's statement is '2 times the first number is 13 more than the second number', which transforms to 2x = y + 13. The second equation is 'the sum of the two numbers is 62', which converts to x + y = 62.

Solving this system of equations can reveal the two numbers your friend has. We can utilize the substitution method, where we express y from the first equation as y = 2x - 13 and plug it into the second equation. This substitution gives us x + (2x - 13) = 62. This simplifies to 3x - 13 = 62, and by rearranging, we find 3x = 75. Dividing by 3 we get x = 25.

Using the value of x = 25, now we can find y = 2(25) - 13 = 37.

So, your friend's numbers are 25 and 37.

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1.   1.5x - 10 = 3 (2x - 4)

Step 1: Distribute 3 to the numbers in the parentheses

1.5x - 10 = (3 *2x) + (3* - 4)

1.5x - 10 = (6x) + (-12)

1.5x - 10 = 6x- 12

Step 2: Combine like terms (x's go with x's). Subtract 6x from both sides so that it is canceled out from the right side and brought to the left side.

(1.5x-6x) - 10 = - 12

-4.5x -10 = -12

Step 3: Continue combining like terms by adding 10 to both sides. This will cancel out -10 from the left side and move it to the right

-4.5x = -12 + 10

-4.5x = -2

Step 4: Divide -4.5 to both sides to isolate x

(-2/-4.5) = x

4/9 = x

2.  3 (-3x + 2) +4x = 1/2(5x - 30) - 9

Step 1: distribute 3 to the numbers in the parentheses.

(3*-3x) + (3*-2) +4x = 1/2 (5x - 30) -9

-9x + (-6) +4x = 1/2 (5x -30) -9

Step 2:

The first one is three

The second one is twelve

The last one is 2

Answer:

24

Step-by-step explanation:

Recall that in an equilateral triangle, all the interior angles are the same, that is, all are 60°.  If we look at the lower right 60° angle, we see that the side opposite this angle is the altitude (height) of the triangle.

In this problem the height is 4√3.  What is the hypotenuse?  We need to find the hypotenuse, because 3 times the length of this hypotenuse is the perimeter of the triangle.  

Consider the sine function.  Here, sin 60° = 4√3 / hyp, or:

√3        4√3

------- = -----------

    2        hyp

thus, the length of the hypotenuse is 8 and the perimeter of the triangle is 3 times that, or 24.

Answer:

The slope will be 1 so one point down and one up.

The y-intercept is -2.

Step-by-step explanation:

s=slope

i=intercept

y=s*x+i

Answer:

[tex](-\infty,+\infty)[/tex]

Step-by-step explanation:

The given function is

[tex]y=\sqrt[3]{x+8}[/tex]

The range refers to the values of y for which  x is defined.

We solve for x to obtain;

[tex]y^3=x+8[/tex]

[tex]x=y^3-8[/tex]

This is a polynomial function in y.

x is defined for all values of y.

Therefore the range is all real numbers.

or

[tex](-\infty,+\infty)[/tex]

The first choice is correct.

Answer:

range is -∞<y<∞

Step-by-step explanation:

[tex]y=\sqrt[3]{x+8}[/tex]

Range of the given function is same as the domain of the inverse function

LEts find the inverse for the given equation

Swap the variables x and y . then solve for y

[tex]y=\sqrt[3]{x+8}[/tex]

[tex]x=\sqrt[3]{y+8}[/tex]

Take cube on both sides

[tex]x^3= y+8[/tex]

Subtract 8 from both sides

[tex]y=x^3-8[/tex]

Inverse function is a cubic function. For cubic function the domain is set of allr eal numbers. -∞<x<∞

Range of the given function is same as the domain of the inverse function

So range is -∞<y<∞

Answer:

A. y = x^2 -6x + 13

Step-by-step explanation:

The parabola that opens up and has line of symmetry x=3 and a minimum at x=3  is

[tex]y=x^2-6x+13[/tex]

The reason is that, we can write this function in the vertex form to get;

[tex]y=x^2-6x+(-3)^2+13-(-3)^2[/tex]

[tex]y=(x-3)^2+13-9[/tex]

[tex]y=(x-3)^2+4[/tex]

Hence the line of symmetry is x=3 and the vertex is (3,4)

Answer:

option A

y = x² - 6x + 5

Step-by-step explanation:

step 1

Find out if a is positive or negative.

