A company in its first year of business produced 150 training manuals for a total cost of $2.350. The following
year, the company produced 50 more manuals at a cost of $ 1,450. Use this information to find a linear equation
that gives the total cost of producing training manuals from the number of manuals produced.

Answers

Answer 1

Answer:

  y = 9x +1000

Step-by-step explanation:

The relation for the total cost of manuals based on the number produced will be the sum of a base cost and a variable cost. The variable cost is the product of the cost per manual and the number of manuals.

Cost per manual

The cost per manual can be found by looking at the increase in cost relative to the increase in the number of manuals produced:

  cost per manual = (increase in cost)/(increase in production)

  = ($2350 -1450)/(150 -50) = $900/100 = $9

Base cost

The base cost will be added to the product of the cost per manual and the number of manuals. For the 2nd year purchase, this is ...

  $1450 = base cost + (50 manuals)×($9/manual)

  $1450 = base cost + $450

  base cost = $1450 -450 = $1000

Equation

The equation for the cost in dollars (y) of producing x manuals can now be described by ...

  y = (cost per manual)x +(base cost)

  y = 9x +1000


Related Questions

Whats the correct answer answer asap for brainlist

Answers

Answer:

option C: Asian

explanation:

Asian countries, such as China, produce goods like the European products, but for much cheaper prices.

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 and from a second position L=30 farther along this path it is B=50 What is the height of the​ tree?

Answers

The height of the tree based on the information is 229.23.

How to calculate the height?

Based on the information given,

tan 50 = h/x + 60

h = (x + 60)tan 50°

x tan 60 = (x + 60)tan 50°

x(tan 60° - ta 50°) = 60 ta 60

x = 132.34

Therefore, the height will be:

= x tan60°

= 132.34 × tan 60

= 229.23

Therefore, the height is 229.23.

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The sum of two numbers is 32. One number is 3 times the other. Find the numbers.

Answers

The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.

Equation of the unknown

Let

x = one of the unknowns3x = second unknown

x + 3x = 32

4x = 32

x = 32/4

x = 8

So,

3x = second unknown

= 3(8)

= 24

Check:

x + 3x = 32

8 + 24 = 32

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Question 1 of 10
The Quadratic Formula gives which roots for the equation 2x²+x-6=0?

Answers

Answer:

x=-3/2 or-2

Step-by-step explanation:

hope this helps

The average student loan debt for college graduates is $25,150.
Suppose that that distribution is normal and that the standard deviation
is $12,050. Let X = the student loan debt of a randomly selected college
graduate. Round all probabilities to 4 decimal places and all dollar
answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $14,200
and $33,950 in student loan debt.
c. The middle 10% of college graduates' loan debt lies between what
two numbers?
Low: $
High: $

Answers

Using the normal distribution, it is found that:

a) [tex]X \approx N(25150, 12050)[/tex]

b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

c) Low: $23,519.65, High: $26,580.35.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 25150, \sigma = 12050[/tex].

Hence the distribution of X can be described as follows:

[tex]X \approx N(25150, 12050)[/tex]

The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:

X = 33950:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33950 - 25150}{12050}[/tex]

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

X = 14200:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14200 - 25150}{12050}[/tex]

Z = -0.91

Z = -0.91 has a p-value of 0.1814.

0.7673 - 0.1814 = 0.5859.

There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = -0.127(12050)

X = $23,519.65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = 0.127(12050)

X = $26,580.35.

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14. Find the value of X round the nearest degree 12 15

Answers

The measure of the angle x is 53.13 degrees after applying the sin ratio.

What is the trigonometric ratio?

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Applying sin ratio:

sinx = 12/15

sinx = 0.8

x = 53.13 degrees

Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.

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A body of mass 50 kg explodes and splits into three pieces. The first piece has a mass of 10 kg and a velocity of [-3,2] m/s, the second piece has a mass of 18 kg and a velocity of [5,-4]m/s. What is the velocity of the third piece?​

Answers

Step-by-step explanation:

From the conversation of angular momentum

Initial momentum=final momentum

Here,

Since body is initially resting, it's momentum must be zero.

Let v be velocity of third piece. Then

0= 10(-3i+2j) + 18(5i-4j) + 22v

Solving this we get,

v= 4/22(15i+13j).

The velocity of third piece is 2/11(13 j - 15i)

What is velocity?

Velocity defines the direction of the movement of the body or the object.

Given:

As the body is at rest so the initial momentum is zero.

Let v be velocity of third piece.

so,

0= 10(-3i+2j) + 18(5i-4j) + 22v

0= -30i + 20j + 90i -72j + 22 v

0= 60i - 52j + 22 v

-60i +52j = 22v

v= 2/11( 13j - 15 i)

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Simplify the following.
7² =
4⁰ =
6-¹=

Answers

Answer:

49

1

1/6

Step-by-step explanation:

7^2 is just 7 * 7 = 49

4^0 = 1, since anything to the power of 0, is 1.

[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6

Answer:

491

Step-by-step explanation:

hey

please like my question

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.



I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.



Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?



