In the short run, if average variable cost equals $50, average total cost equals $75, and output equals 100, the total fixed cost must be
A. $25
B. $2,500
C. $5,000
D. $7,500

The variable part is  x and b.

A mathematical object is represented by a symbol known as a variable. A variable can be a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations using variables solve a variety of problems in a single operation. By substituting the numerical values of the equation's coefficients for the variables that represent them in the quadratic formula, the quadratic formula, for instance, can be used to solve any quadratic equation.

Given a equation -6bx

here -6  is constant because it cannot be changed;

a number that has a proper worth in a given circumstance or generally or that is normal for some substance or instrument.

and x, b are variables,

A variable is an amount that might change inside the setting of a numerical issue or examination.

Hence for the equation x and b are variables.

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Answer:

7w^2+3x^2-24wx

Step-by-step explanation:

we distribute

(3x-w)(3x-7w)

3x(3x)+3x(-7w)-w(3x)-w(-7w)

3x^2-21wx-3wx+7w^2

combine like terms

3x^2-24wx+7w^2

order correctly

7w^2+3x^2-24wx

hopes this helps

Answer:

[tex]9x^2-24xw+7w^2[/tex]

Step-by-step explanation:

Given expression:

[tex](3x-w)(3x-7w)[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{FOIL Method}\\\\$(a+b)(c+d)=ac+ad+bc+bd$\\ \end{minipage}}[/tex]

Apply the FOIL method to expand the brackets:

[tex]\implies 3x \cdot 3x +3x \cdot(-7w)+(-w) \cdot 3x+(-w) \cdot (-7w)[/tex]

[tex]\implies 9x^2-21xw-3xw+7w^2[/tex]

Combine like terms:

[tex]\implies 9x^2-24xw+7w^2[/tex]

since to> t∝/ ₂₁n-2 we reject H₀ and conclude that the exam grade is significant related to the no of hours of studying

X = 1         3         3           3       5

Y=  55      75      80       85      100

What is hypothesis ?

A hypothesis is an unproven claim that is backed up by all the information that is now available and a lot of weaker results in mathematics.

n=5

∑x=15

∑x²=53

∑y=395

∑x²=32275

∑xy=1275

Sxx= ∑x²-1/n (∑x)² =8

Syy= ∑y²-1/n (∑y)² =1070

Sxy= ∑xy²-1/n (∑x)(∑y) =90

= Sxy/sxx =90/8 =11.25

x= 395/5 =11.25 (15/5)

=45.25

y=45.25 +11.25 x

if x=2, y=45.25 +11.25 (2) = 67.75

3. coefficient of determination

R² = SSR/SST = β₁ SXY/SYY

R₂ = 11.25 X 90/1070

=0.946

4. M = SYY -β₁ SXY/n-2

=1070-11.25(90)

=19.167

Hypothesis = H₀ :β₁ =0

H₀ :β₁ [tex]\neq[/tex]0

Test statistic = t = β₁/

t₀ =11.25/

t₀=7.27

critical value= t∝/₂₁n-2

= t0.005

=5.841

since to> t∝/ ₂₁n-2 we reject H₀  ( Hypothesis) and conclude that the exam grade is significant related to the no of hours of studying

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The correct interpretation for the statement D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.

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

The function D gives the depth of the water, in meters, t hours after midnight on a certain day

This means that

D = depth in meters

t = time in hours

From the question, we have

Notation = D(n)

Also, from the question, we have

D'(8) = -0.5

This is the inverse of the function D(t)

So, the values of the parameters are

D(t) = -0.5

t = 8

This means that the number of hours is 8 and the depth is -0.5 meters

Hence, the interpretation of D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.

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The distance traveled by a particle with position (x, y) as t varies in the time interval 0 ≤ t ≤ 3π be, 6π units.

Given, a particle with position (x, y) move across a distance as t varies in the given time interval 0 ≤ t ≤ 3π

where, x = sin2t, y = cos2t

On using the length of the curve concept, we get

d = ∫√((dx/dt)² + (dy/dt)²) dt

as, x = sin2t and y = cos2t

dx/dt = 2cos2t

dy/dt = -2sin2t

On substituting the values, we get

d = ∫√(4cos²2t + 4sin²2t) dt

d = ∫2 dt

d = 2∫dt

d = 2×(3π - 0)

d = 6π

So, the distance traveled by the particle be, 6π

Hence, the distance traveled by the particle be, 6π

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Answer:

1.362 kilograms

Step-by-step explanation:

3 x .454 = 1.362 Kilograms

The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.

