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The volume of the given shapes are listed below with their options:

11.) 12 in³ = C

12.) 108 in³ = D

13.) 293.33 cm³ = C

14.) 287 mi³ = B

15.) 3801.33 cm³ = D

16.) 452.39 yd³ = C

17.) 3619.11 in³= B

18.) 16 ft³ = C

19.) 64 m³ = A

20.) 769.69 cm³ = C

The formula used to calculate the volume of a cylinder= πr²h

The formula used to calculate the volume of triangular prism = 1/3Bh

For a square based pyramid = 1/3b²h

For a rectangular pyramid = 1/3 lwh

Volume of a cone = 1/3πr²h

For question 11;

Volume of the triangular pyramid =1/3Bh= 1/3×6×6 = 12 in³

For question 12;

Volume of square pyramid =1/3b²h = 1/3 ×6×6×9 = 108 in³

For question 13.)

Volume of a rectangular pyramid = 1/3 lwh= 1/3×11*8*10=293.33 cm³

For question 14.)

Volume of square pyramid =1/3b²h = 1/3*9*9*11= 287 mi³

For question 15.)

Volume of a cylinder = πr²h = 3.14×11*11*10 = 3801.33 cm³

For question 16.)

Volume of a cone= 1/3πr²h= 1/3*3.14*6*6*12= 452.39 yd³

For question 17.)

Volume of a cone= 1/3πr²h= 1/3*3.14*12*12*24= 3619.11 in³.

For question 18.)

Volume of the triangular pyramid =1/3Bh = 1/3*6*8= 16 ft³

For question 19.)

Volume of the triangular pyramid =1/3Bh = 1/3*24*8= 64 m³

For question 20.)

Volume of a cylinder = πr²h = 3.14×7*7*5 = 769.69 cm³

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The error is made because two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. The Option D is correct.

All similar shapes are two or more given shapes that share some properties in terms of their corresponding sides or angles. As a result, if the corresponding sides or angles are related, they are similar. It is important to note that similarity does not imply congruency.

When the sides and angles of the given triangles LMN and QRS are compared, it is clear that: angle Side Angle (ASA) similarity implies that the included side between two pairs of congruent angles is similar. As a result, the Option D explains the error in the diagram.

Missing options "a.Your​ friend's paper does not name the triangles correctly for them to be congruent. b. Your​ friend's paper shows that the SAS Postulate should be used to show congruence because a pair of congruent angles is included between two pairs of congruent sides. c. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the triangles do not have two pairs of congruent angles. d. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.

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1241 student tickets were sold. Below, you will learn how to solve the problem.

2566 concert tickets were sold for a total of $10,348, and if students paid $3 and nonstudents paid $5, then the number of student tickets sold can be calculated.

To solve this problem, we can set up an equation using the given information.

X + Y = 2566

3X + 5Y = 10348

Find the value of X:

Y = 2566 - X

3X + 5(2566 - X) = 10348

3X + 12830 - 5X = 10348

2X = 12830 - 10348

2X = 2482

X = 1241

Therefore, 1241 student tickets were sold.

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Answer:

To find the slope of the line passing through (-3, 1) and (2, -3), we can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-3, 1) and (x2, y2) = (2, -3).

slope = (-3 - 1) / (2 - (-3))

= -4 / 5

So, the slope of the line passing through (-3, 1) and (2, -3) is -4/5.

To find the slope of a line parallel to this line, we need to remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also -4/5.

Answer:

x = -1

y = -8

Step-by-step explanation:

2x+3y= −26

5x+3y= −29

Time the first equation by -1

-2x - 3y = 26

5x + 3y = -29

3x = -3

x = -1

Now put -1 in for x and solve for y

2(-1) + 3y = - 26

-2 + 3y = -26

3y = -24

y = -8

Let's check

2(-1) + 3(-8) = -26

-2 - 24 = -26

-26 = -26

So, x = -1 and y = -8 is the correct answer.

