For a certain company, the cost function for producing x
items is C(x)=50x+250
and the revenue function for selling x
items is R(x)=−0.5(x−120)2+7,200
. The maximum capacity of the company is 170
items.

The questions have been answered below based on the concept of apportionment.

Here, we have,

Apportionment is the challenge of distributing a certain number of items among groups of varying sizes. The Mathematics of Apportionment discusses the mathematical concepts and methods used to allocate identical things fairly among parties with differing claims.

In question 1, the quantity that does not vary from state to state when we apportion congress representatives to different states is called the standard quota.

In question 2, the standard quota is found by dividing the state's population by the standard divisor.

In question 3, the modified divisor in Webster's method is found by dividing the state's population by the modified divisor.

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Based on an equation, the minimum number of years it will take the population of North Dakota to equal the population of South Dakota given the current rates of growth is 15.3 years.

An equation describes the equality or equivalence of two or more mathematical expressions.

Equations use the equal symbol (=), while mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

The population of North Dakota in 2012 = 0.7 million

The yearly population growth rate = 0.028 million

The population of South Dakota in 2012 = 0.83 million

The annual population growth rate = 0.0195 million

Let the number of years for the populations to equal = x

0.7 + 0.028x = 0.83 + 0.0195x

0.0085x = 0.13

x = 15.3 years

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The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.

[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]

=1+4+25+16

=46

[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]

=1+1+1+100

=103

[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]

Therefore, [tex]A_2B_2=4738[/tex]

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

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An equation and solution that describe the situation is: B. The equation 1/8(x + 16) = 76 represents the situation, where x is the food bill.

In order to write a linear equation to describe this situation, we would a assign variable to the food bill, and then translate the word problem into a linear equation as follows:

Let the variable x represent the total amount of the food bill.

Since this group of 8 friends spent a total of $76, which included the food bill and a tip of $16, and decided to split the bill and tip evenly among themselves, a linear equation that can be used to model this situation is given by;

1/8(x + 16) = 76

(x + 16) = 76(8)

x + 16 = 608

x = 608 - 16

x = $592.

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"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".

A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.

The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.

In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.

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Changing the base from 5/7 to 7, the end behavior of the function would be given as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

Changing the base to 7, it would have an absolute value greater than 1, hence the function would be increasing with the end behavior given as follows:

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The equation of the function g(x) is g(x) = f(x+3) + 4 and g(x) = log₂(x+3) + 4

To shift the function 3 units left, we replace x with x+3. To shift it 4 units up, we add 4 to the function.

Therefore, the expression for g(x) in terms of f(x) is:

g(x) = f(x+3) + 4

Substituting f(x) = log₂(x), we get:

g(x) = log₂(x+3) + 4

The equation of the function g(x) is g(x) = log₂(x+3) + 4.

The domain of g(x) is all x such that x+3 > 0, since the argument of the logarithm must be positive.  This gives x > -3.

The range of g(x) is all real numbers, since the logarithm takes on all real values.

The vertical asymptote is x = -3, since this is where the function becomes undefined (the argument of the logarithm becomes 0).

The horizontal asymptote is y = 4, since as x approaches infinity or negative infinity, the function approaches 4.

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The graph of the inequality y ≥ (x+2)^2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y is greater than or equal to (x+2)^2

Express the statement properly

So, we have

y ≥ (x+2)^2

The above expression is a an inequality of a quadratic function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the expression in a graphing tool and attach the display

See attachment for the graph

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An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 6)/(-6 - 0)

Slope (m) = 0/-6

Slope (m) = 0.

At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 0(x - 0)

y - 6 = 0

y = 6

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The framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

Explanation :

The statement that best explains that Article III of the constitution gives congress the ability to create lower courts inferior to the supreme court from "time to time" is that the framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

As there will be more framers of the constitution which gave them as a  congress the power to create lower courts as they wanted that the congress should have authority over the courts and to control them.

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complete question:

Which statement best explains why Article lll of the constitution gives Congress the ability to create lower courts inferior to the Supreme Court “from time to time”?

The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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Answer: [tex]\frac{8}{15}[/tex]

Step-by-step explanation: In total, Patty placed 45 slips of paper in a bag(10+9+8+7+6+5). Out of those 45 slips of paper, only 24 had even numbers on them(10+8+6), resulting in the fraction [tex]\frac{24}{45}[/tex]. If you divide both 24 and 45 by 3, the fraction can be simplified to [tex]\frac{8}{15}[/tex].

Answer:

180 square inches

5 x 6 = 32.5

32.5 x 4 = 130

5 x 5 = 25

25 x 2 = 50

130 + 50 = 180

Step-by-step explanation:

first find the area of all the sides (length times width)

width = 5

length = 6.5

5 x 6.5 = 32.5

32.5 is the area for one side. there are 4 others identical to it

32.5 (one side) x 4 (the amount of sides identical) = 130

then you need to find the area for the bottom/top side

5 = length

5= width

5(L) x 5(W) = 25

25 is the area for the bottom. the top is identical to it

25(bottom side) x 2 (the amount of sides identical)

now add all of the sides up

130 + 50 = 180

The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The value of x in the rectangle is,

⇒ x = 6

We have to given that;

Corresponding angles are,

⇒ (8x + 19)° and (21x - 13)°

Hence, We can say that;

⇒ (8x + 19)° + (21x - 13)° = 180°

⇒ 29x + 6 = 180

⇒ 29x = 174

⇒ x = 174/29

⇒ x = 6

Thus, The value of x in the rectangle is,

⇒ x = 6

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Check the picture below.