To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:

Step 1: Start with the number 625.

Step 2: Take the fourth root of 625.

Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.

Step 3: Determine the number that, when raised to the power of 4, equals 625.

To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..

Step 4: Solve the equation [tex]x^4 = 625[/tex].

To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]

The fourth root of 625 is (625)^(1/4).

Step 5: Simplify the expression.

We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:

[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]

Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.

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The number of ways to put eight different books in five boxes, of no box is allowed to be empty will be 403200.

As, it is given that,

No box is allowed to be empty.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. For instance, the set A=1,2 has a permutation of 2, which is 1,2, or 2,1. There is no alternative way to organize the components of set A,

So, we can put one book in each box in [tex]8 P_5[/tex] mays.

Now remaining 3 books we can put in by [tex]${ }_5 P_3$[/tex] ways

Total number of ways will be [tex]$=8 P_5 \cdot 5 P_3$[/tex]

Now calculating the value,

[tex]=\frac{8 !}{(8-5) !} * \frac{5 !}{(5-3) !}\\\\=\frac{8 !}{3 !} \times \frac{5 !}{2 !}\\\\=403200[/tex]

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The homeowner should go with option 1 for his budget of $40,200 to use complete budget.

Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").

ax² + bx + c = 0

where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.

Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.

Given a rectangular pool of  35-foot by 20-foot

area of pool = 35 x 20 = 700 sq. foot

and to built a patio around pool of equal width,

budget of patio of $40,200 all amount to be used,

Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.

the area covered by amount is 40200/50 = 804

let width of patio be x

new length = 35 + x and new breadth = 20 + x

area covered by patio = new area including width - area of pool

new area including width = area covered by patio +  area of pool

new area including width = 804 + 700 = 1504

1504 =  (35 + x)(20 + x )

1504 = x² + 35x + 20x + 700

x² + 55x - 804 = 0

solving the equation by quadratic formula

x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/ 2a

where a = 1, b = 55, and c = -804

x = (-55 ± [tex]\sqrt{(55)^{2} - 4*1*(-804) }[/tex])/2

x = (-55 ± √(3025 + 3216))/2

x = (-55 ± 79)/2

taking positive values

x = (-55 + 79)/2 = 12

new length = 35 + 12 = 47 foot

new breadth = 20 + 12 = 32 foot

area covered by patio = (47x32) - (35x20)

area covered by patio = 804 sq. foot

and cost will be 804 x 50 = $40,200

for option 2:  Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.

area for patio = 40200/80 = 502.5

since the area is in fraction the cost will come in approximation.

Hence the homeowner should go with option 1 for complete use of budget.

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The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.

What is trigonometric form ?

Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.

Given

8 + 3i

Required

Rewrite in trigonometric form.

The trigonometric form of a complex equation is

z = r[cosθ + isinθ]

Let a = 3 and b = 8

Where

r is calculated by

r² = b² + a²

And

θ is calculated by

θ = arctan(a/b)

Substituting 3 for a and 8 for b

r² = a² + b² becomes

r² = 3² + 8²

r² = 9 + 64

r² = 73

√r² = √73

r = √73

r = 8.544

Calculating θ

θ = arctan(a/b) becomes

θ = arctan(3/8)

θ = arctan(0.375)

θ = 20.556°

θ = 20.6 --- Approximated

Hence, z = r[cosθ + isinθ] becomes

z = 8.544[cos(20.6) + isin(20.6)}

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Answer:

4x³ + 5x² - 30x + 18

Step-by-step explanation:

(4x - 3)(x² + 2x - 6)

each term in the second factor is multiplied by each term in the first factor.

4x(x² + 2x - 6) - 3(x² + 2x - 6) ← distribute parenthesis

= 4x³ + 8x² - 24x - 3x² - 6x + 18 ← collect like terms

= 4x³ + 5x² - 30x + 18

Five 1/2 inch cubes fit along it’s 2 1/2 length.

