a company produces a product for which the variable cost is $12.13 per unit, and the fixed costs are $92,000. the product sells for $17.10. let x be the number of units produced and sold.(A). The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. C = _____(B). Write the revenue ft as a function of the number of units sold. R = _____(C). Write the profit P as a function of the number of units sold. P = _____

If there are 4 boys and 4 girls , then the number of ways in which

(i) there is no restriction is 40320 ways  ,

(ii) not all girls sit together is 37440 ways  ,

(iii) no two girls sit together is 2880 ways  .

the number of boys in the class is =  4 boys ;

the number of girls in the class is = 4 girls ;

Part(i) ,

we have to find number of ways in which they can sit in a row where there is no restriction .

there are total of 8 persons ,

So ,the number of ways in which 8 persons can be arranged without any restrictions is = 8! ways.

= 40320 ways

Part(ii) ,

we have to find number of ways in which they can sit in a row where not all girls sit together.

the cases where all gets sit together is written as :

= B₁ , B₂ , B₃ , B₄ , G ⇒ 5! ways ;

= B: G₁ , G₂ , G₃ , G₄ ⇒ 4! ways ;

the number of ways all girls are together is = 5! × 4! ;

So , the number of ways not all girls are together is = 8! - 5!×4!  ;

= 37440 ways

Part(iii) ,

we have to find number of ways in which they can sit in a row where no two girls sit together.

this case can be denoted as : G , B₁ , G , B₂ , G , B₃ , G , B₄ .

So , the boys can be arranged in 4! ways ;

and there will be 5 places for 4 girls , which can be arranged in ⁵P₄ ways ;

total number of ways is = 5!×4! =  2880 ways .

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The solutions to the equation 5x² - 45 = 0 are -3 and 3.

Given the equation in the question;

5x² - 45 = 0

To solve using square root property, add 45 to both sides.

5x² - 45 + 45 = 0 + 45

5x² =  45

Divide both sides by 5

5x²/5 =  45/5

x² =  45/5

x² =  9

Take the square root of both sides.

√(x²) =  √9

x =  ±√9

x =  -3, 3

Therefore, the value of x are -3 and 3.

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The medians and IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

a. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 4.

b. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 2.c. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 3 and an IQR of 2, while distribution (2) has a median of 8 and an IQR of 2.

d. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 50 and an IQR of 50, while distribution (2) has a median of 500 and an IQR of 400.

The median IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

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The value of the expression when y = 10 and z = 5 is 5

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

0.3y + y/z

Also, from the question, we have the following values:

y = 10 and z = 5

substitute the known values in the above equation, so, we have the following representation

0.3y + y/z = 0.3 * 10 + 10/5

Evaluate the expression

0.3y + y/z = 5

Hence, the solution is 5

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A confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps. Thus, the correct answer is option D.

A confidence interval is a range of values that is likely to contain the true population parameter (in this case, the true probability of the cricket landing on its feet) with a certain level of confidence. The width of the interval depends on the sample size and the level of confidence.

In the first 50 jumps, the cricket landed on its feet 35 times out of 50, giving a proportion of 0.7. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively wide due to the small sample size.

In the final 10 jumps, the cricket landed on its feet only twice out of 10, giving a proportion of 0.2. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively narrow due to the large sample size.

When comparing the two intervals, it is clear that the interval based on the final 10 jumps is narrower than the interval based on the first 50 jumps. This means that after the final 10 jumps, Courtney has a more precise estimate of the true probability of the cricket landing on its feet than she did before the final 10 jumps.

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The complete question is -

Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the

time and on its back the other half of the time. In the first 50 jumps, Courtney's cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice.

Based on this experience, Courtney can conclude that -

A. the cricket was due to land on its feet less than half the time during the final 10 jumps since it had landed too often on its feet during the first 50 jumps

B. a confidence interval for estimating the cricket's true probability of landing on its feet is wider after the final 10 jumps than it was before the final 10 jumps

C. a confidence interval for estimating the cricket's true probability of landing on its feet after the final 10 jumps is exactly the same as it was before the final 10 jumps

D. a confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps

E. a confidence interval for estimating the cricket's true probability of landing on its feet based on the initial 50 jumps does not include 0.2, so there must be a defect in the cricket's construction account for the poor showing in the final 10 jumps

8/10m

1/2 + 3/10 =

5/10 + 3/10= 8/10

The surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.

The equation for the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane is given by -

x = 3y2 + 3z2

To explain this equation, let us consider a point P(x, y, z) on the surface. The distance from this point P to the x-axis is given by |x|, and the distance from P to the yz-plane is given by √y2 + z2.