'a' is the coefficent of x

If the parabola is facing up , then a must be positive.

a = 1

Step 2

To find the minimum point

x = -b/2a

using the standard equation y = ax² + bx + c

x must be equal to 3

Equation 1

y = x² -6x + 13

x = -(-6)/2(1)

x =  3(ACCEPTED)

Equation 2

y = x² + 6x + 5

x = -6/2(1)

x = -3      

Equation 3

x² - 3x + 6

x =  3/2(1)

x =  3/2

Equation 4

x² + 8x + 19

x = -8/2(1)

x = -4

Step 3

At the minimum point there will be line of symmetry hence x = 3

feet will be the best way to measure the high jump

Answer:

median, mean , and mode

Step-by-step explanation:

ANSWERS

A.

[tex] \frac{19}{20} [/tex]

EXPLANATION

It was given that triangle LMN is a right triangle and angle L and M are complementary.

This implies that:

[tex] \sin(L) = \cos(M) [/tex]

It was given in the question that:

[tex] \cos(M) = \frac{19}{20} [/tex]

This implies that:

[tex] \sin(L) = \frac{19}{20} [/tex]

Answer:

x = 3.391

Step-by-step explanation:

first you calculate.

7.9% - 0.25 = 3.22 + x

divide the numbers

[tex]\frac{7.9}{100}[/tex] - 0.25 = 3.22 + x

calculate again.

0.079 - 0.25 = 3.22 + x

move the terms

-0.171 = 3.22 + x

add the numbers

-x = 3.22 + 0.171

then change the signs

-x = 3.391

Final ans : x = -3.391

or some alternate answer's

x = -[tex]\frac{3391}{1000}[/tex] , x = -3[tex]\frac{391}{1000}[/tex]

Answer:x=−3.371

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7.9

100

−0.25=3.2+x

0.079+−0.25=3.2+x

(0.079+−0.25)=x+3.2(Combine Like Terms)

−0.171=x+3.2

−0.171=x+3.2

Step 2: Flip the equation.

x+3.2=−0.171

Step 3: Subtract 3.2 from both sides.

x+3.2−3.2=−0.171−3.2

x=−3.371

Answer:

4,1,2,3

Step-by-step explanation:

1.8+7=15

2.10/5=2

3.8+10=18

4.2(5)=10

The function g(x) increases the slope of the line by a factor of 8.

We have,

Parent function f(x)=x.

We have to find the change will occur in the function when the parent function f(x) is replaced by 8f(x).

let g(x) be the function by replacing f(x) with 8f(x)

g(x)=8 f(x)

g(x) = 8x

Here, the slope of function is 8 and slope of g(x) is 1.

Thus, g(x) increases the slope of the line by a factor of 8.

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Replacing f(x) with 8f(x) scales up the output values of the function by 8 times. This results in the graph of the function stretching vertically i.e., it gets steeper.

The question is asking about the change in the parent function f(x)=x when we replace f(x) with 8f(x). This operation vertically stretches the graph of the parent function by a factor of 8. In mathematic terms, it scales up the output (or 'y' values) of the function by 8 times. To visualize this, if the original function produced a straight 45 degree line (for f(x)=x), this line will now become steeper, with all y-values multiplied by 8 i.e., the steepness or the slope of the line significantly increases. On a graph, instead of a point (1,1) on the line, you will see the point has moved up to (1, 8).

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ANSWER

4.2kg

EXPLANATION

We want to convert the weight of Eliot's backpack, which weighs 4,200 grams into kilograms.

We know that:

1,000 grams =1kg

Therefore :

[tex] 4200g = \frac{4200}{1000} = 4.2kg[/tex]

Therefore the weight of Elliot backpack in kilograms is 4.2kg

Answer:

16

Step-by-step explanation:

a/(1-r)

Use the infinite geometric series formula.

ANSWER

[tex]S_{\infty} = 16 [/tex]

EXPLANATION

Given the series:

8 + 4 + 2 + . . .

The first term of the series is

[tex]a_1 = 8[/tex]

The common ratio is

[tex]r = \frac{4}{8} = \frac{1}{2} [/tex]

The sum of this series is given by

[tex]S_{\infty} = \frac{a_1}{1 - r} [/tex]

[tex]S_{\infty} = \frac{8}{1 - \frac{1}{2} } [/tex]

Simplify:

[tex]S_{\infty} = \frac{8}{\frac{1}{2} } = 8 \times 2 = 16 [/tex]