An object's longest or largest dimension is a measured distance. Dimensions: 10 ft. see Weights and Measures, Metric System Table

An object's length, which is a measurement of its longest side, is its most stretched dimension. Your dog, for instance, would measure its length from the point of its nose to the end of its tail. The space between its top and bottom feet is greater than that of the creature's head.

In addition to utilizing handspan, foot span, and other methods, one can measure length in many units, such as centimeters, inches, meters, and so on.

Let x be the number of 1/2 cubes to fit 2 1/2 length

(1/2)x= 2 1/2

(1/2)x=5/2

x=5

Therefore, five 1/2 inch cubes fit along it’s 2 1/2 length.

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The range and domain of the graph shown is

domain -4 ≤ x < ∞

range ∞ ≤ x < 3

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a graph is every value in the graph, from left to right.

Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as

-4 ≤ x < ∞

The graph's entire range, from lower to higher numbers, in the vertical line represents the range.

Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as

∞ ≤ x < 3

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Answer:

22

Step-by-step explanation:

(8 + 20) - ((8 * 9) ÷ 12)

Using PEMDAS, let us find the product to get;

(8 + 20) - (72/12)

Next operation is to divide what is in the bracket to get:  

(8 + 20) - 6

Next operation is addition of the bracket content to get; 28 - 6

Next operation is to carry out subtraction to get:  22

Thus, the total number of days taken to make the batch of pens is 22.

Answer: a. 40%

Step-by-step explanation: 48% of 120 is 40

Answer: a. 40%

Step-by-step explanation:

48/120 = x/100

butterfly method

120x/120 = 4800/120

simplify.

x = 40%

Answer: 7

Step-by-step explanation: 13+1=14

2*?=14            2*7=14

The present p value which have to be invest in future is $7619.05 at simple interest rate r.

Simple Interest:

Simple interest (S.I) is a method of calculating the amount of interest on a specific amount of money.

The simple interest formula helps determine the amount of interest given a principal, interest rate, and term.

The formula for simple interest is:

SI = PTR/100

where SI = simple interest

P = principal

R = interest rate (percentage)

T = term (years)

For calculating total amount

             Amount (A) = principal Book (P) + Interest (I)

where

Amount (A) is the total amount repaid at the end of the borrowed period.

The simple interest total amount formula can also be written as:

                                    A = P(1 + RT)

where

A = Total amount after specified period

P = Principal or original loan amount

R = Interest rate (annual)

T = Time (annual )

According to the Question:

Simple interest: I = PTR            ---------------------------- (1)

Future amount : A = p + I = p + PTR         ------------------ (2)

Given that:

r = 10% = 0.1

t = 6 months = 0.5 year

A = future amount = 8000

Now,

8000 = p + p (. 1)(0.5)

⇒ 8000 = 1.05 p

⇒ p = 8000/1.05

⇒ p = $ 7,619.05

Now,

Putting the value of p in equation (2)

I = 7619.05 (0.1) (0.5 ) = 380.95

7619.05 + 380.90 = $8,000

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Note that Option A is pairwise and is relatively prime.

If every pair of elements in a list of integers is relatively prime, the list is pairwise relatively prime. For example, the numbers 121, 122, and 123 are relatively prime pairwise (even though they are each composite).

You can tell if a set of numbers are relatively prime if they do not share a common factor other than ±

Looking at set a:
11, 15, 19

Writing their prime factorization

11 = 11

15 = 3 x 5

19 = 19, hence since any pair of these numbers does not have any common factor, hence they are relatively prime.

Looking at set b:

14, 15, 21
Writing their prime factorization, we have:

14 = 7 x 2
15 = 3 x5

21 = 3 x 7

15, and 21 share a common factor of 3 while

14 and 21 share a common factor of 7, therefore, they are NOT relatively prime.

Looking at set c)
12, 17, 31, 37
Writing their prime factorization,
12 = 3 x 2²
17 = 17

31 = 31

37 = 37

In this case, no pair of these numbers have any common factor. Hence they are relatively prime.

Looking at set d)

7,8,9, 11, spelling out their prime factorization

7=7

8=2³
9=3²
11=11

Thus, any pair of these numbers do not have a common factor, hence they are relatively prime.