Now, the given condition states that the distance from P to the x-axis is 3 times the distance from P to the yz-plane. This can be written as |x| = 3√y2 + z2. By squaring both sides, we get x2 = 9(y2 + z2), which can be rearranged to give the equation x = 3y2 + 3z2.

This equation thus gives the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.

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All of the statements about quadrilaterals that are true include the following:

A. all squares are rhombuses, but not all rhombuses are squares.

B. opposite angles in a parallelogram are congruent.

In Geometry, there are different types of quadrilateral and these include the following:

Generally speaking, a typical characteristics of all squares are rhombuses is simply that all squares are classified as rhombuses, but it is not all rhombuses that are classified as squares.

Additionally, the opposite angles of any parallelogram are always congruent because they form parallel lines. However, the diagonals of a rectangle, parallelogram, and trapezium are not perpendicular.

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Two points should be noted: The 15% is first calculated using your annual gross wage rather than your take-home pay. Second, the business match is not included in your 15%.

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The length of sides in congruent triangles are MN=30, MP=18, PN=30

QR=30, RS=30,  SQ=18

In the diagram two congruent triangles are given ΔPMN ≅ ΔQSR.

So by CPCTC (corresponding parts of congruent triangles are congruent)

In ΔPMN and ΔQSR

PN=QR=30 in.

PM=SQ=18 in.

MN=RS= 30 in.

PN=QR=30 then PN=30

PM=SQ =18 then PM=18

MN=RS =30 then MN=30

Congruent triangles are the triangles of which all the sides and all the angles are congruent.

If two triangles are said to be congruent then its all corresponding parts must be equal.

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Answer:

me neither bro

Step-by-step explanation:

The value of b1 = -21, b2 =33, and b3 = 6 in the given matrix.

A collection of integers lined up in rows and columns so to produce a rectangular array is called a matrix. The elements, or inputs, of the matrix are the integers.

A single matrix is created through matrix multiplication, sometimes referred to as matrix product and the multiplication of two matrices. This kind of binary operation is used. A scalar multiplication occurs when an integer is multiplied by a matrix. Scalar multiplication is the process of multiplying a matrix by a scalar value.

For the given matrix multiply each term of the matrix with 3 to obtain the value of b1. b2, and b3.

[tex]3\left[\begin{array}{ccc}-7\\11\\2\end{array}\right] = \left[\begin{array}{ccc}-21\\33\\6\end{array}\right][/tex]

Hence, the value of b1 = -21, b2 =33, and b3 = 6.

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Answer:x=1 y=5

Step-by-step explanation:

An equation of the line that passes through two points (x1,y1) and (x2,y2) can be found using the slope-intercept form:

Slope intercept form: what is it?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we use the following formula:

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

Plugging in the coordinates of the points given, we get:

m = (10 - 1) / (0 - 3) = -9/3

To find the y-intercept, we can use either of the given points and the slope:

b = y - mx

Plugging in the coordinates of the point (3,1) and the slope, we get:

b = 1 + (9/3) * 3 = 4

So the equation of the line that passes through (3,1) and (0,10) is:

y = -3x + 4

It's also possible to use the point slope form of a linear equation, which is y-y1=m(x-x1)

y - 1 = -3(x-3)

y = -3x + 9

Both equations are valid and represent the same line.

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The inequality is z = 3 a solution. The correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per option (A), the inequality is given as follows:

z+5 ≥ 9

z ≥ 9 - 5

z ≥ 4

As per option (B), the inequality is given as follows:

z+5 > 9

z > 9 - 5

Apply the subtraction operation,

z > 4

As per option (C), the inequality is given as follows:

z + 5 ≤ 8

z ≤ 8 - 5

z ≤ 3

Since the solution is less than or equal to three,

Then, this inequality is z = 3 a solution.

Hence, the correct answer would be option (C).

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This question seems incomplete, the complete question would be as:

For which inequality below is z = 3 a solution?

A. z+5 ≥ 9

B. z+5 > 9

C. z+5 ≤ 8

D. z+5 <8

The values of x and y that makes the figure a parallelogram are x = 17 and y = 26

A parallelogram is a four-sided geometric shape that has opposite sides that are parallel to each other.

The opposite sides of a parallelogram have the same length, and the opposite angles are also equal. The opposite sides of a parallelogram are also known as the bases, and the other two sides are known as the legs.

Since the opposite sides of a parallelogram are equal in length, we can say:

3x + 6 = 4 - x

3x + x = 4 - 6

4x = -2

x = -2/4

x = -1/2 = -0.5

y + 2 = 2y - 3

2 + 3 = 2y - y

5 = y

y = 5

Likewise, the opposite angles of a parallelogram are equal, so we can say:

(4x - 12)° = (3x + 5)°

4x - 12 = 3x + 5

4x - 3x = 5 + 12

x = 17

(3y + 46)° = (5y - 6)°

3y + 46 = 5y - 6

46 + 6 = 5y - 3y

52 = 2y

2y = 52

y = 52/2

y = 26

Thus, x = 17 and y = 26 makes the figure a parallelogram

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The volume of the solid that is in the parabola is 3.48[tex]\pi[/tex] after integration will carried out.

Parabola is a U shape curve whose eccentricity is 1.

The equation of parabola is y = 2-3x² and the x axis.

The cross section is perpendicular to y axis and the square.

The parabola is passes through the x axis put y = 0 in the equation of parabola.

0 = 2-3x²

x = [tex]\sqrt{\frac{2}{3} }[/tex]

Volume of the solid = [tex]\pi r^{2}h[/tex]

here r = y and h = dx

[tex]\pi (2-3x^{2} )^{2} dx=dv\\dv = \pi (9x^{4}-12x^{2} +4)dx\\[/tex]

Now, integrate the given equation to get the volume of the solid.

∫dv = ∫π(9x⁴-12²+4)dx

Put limits [tex]\sqrt[2]{\frac{2}{3} }[/tex] to 0

After integration and putting the limit we got V = 3.48[tex]\pi[/tex].

Hence, the volume of the solid is 3.48π.

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The complete question is:

Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 2 − 3x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

The inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).

(a). G(s)= 1 / s(s+2)(s+3)

Using partial fraction expansion, we can write G(s) as 1/s + 2/s+2 + 3/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 1/s is 1, the inverse Laplace transform of 2/s+2 is 2e^(-2t) and the inverse Laplace transform of 3/s+3 is 3e^(-3t). Therefore, the inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).

(b). G(s)= 10 / (s +1)^2(s+3)

Using partial fraction expansion, we can write G(s) as 5/s+1 + 5/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 5/s+1 is 5e^(-t) and the inverse Laplace transform of 5/s+3 is 5e^(-3t). Therefore, the inverse Laplace transform of G(s) is 5e^(-t) + 5e^(-3t).

(c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x

Using partial fraction expansion, we can write G(s) as 50/s + 50/s+1 + 50/s+2 + 50/s+4. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 50/s is 50, the inverse Laplace transform of 50/s+1 is 50e^(-t), the inverse Laplace transform of 50/s+2 is 50e^(-2t) and the inverse Laplace transform of 50/s+4 is 50e^(-4t). Therefore, the inverse Laplace transform of G(s) is 50 + 50e^(-t) + 50e^(-2t) + 50e^(-4t)e^-x.

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The distribution of z-scores would be a normal distribution centered at 0, with a standard deviation of 1.

The distribution of time it takes for people to solve a certain Sudoku puzzle is strongly skewed to the right. This means that most people take a shorter amount of time to solve the puzzle, but some take a longer amount of time. The mean (average) of this distribution is 30 minutes and the standard deviation is 15 minutes.

To find the distribution of z-scores, we need to convert the times into z-scores, which is done by subtracting the mean (30) from each time and then dividing by the standard deviation (15). This gives us a new distribution of z-scores, which is centered at 0 (since the mean of the times was subtracted from each time) and has a standard deviation of 1.

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The amount of hardwood floor that Jahidel waxed is 3 8/9 yards²

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 amount of hardwood floor that Jahidel waxed be A

Now , the equation will be

The total area of the hardwood floor is = 4 3/8 yards²

The total area of the hardwood floor is = 35/8 yards²

The amount of floor waxed by Jahidel A = ( 8/9 ) x total area of the hardwood floor

Substituting the values in the equation , we get

The amount of floor waxed by Jahidel A = ( 8/9 ) x ( 35/8 ) yards²

On simplifying the equation , we get

The amount of floor waxed by Jahidel A = ( 35/9 ) yards²

The amount of floor waxed by Jahidel A = 3 8/9 yards²

Hence , the amount of floor waxed is 3 8/9 yards²

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Answer:

Is it 0? sorry if this is wrong

Step-by-step explanation:

Answer:

f(g(0)) = -2

Step-by-step explanation:

We have our two equations, f(x) and g(x).

We work our way from the inside to the outside. Our inside equation is g(0). If we match g(x) to that, that would mean x = 0. So on that g(x) graph, when the x=0, the graph intercepts the y axis at y = 1.

Now that we know that g(0) = 1, we can plug that into the original equation, making it f(1) instead of f(g(0)). Now that we have f(1), we can go to our f(x) equation.

Matching the equations, it shows the x=1. On our f(x) graph, we'll find x=1 and trace down or up (down in this case) to the point where the graph intercepts at that point. Thats where we can then trace that point to the y axis and we see that our line hits the y axis at -2, making that the answer.

The solution for the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p is p = -4.19/6.1

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

2.3p - 10.1 = 6.5p - 4 - 0.01p

Solve for p.

2.3p - 10.1 = 6.5p - 4 - 0.01p

Combining the like terms.

2.3p - 10.1 = 6.49p - 4

4 - 10.1 = 6.49p - 2.3p

-6.1 = 4.19p

p = -4.19/6.1

Thus,

The solution is p = -4.19/6.1

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Answer:

1. Funnel cakes- 12

2. Oreos- 21

Step-by-step explanation:

1. x= 42/3.50

x=12

2. y= 42/2

y= 21

Paul will not be able to buy what he wants in terms of White Fabric and will need to buy 21 centimeters of white fabric elsewhere.

To find out if Paul will be able to buy all that he needs from the store, you need to convert the fabrics needed to a similar unit as the fabrics the shops have.

The stores have 3 meters of red fabric and 3 meters of white fabric. In centimeters this is:

1 meter = 100 centimeters

The centimeters are:

= 3 x 100

= 300 cm of each material

Paul needs 254 centimters of red fabric so will find what he needs.

He needs 321 centimeters of white fabric and so will need to buy elsewhere:

= 321 - 300

= 21 centimeters

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Answer:

y=4/3x-3

Step-by-step explanation:

By using rise/run, you can see the slope in the equation, as it goes 4 units up and 3 units to the right.

For the y-intercept, you can see that the line intercepts (0,-3), which makes it the y-intercept.

Answer: y=-3+4/3x

Step-by-step explanation:

You get -3 because that is the point on the y axis

You get 4/3x from rise every additional point after
                               -------

                               run

Answer:

  75 minutes

Step-by-step explanation:

You want to know when both buses will be at the stop again if bus A arrives every 25 minutes, and bus B arrives every 15 minutes.

The number of minutes until both buses are at the stop again is the least common multiple (LCM) of their arrival times.

Factors of the times are ...

  25 = 5·5

  15 = 3·5

A common multiple must have all of these factors, so will have factors ...

  LCM = 3·5·5 = 75

After 75 minutes, both buses will be at the stop again.

__

Additional comment

You can see that 5 is a common factor of the two numbers. The LCM can also be found as the product of the two numbers, divided by their greatest common factor (GCF).

  LCM(a, b) = a·b/GCF(a, b)

  LCM(15, 25) = 15·25/5 = 75

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Classes           Frequency

0-4                7

5-9                5

10-14              2

15-19              4

20-24              1

The frequency of each class is determined by counting the number of waiting times that fall within each range. For example, the class 0-4 has a frequency of 7, meaning 7 customers waited between 0 to 4 minutes for their oil change.

The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.

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It takes 0.7143 seconds for the ball in the air to hit the ground.

Therefore the answer is 0.7143 s.

The time it takes for the ball to hit the ground can be calculated using the formula for vertical motion with constant acceleration (g = 9.8 m/s²):

t = √(2 * h / g)

where h is the height the ball is thrown and t is the time it takes to hit the ground.

Plugging in the values to find time:

t = √(2 * 2.50 m / 9.8 m/s²)

t = √(0.51) s

t = 0.7143 s

So, the ball is in the air for approximately 0.7143 seconds before it hits the ground.

--The question is incomplete, answering to the question below--

"A student standing on the wall throws a ball straight up. The ball leaves the student's hands with a speed of 19.0 m/s when the hand is 2.50 m above the ground.

How long is the ball in the air before it hits the ground? (the student moves her hand out of the way.)"

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The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars are 0.0099.

A normal distribution in statistics is defined as the type of continuous probability distribution where the datas are arranged in a symmetrical bell shaped graph.

Given that,

Mean, μ = 87

Standard deviation, σ = 8

We have to calculate P (104.60 < x < 108.20).

For that find z score.

z = (x - μ) / σ

At x = 104.60, z = (104.60 - 87) / 8 = 2.2

At x = 108.20, z = (108.20 - 87) / 8 = 2.65

From the z table,

P(z < 2.65) = 0.9960 and P(z < 2.2) = 0.9861

P (104.60 < x < 108.20) = 0.9960 - 0.9861 = 0.0099

Hence the proportion is 0.0099.

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