[tex]2x + 3y = - 26 \\ \implies \: 2x + 3y + 26 = 0[/tex]

[tex]5x + 3y = - 29 \\ \implies \: 5x + 3y + 29 = 0[/tex]

For finding what sort of solution the pair of equations give , we need to check the type of equality between

[tex] \frac{ a_{1}}{ a_{2} \: } , \: \frac{ b_{1} }{ b_{2} } , \: \frac{ c_{1}}{ c_{2} } \\ [/tex]

The following results can be obtained ,

[tex]if \: \: \frac{ a_{1} }{a _{2} } \neq \: \frac{ b_{1}}{ b_{2}} \\ \\ \implies \: we \: obtain \: a \: unique \: solution[/tex]

[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: \neq \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: no \: solution[/tex]

[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: = \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: infinitely \: many \: \: solutions[/tex]

Considering the equations provided ,

[tex] a_{1} = 2 \: \: , \: \: b_{1} = 3 \: \: , \: \: c_{1} = 26 \\ a_{2} = 5 \: \: , \: \: b_{2} = 3 \: \: , \: \: c_{2} = 29[/tex]

[tex]\therefore \frac{ a_{1}}{ a_{2} } = \frac{2}{5} \: \: \: , \: \: \: \frac{ b_{1}}{ b_{2} } = \frac{3}{3} = \frac{1}{1} \: \: \: , \: \: \: \frac{ c_{1} }{ c_{2} } = \frac{26}{29} \\ [/tex]

Since ,

[tex] \frac{ a_{1} }{ a_{2}} \neq \: \frac{ b_{1} }{ b_{2}} \\ [/tex]

The system of equations has a unique solution .

On further calculations done by elimination method , the solution of the equations comes out to be

[tex]\boxed{x = - 1} \\ \boxed{y = - 8}[/tex]

let's have a look at how it'll be done now.

the equations given in the question are -

[tex]2x + 3y + 26 = 0 \: ...(1) \\ 5x + 3y + 29 = 0...(2) \\ \\ multiplying \: equation \: (1) \: by \: - 1 \\ \implies \: - 2x - 3 - 26 = 0...(3) \\ \\ solving \: eqs. \: (2) \: and \: (3) \\ \\ 5x + \cancel{3y} + 29 = 0 \\ \underline{ - 2x \cancel{- 3y} - 26 = 0} \\ 3x + 3 = 0 \\ \\ \implies \: 3x = - 3 \\ \implies \: \boxed{x = - 1} [/tex]

substiting the value of x in equation 1

[tex]2( - 1) + 3y + 26 = 0 \\ 3y + 26 - 2 = 0 \\ 3y + 24 = 0 \\ 3y = - 24 \\ \implies \: \boxed{y = - 8}[/tex]

hope helpful! :)

Answer: its all 3

Step-by-step explanation: https://socratic.org/questions/is-12-an-integer-rational-or-real-number#:~:text=Reals%3A%20any%20number%20that%20is%20rational%20or%20irrational,be%20found%20on%20the%20number%20line.%20Answer%20link

The solution to this linear programming problem is (x,y) = (3,4) and f = 22.

To solve this linear programming problem, we need to find the feasible region by graphing the constraints and then use the objective function to find the maximum value of f.

1. Graph the constraints:

x + y ≤ 7 can be rewritten as y ≤ -x + 7
2x + y ≤ 12 can be rewritten as y ≤ -2x + 12
y ≤ 4

2. Find the feasible region:

The feasible region is the area that satisfies all of the constraints. In this case, it is the area bounded by the three lines and the x and y axes.

3. Use the objective function to find the maximum value of f:

f = 2x + 4y

To find the maximum value of f, we need to find the corner points of the feasible region and plug them into the objective function. The corner points are (0,4), (3,4), and (4,3).

f(0,4) = 2(0) + 4(4) = 16
f(3,4) = 2(3) + 4(4) = 22
f(4,3) = 2(4) + 4(3) = 20

The maximum value of f is 22 at the point (3,4).

Therefore, the solution to this linear programming problem is (x,y) = (3,4) and f = 22.

Answer:

(x,y) = (3,4)

f = 22

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases}[/tex]

[tex]1600 = 800e^{0.08\cdot t} \implies \cfrac{1600}{800}=e^{0.08t}\implies 2=e^{0.08t} \\\\\\ \log_e(2)=\log_e(e^{0.08t})\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}[/tex]

Answer:

Here is a table showing the relationship between the number of coins collected and the total points earned:

Number of coins (c) Total points (p)

0 0

1 20

2 35

3 50

4 65

5 80

6 95

7 110

8 125

9 140

10 155

To graph these ordered pairs, we can plot the number of coins collected (c) on the x-axis and the total points earned (p) on the y-axis. Then we can plot each ordered pair as a point on the graph and connect the points with a line. The resulting graph should show a linear relationship between c and p, with a slope of 15 and a y-intercept of 0.

Analyzing the graph, we can see that as the number of coins collected increases, the total points earned also increases at a constant rate. This suggests that collecting coins is an important part of the game, as it significantly increases the player's total score. Additionally, the slope of the line (15) tells us that each additional coin collected is worth 15 points, while reaching the next level is worth only 5 points.

For rational function, n < m. There is a horizontal asymptote at y = 0.

A rational function is one whose denominator is not zero and which can be expressed as the ratio between two polynomials.

f(x) = p(x) / q(x)

By examining the degrees of a numerator (n) and denominator, we can locate the horizontal asymptote (m).

Thus, For rational function, n < m. There is a horizontal asymptote at y = 0.

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The both triangles are not similar.

Similar triangles are triangles that have the same shape but may have different sizes. Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are in proportion or have the same ratio.

In other words, if two triangles have the same angles, then they are similar. The ratio of the lengths of the corresponding sides of similar triangles is the same, and this ratio is called the scale factor.

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The result obtained from the long division of the polynomial is n² + 2n - 1 + 3/(n - 9).

The quotient of the polynomial is obtained by applying long division method as shown below.

        n²   +   2n   -   1

   ________________________

n - 9 √ (n³ - 11n² + 21n - 24)

            (n³ -  9n²)  

       ____________

               -2n² + 21n

               -2n² + 18n

               __________

                       3n - 24

                       3n - 27

                       ______

                            3

Therefore, the quotient is n² + 2n - 1 and the remainder is 3.

n³ - 11n² + 21n - 24 =  (n - 9)(n² + 2n - 1) + 3.

So when we divide the polynomial using long division method we would obtain the following result.

(n³ - 11n² + 21n - 24) ÷ (n - 9) = n² + 2n - 1 + 3/(n - 9)

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Find the quotient of this long division; (n³ - 11n² +21n-24)÷(n-9)

The median of class A is equal to 40.

The median of class B is equal to 8.

The difference between the median of the two classes is 32.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the median of class A can be determined by sorting the data set in ascending order;

10, 10, 10, 20, 20, 30, 40, 40, 40, 40, 50, 50, 50, 70, 70

Median of class A = 40.

Based on the dot plot, the median of class B can be determined by sorting the data set in ascending order;

4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 16

Median of class B = 8.

For the difference, we have:

Difference = 40 - 8

Difference = 32.

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The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.

An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷.  They can be used to find unknown values, such as the area of a circle or the speed of a moving object.

The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.

Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.

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The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.

An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷.  They can be used to find unknown values, such as the area of a circle or the speed of a moving object.

The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.

Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.

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Complete question -

Find the value of 4x - 3y when x=1/2 and y=-5.

The solution of the system of equation is

1) The solution to the system of equations is x = -7 and y = -2.

2) The solution to the system of equations is x = -7 and y = -2.

3) The solution to the system of equations is any point on the line 2x + 5y = 0

4) The solution to the system of equations is x = -2 and y = 1.

5) The solution to the system of equations is x = 1 and y = -16.

In mathematics, a system of equations refers to a set of two or more equations that must be solved simultaneously. Solving a system of equations involves finding the values of the variables that satisfy all the given equations. In this response, we will go through the process of solving five different systems of equations.

−2x−8y=10 and 2x−6y=18, in order to solve this system of equations, we need to eliminate one of the variables, x or y. One way to do this is to add the two equations together. When we add them, the x term cancels out, leaving us with -14y = 28. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.

And then the equations, −2x+9y=−4 and 2x+3y=−20, to solve this system of equations, we can use the method of elimination again. If we add the two equations, the x term cancels out, leaving us with 12y = -24. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.

Then the third one 2x+5y=0 and x + 5y = −10 is in this system of equations, we notice that the second equation is just the first equation with a constant term added. Therefore, these equations are dependent, meaning that they represent the same line. Any point that satisfies one equation will also satisfy the other equation.

And the fourth one has −4x+y=9 and −4x+9y=17, to solve this system of equations, we can use the method of substitution. We can solve the first equation for y, getting y = 4x + 9. Substituting this expression for y into the second equation, we get -4x + 9(4x + 9) = 17. Simplifying, we get 25x + 72 = 17. Solving for x, we get x = -2. Substituting this value of x into the first equation, we get y = 1.

−6x − y = 10 and −16x + 6y = −24,  To solve this system of equations, we can use the method of elimination. If we multiply the first equation by -6 and the second equation by -1, we can add the two equations to eliminate y. Doing so, we get 80x = 80. Solving for x, we get x = 1. Substituting this value of x into either equation, we get y = -16.

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Complete Question:

Solve the system of equations

1) −2x−8y=10 and 2x−6y=18

2) −2x+9y=−4 and 2x+3y=−20

3) 2x+5y=0 and x + 5y = −10

4) −4x+y=9 and −4x+9y=17

5) −6x − y = 10 and −16x + 6y = −24

The final factored form of the polynomial is b(a-b) and the category of the remaining polynomial is a binomial.

The first step in factoring out the GCF from the polynomial ab+ay-b^(2)-by is to identify the greatest common factor of all the terms. In this case, the GCF is b. Once we have identified the GCF, we can factor it out from each term by dividing each term by the GCF. This gives us:

ab+ay-b^(2)-by = b(a+y)-b(b+y) = b(a+y-b-y)

Next, we can simplify the remaining polynomial by combining like terms:

b(a+y-b-y) = b(a-b)

Finally, we can identify the category of the remaining polynomial. Since it has two terms and each term has a degree of 1, the remaining polynomial is a binomial.

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Answer:

-3/2

Step-by-step explanation:

To find:-

Answer:-

We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,

[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

Now on substituting the respective values, we have;

[tex]:\implies \sf m = \dfrac{0-3}{1-(-1)} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3}{1+1}\\[/tex]

[tex]:\implies \sf \pink{m=\dfrac{-3}{2}}\\[/tex]

Hence the slope of the line is -3/2.

The value of x is -11

The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

represent the other two base angles as z and y

z= 80(opposite angles)

y = 60( opposite angles)

z+y +x+51 = 180

80+60 +x +51 = 180

140+51+x = 180

x+191 = 180

x = 180-191

x = -11

therefore the value of x is -11

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The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).

Divisor = 1 7/9

Convert the divisor (mixed fraction ) into improper fraction,

1 7 /9

= [( 9× 1 ) + 7]/ 9

= 16/9

Dividend = 2 1 / 2

Convert the dividend (mixed fraction ) into improper fraction,

2 1 / 2

=[ ( 2 ×2 ) + 1] /2

= 5 /2

Divide the 5 / 2 by 16 /9 to get the estimated quotient ,

( 5 / 2 ) ÷ ( 16 / 9)

= ( 5 / 2 ) × ( 9 / 16 )

= ( 5 × 9 ) / ( 2 × 16 )

= 45 / 32

= 1.40625

= 1.41 ( round off up to the two decimals )

Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).

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Using the definition of the tangent function, we will get that:

5√(6)/12 = sin(θ)

Here you need to remember how the tangent function is defined, we know that:

tan(θ) = sin(θ)/cos(θ)

Here we know that:

tan(θ) = √15/3

cos(θ) = √10/4

Replacing that we can write:

√15/3 = sin(θ)*(4/√10)

Solving for the sine, we will get:

(√15/3)*(√10/4) = sin(θ)

(√15*√10)/(3*4) = sin(θ)

(√150)/(12) = sin(θ)

(√(25*6))/(12) = sin(θ)

5√(6)/12 = sin(θ)

That is the answer.

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Truth Table

This statement can be simplified using proportional algebra as follows: (p ∨ ∼r) ∧ (q ∨ (p ∧ r)). This can be verified using a truth table.

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The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function (g o f)(x).

(g o f)(x) = g( f(x) )

g( x )  = 2x - 1

g( f(x) ) = 2( f(x) ) - 1

g( f(x) ) = 2( x² - 3 ) - 1

Now, simplify the function by applying distributive property.

g( f(x) ) = 2( x² - 3 ) - 1

g( f(x) ) = 2 × x² - 2 × 3 - 1

g( f(x) ) = 2x² - 6 - 1

Add -6 and -1

g( f(x) ) = 2x² - 7

Therefore, the function operation ( g  o f ) is 2x² - 7.

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a) On average, 0.5 * 24 = 12 of the digits would be even. b)  No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12

a. On average, you would expect 12 of the 24 digits to be even. This is because there are an equal number of even and odd digits (0, 2, 4, 6, 8 are even and 1, 3, 5, 7, 9 are odd), so the probability of a digit being even is 0.5. Therefore, on average, 0.5 * 24 = 12 of the digits would be even.

b. No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12, it is possible to get more or less than 12 even digits in a sample of 24.

This is due to the randomness of the random number table and the fact that samples do not always perfectly match the population proportion.

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The value of probabilities are,

P (1, 1) = 1 / 36 = 0.027

P (both odd) = 0.166

P (even, odd) = 0.25

P (2 anywhere) = 0.3055

P (sum 8) = 0.1389

P (sum 1) = 0

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given that;

Two dice are rolled at the same time.

Hence, There are total number of possibilities = 36

Thus, The value of P (1, 1) is,

P (1, 1) = 1 / 36

Since, There are 6 possibilities when both dice have rolled to get odd.

Hence, The value of P (both odd) is,

P (both odd) = 6 / 36

                   = 1/ 6

Since, There are 9 possibilities to get first dice even and second odd.

Hence, The value of P (even, odd) is,

P (even, odd) = 9/36

                     = 1/4

Since, There are 11 possibilities when 2 is in anywhere.

Hence, The value of P (2 anywhere) is,

P (2 anywhere) = 11/36

Since, There are 5 possibilities to get sum 8.

Hence, Value of P (sum 8) is,

P (sum 8) = 5/36

Since, There are no possibilities to get sum 1.

Hence, P (sum 1) = 0

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Shea needs to do 600 carpet cleaning per year to break even.

What is revenue?

Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.

To break even, the total revenue Shea generates from the carpet cleaning business must be equal to the total cost of running the business.

Let's first calculate the total cost of running the business per year:

Total Cost = Fixed Costs + Variable Costs

Since the fixed plus variable costs per month total $1,500, the total cost per year would be:

Total Cost = $1,500 x 12

Total Cost = $18,000

Now, let's calculate the profit that Shea makes per cleaning:

Profit per Cleaning = Price per Cleaning - Cost per Cleaning

Profit per Cleaning = $60 - $30

Profit per Cleaning = $30

So, Shea makes a profit of $30 per cleaning.

To break even, the total profit generated by the number of cleanings Shea does per year should be equal to the total cost of running the business per year:

Total Profit = Total Revenue - Total Cost

If x is the number of carpet cleaning Shea needs to do per year to break even, then:

Total Revenue = Price per Cleaning x Number of Cleanings per Year = $60x

Total Profit = Profit per Cleaning x Number of Cleanings per Year = $30x

Setting Total Profit equal to Total Cost:

$30x = $18,000

x = $18,000 / $30

x = 600

Therefore, Shea needs to do 600 carpet cleaning per year to break even.

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The height of this prism is equal to 1.5 centimeters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula for the volume of a rectangular prism, we have;

2.76 = 2.3 × 0.8 × H

Height, H = 2.76/1.84

Height, H = 1.5 centimeters.

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The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.

The given expression is:

[tex]y^6 * y^3[/tex]

We can simplify this expression by adding the exponents of y:

[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]

Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

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To factor a trinomial, you need to find two binomials that, when multiplied together, give you the original trinomial.

The key to finding binomials is to identify the factors of the quadratic term and the constant term, and then use those factors to construct the binomials.

Here's a step-by-step process for factoring a trinomial:

It's important to note that not all trinomials can be factored using this method.

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Answer:

  b (3, −2)

Step-by-step explanation:

You want the solution to the system of equations ...

We see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:

  (d +e) +(-d +e) = (1) +(-5)

  2e = -4 . . . . . . . . simplify

  e = -2

Substituting into the first equation, we have ...

  d +(-2) = 1

  d = 3 . . . . . . add 2

The solution is (d, e) = (3, -2).

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Additional comment

We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.

  (d +e) -(-d +e) = (1) -(-5)

  2d = 6 . . . . . . . simplify

  d = 3 . . . . . . . . divide by 2; matches the solution above.

The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.