Find the length of the segment. Write the mixed number in simplest form.

The breakeven point after the adjustment in the expense function.

What is the revenue?

Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.

Revenue is the product of the number of units and the price per unit. It is given by:

Revenue = number of units * price per unit

Revenue = x * p(x)

Revenue = 8q Expense = 4.55q + 69,000

To find the breakeven point Revenue = Expense

8q = 4.55q + 69,000 3.3.45q = 69,000 q = 20,000

Equate both and find q

E = 4.55(20,000) + 69,000 = 160,000

E at q = 20,000

(20,000, 160,000)

Hence, the breakeven point after the adjustment in the expense function.

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A sample of 38 adults who has own an answering machine,

a) The probability that in a sample of 38, exactly 15 people own an answering machine is 0.061.

b) The probability that in a sample of 38, at most 15 people own an answering machine is 0.92381.

We have three in ten adults own an answering machine . That is probabilty of success, p = 3/10

Sample size, n = 38

Using Binomial Probability distribution,

X ~ Binom( 38, 0.3)

where X is random variable of adults has own an answering machine.

P(X= x) = ⁿCₓ (p)ˣ1-p)⁽ⁿ⁻ˣ⁾

The probability that in a sample of 38, exactly 15 people own an answering machine. , P(X= 15)

= ³⁸C₁₅(0.3)¹⁵ )(1 - 0.3)²³

= 38!/15!23! (0.3)¹⁵5(0.7)²³

= 0.06075 ~ 0.061

so, P(X= 15) = 0.061

b) The probability that in a sample of 38, at most 15 people own an answering machine, P(X<= 15)

Now, P(X≤ 15) = P( X= 1 ) + P(X= 2) + ... + P(X= 15) or 1 - P(X>15)

= 0.923814121

Hence, required probabilities

are 0.061 and 0.9238.

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Answer:

height = 4

Step-by-step explanation:

b = 3h

b * h = 48

3h * h = 48

3h² = 48

3/3 h² = 48/3

h² = 16

h = √16

h = 4

b = 4 * 3

b = 12

If the number of subscribers increases by 75% each year, then the number of subscribers each year is 175% the number of the previous year.  So we need to multiply by 1.75 each year to get the next years number.

Since 2008 is 23 years after 1985, we'd have to multiply the 1985 number by 1.75 twenty-three times:

     285 (1.75)^23 ≈ 110,845,988

That seems a bit crazy, since Glenwood is a small town, but so is a 75% growth each year for 23 years.

It takes Sandra 6.44 hour to word process 29 pages.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

It takes Sandra 1 hour to word process 4.5 pages.

Now,

Since, It takes Sandra 1 hour to word process 4.5 pages.

Hence, The time to make 29 pages = 29/4.5

                                                        = 290/45

                                                        = 58/9 hours

Thus, It takes 6.44 hours to complete 29 pages.

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Answer: x = -9 , y = -13

Step-by-step explanation:

Multiply the second equation by 5, then add the equations together.

(−5x+3y=6)

5(x−y=4)

Becomes:

−5x+3y=6

5x−5y=20

Add these equations to eliminate x:

−2y=26

Then solve −2y=26 for y:

−2y = 26

Divide both sides by -2

y= -13

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

−5x+3y=6

Substitute−13 for y in −5x+3y=6:

−5x+(3)(−13)=6

−5x−39=6 (Simplify both sides of the equation)

−5x−39+39=6+39 (Add 39 to both sides)

−5x=45

Divide both sides by -5

x = -9

hope it help

you can proof it in the first equation if you want

The table that represents the relationship between the number of hours Khalil works and his total earnings is Table A.

The ratio connecting two given values in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Mathematicians use the constant of proportionality to determine whether a relationship is direct or indirect and what kind of proportionality it is. Equations involving ratios and proportions can be resolved with the aid of the proportionality constant.

It should be noted that the information given relates to a constant of proportionality. In this situation, Khalil earns $106.50 for 6 hours of work.

The amount that will be earned per hour will be:

= Amount earned / Number of hours

= $106.50 / 6

= $17.67

In this case, 7 hours will be:

= $17.67 × 7

= $123.7

The correct option is A.

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The distance between the two parallel lines with the equations y = 7 and

y = -1 is 8 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the equation of line be y = 7 and y = -1

Now , the slope of both the lines is 0

Slope m = 0

And the y intercept of the equation 1 or line 1 is = 7

So , the point is ( 0 , 7 )

And the y intercept of the equation 2 or line 2 is = -1

So, the point is ( 0 , -1 )

Now , the distance between the points ( 0 , 7 ) and ( 0 , -1 )  is given by the equation ,

[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values in the equation , we get

Distance D = √ ( 7 - ( - 1 ) )²

Distance D = √ ( 8 )²

Distance D = 8 units

Therefore , the value of D is 8 units

Hence , The distance between the two parallel lines with the equations y = 7 and y = -1 is 8 units

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Answer:

subtraction property of equality

Step-by-step explanation:

The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL

The number of water bottles = 6

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of water bottles required be = A

Now , the equation will be

The total distance of the bush walk = 3.5 km

Bernard's requirement of water for every 1.4 km = 1.2 L of water

So , Bernard's requirement of water for every 3.5 km = ( total distance of the bush walk / 1.4 ) x 1.2 L

Substituting the values in the equation , we get

Bernard's requirement of water for every 3.5 km = ( 3.5 / 1.4 ) x 1.2 L

Bernard's requirement of water for every 3.5 km = 2.5 x 1.2 L

Bernard's requirement of water for every 3.5 km = 3 L

Now , the amount of water one water bottle can hold = 500 mL

The value of 3 L = 3000 mL

So , the number of water bottles required to hold 3 L = 3000 / amount of water one water bottle can hold

Substituting the values in the equation , we get

The number of water bottles required to hold 3 L = 3000 / 500

The number of water bottles required to hold 3 L = 6 water bottles

Therefore , the value of A is 6 water bottles

Hence , The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL

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3 × 10² miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

Given that,

car gets 25.00 miles per gallon.

In 1 gallon car covers 25 miles distance.

In 12 gallon the car will cover = 25 × 12 miles distance

                                                = 300 miles distance.

Thus, distance covered in 12 gallons = 300 miles.

                                                             = 3 × 10² miles.

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The domain of the function described in the problem is given as the number of people living in the house. The correct option is (D).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

Suppose the number of rooms in the house be y.

And, the number of people is x.

As per the question, the function can be written as,

y = f(x)

From the definition of the function it is clear that all the possible values of x are domain and all values of y are range.

Thus, the domain of the function is number of people living in the house.

Hence, the domain of the function for the given case is the number of people living in house.

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Answer:

12

Step-by-step explanation:

12 .........

Answer:

640[tex]\pi[/tex]

Step-by-step explanation:

Answer:

640π

Step-by-step explanation:

The formula for a cone volume is

[tex]V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi[/tex]

Answer:

Si es un chiste, me reiría. Pero si es un insulto, agradecería que se preocuparan por mí.

Step-by-step explanation:

The number of child tickets sold is 99.

A system having more than two equations is known as a system of equations.

Given that, the cost of a child ticket and the cost of an adult ticket are $5.60 and $9.50 respectively.

Let the number of child tickets sold and the number of adult tickets sold be s and a, then

s + a = 170

a = 170 - s

The total cost of s child tickets and a adult tickets is:

5.6s + 9.5a = 1228.90

Substitute a= 170 -s into the above equation:

5.6s + 9.5(170 - s) = 1228.90

5.6s + 1615 - 9.5s = 1228.90

3.9s = 386.1

s = 99

Hence, the number of child tickets sold is 99.

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No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.

What is hypotenuse?

The side opposite to the right angle is always the hypotenuse of a right triangle . It is also the longest side in a right triangle.

what is hypotenuse-leg congruence property?

HL (hypotenuse-leg) congruence Property: The hypotenuse-leg congruence property only applies to the right triangles.

According to hypotenuse-leg congruence property, in any two right angle triangles if the length of the hypotenuse of both the triangles are same and the length of one leg of the triangle is the same in both then the triangles are congruent in nature.

In the given case , leg of one triangle is congruent to a leg of the other triangle and also the triangles are right triangles but the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.

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1. The cost 7 Books is $10. 85

2. He can lay 336 bricks

3. n= 1

4.   n= 1

5.   n= 18

6. n= 5

7.n= 3

8.  n=6

9. n= 6

10. n= 2

11.n= 12

12. n= 66

13. n= 10

14. n= 5

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

1. The cost 7 Books is =  7.75/ 5 x 7

                                    = $10. 85

2. He can lay = 144/3 x 7

                      = 336 bricks

3. 4/24 = n/6

6 x4 = 24n

n= 1

4. 30/5 = 6/ n

 30 n = 30

 n= 1

5. n/6 = 27/ 9

  9n = 162

  n= 18

6. 50/ 70= n/7

n= 5

7. 14/7 = 6/n

2n= 6

n= 3

8. n/15= 2/5

 n=6

9. 4/10 = n/ 15

n= 6

10. 4/200 = n/ 100

n= 2

11. 6/n= 5/10

n= 12

12. 32/22 = 96/ n

n= 66

13. 6/3 = n/5

n= 10

14. 2/n = 4/ 10

n= 5

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The two numbers whose sum is 20 and sum of their squares is 218 are

13 and 7 respectively.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Let, The two numbers be a and b.

Given, The sum of two numbers is 20 which is, a + b = 20...(1) and the sum of their squares is 218 which is, a² + b² = 218...(2)

We know, (a + b)² = a² + 2ab + b².

Therefore, 20² = 218 + 2ab.

2ab = 400 - 218,

2ab = 182.

ab = 91...(3)

Now, (a - b)² = a² + b² - 2ab.

(a - b)² = 218 - 182.

(a - b)² = 36.

a - b = 6...(4).

Adding (1) and (4) we get,

2a = 26.

a = 13 and hence b = 7.

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calculator is going to be the most accurate

No, because being older than 55 and being pregnant are not independent events.

If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162 because being older than 55 and being pregnant are not independent events.

A random number is one that is selected by chance, or randomly, from a set of numbers, as the name suggests. There is an equal chance that any one of the numbers in a given distribution will be chosen at random.

The concepts of randomness are formally defined in the fields of mathematics, probability, and statistics. A random variable in statistics is the process of assigning a numerical value to each potential result of an event space. The identification of the events and the estimation of their probabilities are made easier by this association.

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If the degree of the equation is two, then the result leads to the quadratic equation. The following equations are entitled to the quadratic equations.

[tex]- $\mathrm{y}=2 \mathrm{x}^2$- $\mathrm{y}=2 \mathrm{x}^2-8$- $y=2 x^2-3 x-8$[/tex]

What is a quadratic equation?

In the quadratic equation, the maximum power of the variable is 2 . It consists of  [tex]$x^2, x$,[/tex] and the constant term.

Given

1 .[tex]$y=2 x^2$[/tex]

2. [tex]$y=2 x^2-8$[/tex]

3. [tex]$\mathrm{y}=-2+2 \mathrm{x}-8$[/tex]

4.[tex]$\mathrm{y}+3 \mathrm{x}=2 \mathrm{x}^2-8$[/tex]

5. [tex]$\mathrm{y}+3 \mathrm{x}^2=2 \mathrm{x}+3 \mathrm{x}^2-8$[/tex]

[tex]y=2 x^2[/tex]

The above expression is a quadratic equation.

2.

[tex]y=2 x^2-8[/tex]

The above expression is a quadratic equation.

3.

[tex]y=2 x-10[/tex]

The above expression is not a quadratic equation.

4.

[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x} & =2 x^2-8 \\\mathrm{y} & =2 x^2-3 x-8\end{aligned}[/tex]

The above expression is a quadratic equation.

5.

[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x}^2 & =2 x+3 x^2-8 \\\mathrm{y} & =2 x-8\end{aligned}[/tex]

The above expression is not a quadratic equation.

Thus, the third and fifth are not quadratic equations and the first, second, and fourth are quadratic equations.

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Answer:

--------------------

From the series we can observe:

Use the nth term equation to find the value of n:

Apply this to the last term and solve for n:

--------------------------------------------------------------------

Given

Infinite sequence:

It has:

Find the sum of terms:

Correct choice is D.

Answer:

132 square inches

Step-by-step explanation:

The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 6 inches, the area of the base is 36 square inches (6 inches x 6 inches).

To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.

To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.

In this case, the base of the triangle is 6 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 6 inches x 8 inches = 24 square inches.

Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 24 square inches = 96 square inches.

To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 36 square inches + 96 square inches = 132 square inches. Therefore, the surface area of the pyramid is 132 square inches.

The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.

Given that,

A bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook. Three cookbook copies and one copy of the brand-new book were sold the next day, bringing in $89 for the company.

We have to find what the cost of each book was.

We know that,

A bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel.

The next day it took in $ 89 on the sale of 3 copies of the cookbook and 1 copy of the novel.

An algebraic expression-based system of equations is a collection of relationships between several unknown variables.

Now,

Let x= cookbook and y= novel.

So,

On first day, 5x + 3y = 167----->equation(1)

On second day, 3x + 1y = 89----->equation(2)

These equations must be solved in order to determine the cost of each book.

From equation(2), we get;

y = 89 - 3x

Now we use this x solution to solve our first equation.

We get;

5x + 3(89-3x) = 167

5x + 267 - 9x = 167

267-167 = 9x - 5x

100 = 4x

x = 25

So, The price is $25 for the each Cookbooks.

Now, By substituting $25 for x in the second equation, we must get the value of y.

y=89-3(25)

y=89-75

y=14

So, The price is $14 dollars for each novel.

So,

Therefore, The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.

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All potential values of x are represented by the inequality x≤20.

A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.

An inequality displays the difference between two variables, whereas an equation displays the equivalence of two variables.

So, the inequality that also represents all the possible values of x is:

On Mondays, Kelli walks no more than 25 dogs.

Also, Ms. Lincoln's five dogs are walked by Kelli.

Along with Ms. Lincoln's dogs, the inequality to determine how many additional dogs Kelli walks on Monday is written as:

x+5 ≤ 25

Take 5 away from both sides.

x + 5 - 5 ≤ 25 - 5

x ≤  20

Therefore, all potential values of x are represented by the inequality x≤20.

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Complete question:
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?

Answer:

635 kg

Step-by-step explanation:

1 pounds = 0.453592 kg

1400 = 0.453592 x 1400

=635.0288

=635 kg