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Qualitative variables include all observable qualities or characteristics of a group or population that can not be measured numerically.

What is Qualitative?

The goal of qualitative research is to collect and examine non-numerical data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality.

Quantitative Variable

Quantitative variables, as the name implies, are those that can be expressed by a numerical value.

1. Quantitative (Discrete)

2. Quantitative (Continuous)

3. Quantitative (Discrete)

4. Qualitative (nominal)

5. Qualitative (nominal)

6. Qualitative (nominal)

7. Qualitative (nominal)

8. 9. Quantitative (Continuous)

10. Qualitative (nominal)

11. Quantitative (Continuous)

12. Qualitative (ordinal)

13. Qualitative (nominal)

14. Quantitative (Discrete)

15. Qualitative (nominal)

Complete question: Which is the following a qualitative or quantitative variable?

1)ordinal

2)Continuous

3)nominal

4) All of these

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Answer:

A ' ( -21, 14 )

B ' ( 28, 14 )

C ' ( -7, -7 )

Step-by-step explanation:

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x,y)—-> (7x,7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hopes this helps!!

The value of AC according to given equation of Parallelogram is 188 units.

What is parallelogram?

In elementary geometry, a parallelogram may be a  quadrilateral with 2 pairs of parallel sides. the alternative or facing sides of a quadrangle square {measure} of equal length

Main body:

according to question:

AE = 9X-5

AC = 14X+34

as E is midpoint of AC so , we can say

2AE = AC

2(9x-5)= 14x+34

18x-10= 14x+34

4x = 44

x = 11

Now we need to find AC = 14x+34

                                         = 14*11+34

                                         = 188 units

Hence the value of AC according to given equation of Parallelogram is 188 units.

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The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is [tex]-8.6+3.15[/tex].

What is formula for slope and intercept is?

[tex]$$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$[/tex]

The slope is

[tex]$$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$[/tex]

The intercept is

[tex]$$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$[/tex]

The regression equation is

[tex]$$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$[/tex]

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Answer:

Factors are (x-1) (4x²-1)

Zero(s) are x = 1, x = 1/2, x = -1/2

Step-by-step explanation:

Given function is

4x³ - 4x² - x + 1

= 4x³ - x - 4x² + 1

= x(4x² - 1) - 1(4x² - 1)

= (x - 1) (4x² - 1) (Factors of the equation)

To find the zero(s),

Either, Or,

x - 1 = 0 4x² - 1 = 0

or, x = 1 or, x² = 1/4

or, x = √(1/4)

or, x = +- 1/2

Answer:

x = 5

Step-by-step explanation:

To solve this problem, we need to utilize the triangle sum theorem.

⭐What is the triangle sum theorem?

1. Set up the equation as per the triangle sum theorem

(5x+6) + 43 + 106 = 180

2. Add the constants

5x + 155 = 180

3. Subtract 155 from the LHS and RHS

5x = 25

4, Divide the LHS and RHS by 5 to isolate x

∴ x = 5

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The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

Given that,

The complete statement is,

The p-value is given as:

[tex]p=0.013[/tex]

Express as percentage

[tex]p=1.3[/tex] %

This means that the probability that the linear correlation coefficient is at least as extreme is 1.3%.

From the z-table, we have:

[tex]z = 1.81[/tex],  when the p-value is 0.013

This value of z-score is low, compared to the percentage of the scores have a z-score of between -1 and 1.

So, the p-value implies that it is likely that there is a linear correlation between the variables.

Hence, the texts that complete the three blanks are: "1.3%", "low" and "is"

Therefore,

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

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The number of calls she makes per day is 12

A function can be defined as an expression, law or rule that describes the relationship between two variables.

These expressions are termed;

From the information given, we have that the function is;

C = 80-7h

Where;

I day = 24 hours

Now, substitute the value into the formula

C = 180 - 7(24)

expand the bracket

C = 180 - 168

Subtract the values

C = 12

Hence, the value is 12

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Answer:

B

Step-by-step explanation:

the hypotenuse is z

For the Pythagorean theorem:

x² + y² = z²

Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.

First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.

Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.

Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.

Step-by-step explanation: