Our peak time this week will be 8:00 AM to 12:00 PM, which requires 32% more agents than the afternoon requirements of 473 agents.” Representative: “So, you will need to have __________ in the morning shift.

Answers

Answer 1

The number of agents required in the morning shift 8:00 AM to 12:00 PM is 624.36 agents

Percentage

Peak time = 8:00 AM to 12:00 PM

Agent required in the afternoon = 473 agents

Agent required in the morning = (32% of 473) + 473

= (32/100 × 473) + 473

= (0.32 × 473) + 473

= 151.36 + 473

= 624.36 agents

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Related Questions

Find g(x), where g(x) is the translation 2 units left and 4 units down of f(x)=x^2.
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers.
g(x) =

Answers

The function g(x) in the form a(x-h)^2 + k is: [tex]g(x) = (x + 2)^2 - 4[/tex]

Starting with[tex]f(x) = x^2[/tex], the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting[tex]f(x) = x^2:[/tex]

[tex]g(x) = (x + 2)^2 - 4[/tex]

Expanding the square:

[tex]g(x) = x^2 + 4x + 4 - 4[/tex]

Simplifying:

[tex]g(x) = x^2 + 4x[/tex]

Now we need to rewrite this expression in the form [tex]a(x-h)^2 + k.[/tex] To do this, we will complete the square:

[tex]g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4[/tex]

Therefore, the function g(x) in the form a(x-h)^2 + k is:

[tex]g(x) = (x + 2)^2 - 4[/tex]

Where a = 1, h = -2, and k = -4.

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HELPPP

MA.7.DP.1.2
A group of students in the book club are debating whether high school juniors or seniors
spend more time on homework. A random sampling of juniors and seniors at the local high
school were surveyed about the average amount of time they spent per night on homework.
The results are listed in the table below.
Average Amount of Time on Homework Per Night (in minutes)
Juniors 125 90 95
80 100 100 120- 85 95 120 95 85
Seniors 135 70 65 100 35 175 80 80 90 65 120 60
Part A. Calculate and compare the measures of center for the data sets.
Part B. Calculate and compare the variability in each distribution.
Part C. Does the data support juniors or seniors spending more time on homework?
Explain your reasoning.

Answers

Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42

Median (Juniors) = (95 + 95) / 2 = 95

Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25

Median (Seniors) = (80 + 80) / 2 = 80

How to solve for the median of center

Juniors: 125, 90, 95, 80, 100, 100, 120, 85, 95, 120, 95, 85

First, sort the data: 80, 85, 85, 90, 95, 95, 95, 100, 100, 120, 120, 125

Sum = 1085

Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42

Median (Juniors) = (95 + 95) / 2 = 95

Seniors: 135, 70, 65, 100, 35, 175, 80, 80, 90, 65, 120, 60

First, sort the data: 35, 65, 65, 70, 80, 80, 90, 100, 120, 120, 135, 175

Sum = 1095

Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25

Median (Seniors) = (80 + 80) / 2 = 80

Variability

Juniors:

Range = max - min = 125 - 80 = 45

Seniors:

Range = max - min = 175 - 35 = 140

C. Based on the mean and median, it appears that seniors spend slightly more time on homework on average (mean ≈ 91.25) compared to juniors (mean ≈ 90.42).

However, the median time spent for seniors (80 minutes) is less than that of juniors (95 minutes), indicating that the data for seniors might be skewed by some outliers.

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100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!

Answers

The given quadrilateral is a parallelogram by the theorem "The diagonals of a parallelogram bisect each other."

Given is a quadrilateral.

We have to determine that the quadrilateral is a parallelogram or not.

From the shape and the drawing given, the quadrilateral is a parallelogram.

A parallelogram has opposite sides parallel to each other.

Here it is parallel.

Here it is given that the diagonals are bisected by each other, that is two parts of the diagonals are of equal length.

We have a theorem that "The diagonals of a parallelogram bisect each other."

A square, rectangle, rhombus can be included in the group of parallelogram.

So this is a parallelogram.

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1 secX + 3 = cosX + tanX (2+ sinX)​

Answers

The solution for X is X ≈ [tex]tan^{(-1)(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.

Given: 1 secX + 3 = cosX + tanX (2 + sinX)

To simplify the equation, let's express secX and tanX in terms of sinX and cosX:

1/cosX + 3 = cosX + sinX/cosX (2 + sinX)

Now, multiply both sides by cosX to eliminate the denominators:

[tex]1 + 3cosX = cos^2X + sinX(2 + sinX)[/tex]

Expanding the equation:

[tex]1 + 3cosX = cos^2X + 2sinX + sin^2X[/tex]

Since [tex]sin^2X + cos^2X[/tex] equals 1 (based on the Pythagorean identity), we can substitute it into the equation:

[tex]1 + 3cosX = 1 + 2sinX + sin^2X[/tex]

Rearranging the terms:

[tex]3cosX = 2sinX + sin^2X[/tex]

Now, let's express cosX in terms of sinX using the Pythagorean identity:

cosX = √(1 - [tex]sin^2X[/tex])

Substituting this into the equation:

3√(1 - [tex]sin^2X) = 2sinX + sin^2X[/tex]

Squaring both sides to eliminate the square root:

[tex]9(1 - sin^2X) = (2sinX + sin^2X)^2[/tex]

Expanding the right side:

[tex]9(1 - sin^2X) = (2sinX)^2 + 2(2sinX)(sin^2X) + (sin^2X)^2\\9 - 9sin^2X = 4sin^2X + 4sin^3X + sin^4X[/tex]

Rearranging the terms:

[tex]sin^4X + 4sin^3X + 4sin^2X + 9sin^2X - 9 = 0[/tex]

Combining like terms:

[tex]sin^4X + 4sin^3X + 13sin^2X - 9 = 0[/tex]

Unfortunately, this equation does not have a simple algebraic solution. It needs to be solved numerically or graphically. Using numerical methods or a graphing calculator, we can find that one solution to this equation is sinX ≈ 0.7429.

Taking the inverse tangent (arctan) of both sides, we have:

X = arctan(0.7429)

Therefore, the solution for X is X ≈ t[tex]an^{(-1)}(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.

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What half of 4 fourths in a decimal

Answers

Answer:

0.5

Step-by-step explanation:

So what do we mean by half? Half means there are two of the thing, and so all you need to do is divide it by two. Half of 4/4 is just another way of saying 4/4 divided by 2:

: 4/4 ÷ 2

Now we know that "half" means to divide by 2, how do we half 4/4? Remember that a fraction a part of the whole, so the higher the denominator is, the smaller the piece. The answer is that the numerator stays the same and we multiply the denominator by 2:

: 4/4 x 2 = 4/8

Here's a little bonus calculation for you to easily work out the decimal format of half 4/4. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:

: 4/8 = 0.5

Ashley got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13 cents per yard. If after that purchase there was $25.06 left on the card, how many yards of ribbon did Ashley buy?

Answers

Answer:

38 yards

Step-by-step explanation:

First, subtract to find out how much money was spent.

30 - 25.06

= 4.94

Then divide to find out how many groups of $0.13 are in $4.94.

4.94 ÷ .13

= 38

Ashley bought 38 yards of ribbon.

38 × .13 = 4.94

4.94 + 25.06 = 30

This answer does not consider tax at all. Because it wasn't mentioned in the question and it complicates the problem. So probably don't worry about tax. Unless your teacher /book/program said to consider it. I can edit the answer.

Also, if they said to write an equation:

Let x = yards of ribbon

30 - .13x = 25.06

subtract 30

-.13x = -4.94

divide by -.13

x = 38

can some one
factor 7a10 - 112a2

Answers

The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]

How to find the factor 7a10 - 112a2

To factor the expression [tex]7a^{10} - 112a^2[/tex]  we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:

The coefficients 7 and 112 have a common factor of 7.

The lowest power of "a" in each term.

In this case, the lowest power of "a" is 2.

Factoring out [tex]7a^2[/tex] from both terms, we get:

[tex]7a^2(a^8 - 16)[/tex]

Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]

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please help me solve for x image is attached ive been stuck on it for a few days now

Answers

The value of x will be 10.

Given a triangle we need to set a proportion to solve for the value of x,

Therefore, according to the definition of the similar triangles,

x / 5 = 15+5 / x

x² = 5 × 20

x² = 100

x = 10

Hence the value of x will be 10.

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Explain what is meant by a positive relationship between two variables and a negative relationship between two variables. Give an example of a situation in which you would expect to find a positive relationship and when you would expect to find a negative relationship.

Answers

Answer: A positive relationship between two variables means that as the value of one variable increases, the value of the other variable also increases. In other words, there is a direct association or correlation between the two variables. Graphically, a positive relationship is represented by an upward-sloping line or curve.

For example, let's consider the relationship between studying time and exam scores. In general, if a student spends more time studying for an exam, their exam score is likely to increase. This implies a positive relationship between studying time and exam scores.

On the other hand, a negative relationship between two variables means that as the value of one variable increases, the value of the other variable decreases. In this case, there is an inverse association or correlation between the two variables. Graphically, a negative relationship is represented by a downward-sloping line or curve.