The confidence interval of the given data is (117, 107).

Given that:

Sample mean X = 112

Standard deviation σ = 45

Sample size n = 81

Confidence level = 99.7%

Z Score = (x − μ )/σ

Z score = 0.9944

Confidence interval = X±z (σ/√n)

= 112±0.9944(45/√81)

= 112±0.9944(5)

= 112±4.972

= 112+4.972 or 112-4.972

= 116.972 or 107.028

= (117, 107)

Therefore, the confidence interval of the given data is (117, 107).

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The similarity statement is completed as below

Triangle MTA ~ triangle HTM ~ triangle HMA

A similarity statement is a statement in mathematics that expresses the affinity between two or more figures.

These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.

The similar triangles are

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A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.

The discount is the difference between the original price and the discounted price.

Discount = $200 - $94 = $106

To find the percentage discount, we need to calculate what percentage of the original price the discount represents:

Percentage discount = (Discount/Original price) x 100%

Percentage discount = ($106/$200) x 100%

Percentage discount = 53%

Therefore, the discount, as a percentage, is 53%.

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Answer:

Option A is the correct choice that shows a function.

Step-by-step explanation:

What is a function?

A function is when there are no repeating "x" values.

For example:

These set of points: {(1,1), (1,2), (1,3), (1,4)} does not  show a function because there is repeating "x" values.

Option A shows that the points {(4,5), (5,5), (6,1), (8,2) is a function because there is no repeating "x" values.

The correlation coefficient for the data-set in this problem is given as follows:

r = 0.75.

To obtain the correlation coefficient of the data-set in this problem, we must insert the points of the data-set into a correlation coefficient calculator.

From the table, the points of the data-set are given as follows:

(0, 5.9), (0.8, 8.6), (1.3, 15.5), (1.6, 17.3), (13.3, 21.5).

Inserting these points into a calculator, the correlation coefficient is given as follows:

r = 0.75.

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The balance on the loan at the end of month 4 is approximately $289,836.23.

We are given that;

Amount borrowed= $290,000

Time 25 years

Payment=  $1, 530.73

Now,

To calculate the balance on the loan at the end of month 4, we can use the following formula2:

Balance = (Loan amount - Debt payment) * (1 + Interest rate / 12) - Debt payment

Where:

Loan amount is the original amount borrowed ($290,000)

Debt payment is the amount of principal paid in each monthly payment ($564.06 for the first month and $565.94 for the second month)

Interest rate is the annual interest rate divided by 100 (0.04)

Plugging in the values, we get:

Balance = ($290,000 - $564.06) * (1 + 0.04 / 12) - $565.94 Balance = $289,435.94 * 1.003333 - $565.94 Balance = $290,402.17 - $565.94 Balance = $289,836.23

Therefore, by the interest the answer will be $289,836.23.

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Answer:

Step-by-step explanation:

The equation given is:

120 + 1814x = 180 - 134x

We can simplify this equation by adding 134x to both sides:

120 + 1948x = 180

Next, we can subtract 120 from both sides:

1948x = 60

Finally, we can solve for x by dividing both sides by 1948:

x = 60/1948

Therefore, the solution is:

x = 0.0308 (rounded to four decimal places)

Answer:

To solve the equation, we need to first convert the mixed numbers to improper fractions:

120 + 18 1/4 x = 180 − 1 3/4 x

120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)

Multiplying both sides by 4 to eliminate the fractions, we get:

480 + 73x = 720 - 7x

Combining like terms, we get:

80x = 240

Dividing both sides by 80, we get:

x = 3

Therefore, the solution for x is 3.

The solution is,  the tangent of each angle that is not the right angle is:

angle tan A = 1.33

angle tan B = 0.75

Here, we have,

Given:

ABC is a right triangle.

angle ACB = 90

To find:

tan A

tan B

We know that tangent of an angle is given by the ratio

= opposite / adjacent

The opposite side and adjacent side is taken with respect to the angle for which the tangent is to be found.

tan A = BC/ AC

         = 8/6

         = 4/3

         = 1.33

and, tan B = AC/BC

                 = 6/8

                 =0.75

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Answer:

60 (C)

Step-by-step explanation:

65+55=120

180-120=60

Answer:

526.32

Step-by-step explanation:

Let's assume that the cost price of the bag is "C".

Selling Price = Cost Price - Loss

We get:

500 = C - 0.05C

500 = 0.95C

C = 500/0.95

C ≈ 526.32

Therefore, the cost price of the bag was approximately Rs 526.32.