For instance, let's consider the relationship between hours of sleep and levels of fatigue. As the number of hours of sleep decreases, the level of fatigue tends to increase. This indicates a negative relationship between hours of sleep and levels of fatigue.

It's important to note that these examples describe typical scenarios, but individual variations and other factors can also influence the relationships between variables.

Question 8
Match each compound to its correct type.
8.1
CO
hydroxide
8.2
CO₂
carbonate
8.3
SO₂
8.4
CaCO
8.5
NaOH
oxide
trioxide
dioxide

Answers

The correct matching of each compound to its type:

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)

8.5 NaOH - hydroxide

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - carbonate

8.5 NaOH - hydroxide

Here is the correct matching of each compound to its type:

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)

8.5 NaOH - hydroxide

Compound 8.4, CaCO, is not correctly represented. It should have a subscript to indicate the number of atoms present in the compound.

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50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

The exact value of sin θ is 9/13.

Option A is the correct answer.

We have,

In trigonometry,

The sine function (sin) represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.

The cosecant function (csc) is the reciprocal of the sine function, meaning it is equal to 1 divided by the sine of an angle.

In this case,

We are given that csc θ (the cosecant of θ) is equal to 13/9.

To find the value of sin θ (the sine of θ), we can take the reciprocal of csc θ. So,

sin θ = 1/(csc θ) = 1/(13/9) = 9/13.

Therefore,

The exact value of sin θ is 9/13.

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The proportional relationship between cost and pints of blueberries is shown in the table. Blueberries (in pints) 4 10 Cost (in dollars) 18.40 46 Describe what a graph of the proportional relationship would look like.

Answers

The graph of the proportional relationship is a linear graph, with slope of 4.6 and intercept of zero.

What is a proportional relationship?

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

Hence the graph is a linear function with slope of k and intercept of zero.

The cost of 4 pints is of $18.4, and the cost of 10 pints is of $46, hence the slope of the relation is given as follows:

k = 46/10 = 18.4/4 = 4.6.

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The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.

Answers

The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .

How to find the probability ?

The number of adults with some high school degree or some college would be :

= 3, 561 + 6, 058

= 9, 619 people

The probability that a random adult would have high school degree or some college is therefore :

= Adults with high school degree or some college / Total adults in the town

= 9, 619 / 17, 981

= 53. 50 %

In conclusion, the probability is 53. 50%.

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NO LINKS!! URGENT HELP PLEASE!!!

O is the center of the decagon below. Find its area. Round to the nearest tenth if necessary.

Answers

Answer:

752.4

Step-by-step explanation:

Here we are provided with a decagon which has 10 sides.

The total interior angle is 360°.

So each will have 360/10 = 36 degrees

Half of that is 18 degrees inside the triangle.

Refer to the attachment below.

opposite = 16sin(18)

adjacent = 16cos(18)

Find the area of this triangle:

= 1/2 × 16sin(18) × 16cos(18)

= 37.61825

There are 20 triangles just like this so the total area is (37.61825 × 20) = 752.365 ≈ 752.4 unit2

Please help!!! Correct answer gets brainliest!!!

Answers

D.
When the “er” is attached, it’s because the “more” doesn’t enter before the “er”.

La siguiente gráfica muestra las calificaciones de un grupo de 40 alumnos que van desde el mínimo 7 hasta el máximo 10 de calificación. ¿Cuántos alumnos sacaron 9?

Answers

The specific data points or the Frequency distribution of grades for the 40 students.

The specific information from the graph , the exact number of students who received a grade of 9.

If the graph represents the distribution of grades of 40 students on a scale from 7 to 10, we can estimate the number of students who received a grade of 9 by considering the shape of the graph.

the graph is a normal distribution or bell curve, with the majority of students clustered around the mean (which is likely to be around 8.5 or 9), we can expect a significant number of students to have received a grade of 9. In a typical bell curve distribution, the highest density of scores is around the mean.

without additional information about the shape of the graph or the specific values represented on the x-axis, it is difficult to provide an accurate estimation of the number of students who received a grade of 9. The graph may represent a variety of distributions, such as skewed, bimodal, or uniform.

the exact number of students who received a grade of 9,  the specific data points or the frequency distribution of grades for the 40 students.

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Based on the information given regard to the graph, there are 6 students who got 9.

How to explain the value

A graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.

The collection of all points whose coordinates satisfy a given relation such as a function.

The graph shows that there are 4 students who got 7, 8 students who got 8, and 12 students who got 10. This leaves:

40 - 4 - 8 - 12

= 6 students who got 9.

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AC = 3x-10. BD = x+34. Solve for X.

Answers

The value of x in the figure is 22 as the diagonals are equal

Diagonals of a parallelogram are the line segments connecting two non-adjacent vertices of a parallelogram

Both the AC and BD are equal

AC=3x-10

BD=x+34

As two diagonals are equal

3x-10=x+34

We have to solve for x

3x-x=10+34

2x=44

Divide both sides by 2

x=22

Hence, the value of x in the figure is 22

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100 tickets are sold for $1 each. there’s a $25 prize and a $10 prize.what is the expected value for a person that buys a ticket? round to the nearest cent

Answers

The expected value for a person who buys a ticket is $0.35.

We have,

Number of tickets sold = 100

Price of each ticket = $1

Prize value (1st prize) = $25

Prize value (2nd prize) = $10

Let's calculate the expected value step by step:

Calculate the probability of winning each prize:

Since there is only one 1st prize and one 2nd prize, the probability of winning each prize is:

Probability of winning the 1st prize = 1/100

Probability of winning the 2nd prize = 1/100

Calculate the expected value:

Expected value = (Probability of winning 1st prize x Value of 1st prize) + (Probability of winning 2nd prize x Value of 2nd prize)

= (1/100 x $25) + (1/100 x $10)

= $0.25 + $0.10

= $0.35

Therefore, the expected value for a person who buys a ticket is $0.35.

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8. For positive real numbers a, b, and c, the expressions albici and Vabac are equivalent. What are the values
of p, q, and r?

Answers

Answer:

Step-by-step explanation:

To find the values of p, q, and r in the expression albici = Vabac, we need to equate the corresponding parts on both sides.

From the given equation, we have:

p * (a * b) * (c * i) = q * (a * b * a * c)

Comparing the exponents of a, b, and c on both sides, we get:

p = q * a^2

1 = q * c

To determine the value of r, we can use the fact that albici and Vabac are equivalent. The radical symbol (√) represents taking the square root.

√(a * b * c * i) = √(a * b * a * c)

This implies that:

√(a * b * c * i) = √(a^2 * b * c)

Comparing the exponents of a, b, and c on both sides, we get:

1/2 = 2 * p * q * r

Combining all the equations, we have:

p = q * a^2

1 = q * c

1/2 = 2 * p * q * r

To find the specific values of p, q, and r, we need additional information or equations involving a, b, and c. Without more context or equations, it is not possible to determine the exact values of p, q, and r.

use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4

Answers

Answer:

Solution: x = 2, y = -3.

Step-by-step explanation:

Given system of equations:

Equation 1: 2x - 3y = 13

Equation 2: x + 2y = -4

Multiply Equation 2 by 2:

2(x + 2y) = 2(-4)

Simplified: 2x + 4y = -8

Add Equation 1 and Equation 3:

4x + y = 5

Solve Equation 4 for y:

y = 5 - 4x

Substitute y into Equation 2:

x + 2(5 - 4x) = -4

Simplify:

-7x + 10 = -4

Solve for x:

x = 2

Substitute x into Equation 5:

y = 5 - 4(2)

y = -3

Solution: x = 2, y = -3.

A person buy a lot of tickets for Rs.136 each execution class ticket cost rupees12 and each local class ticket cost for Rs 4 each make an equation and fine explain possible solutions

Answers

Answer:

 3.98

Step-by-step explanation:

Answer:

the second method may be through graph

30 POINTS, MULTIPLE CHOICE, TIME SENSITIVE!!
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4

Answers

Answer: x= —5/9

Step-by-step explanation:

Find the slope of the line.

A. 3/2

B. -2/3

C. 4/3

D. -3/4

Answers

Answer:

-3/4, answer D

Step-by-step explanation:

Slope = rise/run. The equation is (y2-y1)/(x2-x1).

So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.

slope = (2-(-4))/(-2-6)

slope = (2+4)/(-2-6)

slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.

slope = -3/4

Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.

Answer:

Step-by-step explanation:

Use 2 points from the line:  (-2, 2) and (6, -4)

slope = y2 -y1  =   -4 - 2  = -6   = - 3

             x2 - x1       6 - -2      8         4

The slope is choice  D    -3/4

Southside High School found that 80% of last year's sold-out plays occurred
during weekend performances. Based on this information, the drama teacher
decided to add another performance time on Saturday. This decision is a
result of
OA. describing data
OB. making an inference
OC. creating involvement
D. collecting data

Answers

Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Use the image to determine the type of transformation shown.

A. Reflection across the x-axis
B. 90° clockwise rotation
C. Horizontal translation
D. Vertical translation

Answers

Answer:

the answer is C. Horizontal translation

Step-by-step explanation:

trust fr

If $850 is invested in an account that earns 2.6% yearly interested compounded quarterly, then which of the
following is the worth of this investment after 5 years?
(3) $967.60
(4) $968.25
(1) $960.50
(2) $966.40

Answers

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]

Which graph has the same end behavior as f(x)=(10x^(3)+x^(2)+3)/(2x^(2)+1)?

Answers

The graph that has the same end behavior as f(x)= (10x³+x²+3)/(2x²+1) is Option A. See the attached.

What is the end behavior of the above graph?

the end behavior of the graph of f(x) is:

As x → +∞ , f(x) → +∞ (approaches positive infinity).

As x → -∞,  f(x) → -∞   (approaches negative infinity).

End  behavior of a function f  defines the behavior of the function's graph at the "ends" of the x- axis.

In other words, the end behavior of a function explains the graph's trend when  we look at the right end of the x-axis (as x approaches +∞) and the left end of the x -axis (as x approaches - ∞ ).

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Table 13-15
Labor Output Marginal
Product Variable
Cost Fixed
Cost
0 0 -- $0 $5
1 100 100 $5 $5
2 250 $10 $5
3 350 $15 $5
4 50 $20 $5
5 25 $25 $5
6 430 $30 $5


5. Refer to Table 13-15. What is the marginal product of the second worker?
150
6. Refer to Table 13-15. What is the total output of five workers?

7. Refer to Table 13-15. What is the marginal product of the sixth worker?




8. Refer to Table 13-15. What is the average total cost of producing 425 units of output?

9. Refer to Table 13-15. What is the average variable cost of producing 400 units of output?

10. Refer to Table 13-15. What is the average fixed cost of producing 430 units of output?

Answers

1. The marginal product of the second worker is 150 units.

2. The total output of five workers is 75 units.

3. The marginal product of the sixth worker is 405 units.

4. The average total cost of producing 425 units of output is $30.

5. The average variable cost of producing 400 units of output is $20.

6. The average fixed cost of producing 430 units of output is $0.07.

What is the answers to the question?

The marginal product of the second worker:

= (Output of 2 workers - Output of 1 worker)

= (250 - 100)

= 150 units

The total output of five workers is:

= Output of 4 workers + Marginal product of the fifth worker

= 50 + 25

= 75 units

The marginal product of the sixth worker is:

= (Output of 6 workers - Output of 5 workers)

= (430 - 25)

= 405 units.

The average total cost to produce 425 units is:

= (Total variable cost + Total fixed cost) / Total output

The total variable cost is $30 * 425 = $12,750

The total fixed cost is $5 * 6 = $30

Total cost = $12,750 + $30 = $12,780

The Average total cost is:

$12,780 / 425

= $30

The average variable cost to produce 400 units is:

= Total variable cost / total output

Total variable cost is $20 * 400 = $8,000

Average variable cost = $8,000 / 400 = $20

The average fixed cost to produce 430 units is:

= Total fixed cost / Total output

Total fixed cost is $5 * 6 = $30

The average fixed cost is:

= $30 / 430

= $0.07.

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What’s the lateral area of this

Answers

Answer:

  240 in²

Step-by-step explanation:

You want the lateral area of a triangular prism with triangular base having sides 6 in, 8 in, and 10 in, and a distance between them of 10 in.

Lateral area

The lateral area of a triangular prism is the area of the three rectangular faces. The width of those faces is the "height" of the prism, given as 10 in. The total length of those faces is the perimeter of the base:

  6 in + 8 in + 10 in = 24 in

The lateral area is ...

  A = LW = (24 in)(10 in) = 240 in²

<95141404393>

Arizona license plates are designed so there
are three letters followed by four digits.
How many different license plates are
possible if letters and digits cannot be
repeated?
A. 175,760,000
B. 47,174,400
C. 78,624,000
D. 115,316,136

Answers

78,624,000 different license plates are possible if letters and digits cannot be repeated.

For the letters:

There are 26 letters in the English alphabet, and we need to choose three of them without repetition.

This can be calculated as a permutation of 26 letters taken 3 at a time:

P(26, 3) = 26! / (26 - 3)!

= 26! / 23!

= 26 x 25 x 24

= 15,600

For the digits:

There are 10 digits (0-9), and we need to choose four of them without repetition.

This can be calculated as a permutation of 10 digits taken 4 at a time:

P(10, 4) = 10! / (10 - 4)! = 10! / 6!

= 10 x 9 x 8 x 7

= 5,040

To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:

Total possibilities = P(26, 3) x P(10, 4)

= 15,600 x 5,040

= 78,624,000

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