%

Answers

The answer would be 0.27

what is the probability of getting a number less than 5 and a head when rolling a die and tossing, help someone quickly

Answers

Probability of getting a number less than 5 is=64=32

Please solve this❣️​

Answers

Answer:

f⁻¹(1/5) = 2

Explanation:

If f(x) = (2x -3)/5

To find inverse of f(x), make x the subject.

[tex]f(x) = \dfrac{2x - 3}{5}[/tex]

[tex]5 f(x) = 2x - 3[/tex]

[tex]2x = 5 f(x) + 3[/tex]

[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]

Then,

[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]

To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]

[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]

which yields

[tex]f^{-1}(0.2) = 2[/tex]

ch circle shows AB that measures 60°?
O
60⁰ -0
A
60°
B
60°
.0
Mark this and return
B
B
Save and Exit
Next
Submit

Answers

Step-by-step explanation:

there are a lot of typos and missing info in your problem and answer option definition.

based on what I understood the answer should be

"the second answer option".

this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.

one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.

but I don't think this is really the meaning of this question here.

Solution
We are given two endpoints here

Point 1: (−1, Answer
)
Point 2: ( Answer
,4)
We know our rise between the two points is 1. So

12= Answer

And our run between the two points is 4. So

42= Answer

We now have rise2+run2=distance2, so we have

1+16=distance2

Answer
=distance2

So once we take the square root of both sides we have

distance=√ Answer

We could also use the actual distance formula we developed to get the same answer.

d=(4−3)2+(−5−(−1)2)−−−−−−−−−−−−−−−−−−−√

d=(12+(−4)2)−−−−−−−−−−√

d=(1+16)−−−−−−−√

d=√ Answer

Answers

The distance between the two points on the plane is √17

Distance between two points

The formula for calculating the distance between two points is expressed as;

D = √(x2-x1)²+(y2-y1)²

From the given plane, we have the following coordinates

(-5, 4) and (-1, 3)

Substitute

D = √(3-4)²+(-1-(-5))²

D = √(-1)²+(4)²

D= √1+16
D=√17

Hence the distance between the two points on the plane is √17

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A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.

Answers

The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 <  [tex]\rm \mu[/tex] < 36.907

What is Probability ?

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]

[tex]\rm \mu[/tex] is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% [tex]\rm \alpha / 2[/tex]  = 0.05

Z = 1.64

34 [tex]\rm \pm[/tex] 1.64 * 8 / √50

34 [tex]\rm \pm[/tex]  1.855

32.145 < [tex]\rm \mu[/tex] < 35.855

(b)  The 99% confidence interval for the population mean

99% [tex]\rm \alpha / 2[/tex]  = 0.005

Z=2.57

34  [tex]\rm \pm[/tex] 2.57 * 8 / √50

34 [tex]\rm \pm[/tex]  2.907

31.093 <  [tex]\rm \mu[/tex] < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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mark: 3,2,0,1,9,12,3,5
if the pass mark is 5, how many students failed the text​

Answers

Answer:

5

Step-by-step explanation:

Anything below 5 is a fail:

3, 2, 0, 1, 3

That's 5 students.


9. The measure of each exterior angle of a regular pentagon is
the measure of each exterior
angle of a regular nonagon.

Answers

Answer:

55,55

Step-by-step explanation:

hereakaigdidjuwjapwwjshd

A 4-sided dice is rolled. The set of equally likely outcomes is {1,2,3,4}. Find the probability of rolling a number less than 14

The probability of rolling a number less than 14 is?

Answers

The probability of rolling a number less than 14 among {1,2,3,4} is 1.

Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.

Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:

Probability= number of events/ total number of events.

Total likely outcomes=4 {1,2,3,4}

Numbers less than 14 = 4

Probability of rolling a number less than 14=1/4

=0.25 because all number less than 14 is present.

1,2,3,4 are all less than 14.

and because all numbers are included that's why the value of probability is 1.

Hence the probability of rolling a number less than 14 is 1.

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Write the equation of a sine or cosine function to describe the graph.

Answers

Answer:

  y = cos(3/2x)

Step-by-step explanation:

A general sine or cosine function will have parameters of amplitude, vertical and horizontal offset, and period. The values of these parameters can be determined from the given graph.

  y = A·cos(2π(x -B)/P) +C

where A is the amplitude, B and C are the horizontal and vertical offsets, and P is the period.

Amplitude

For sine and cosine functions, the amplitude of the function is half the difference between the maximum and minimum:

  A = (3 -1)/2 = 1

Horizontal offset

A sine function has its first rising zero-crossing at x=0. A cosine has its first peak at x=0. The given graph has its first peak at x=0, so it is a cosine function with no horizontal offset.

  B = 0

Vertical offset

For sine and cosine functions, the vertical offset is the average of the maximum and minimum values:

  C = (3 +1)/2 = 2

Period

The period is the difference in x-values between points where the function starts to repeat itself. Here, we can use the peaks to identify the period as 4π/3.

  P = 4π/3

Function equation

Using the parameter values we determined, the function can be written as ...

  y = cos(3/2x) +2

__

Additional comment

The argument of the cosine function is ...

  [tex]\dfrac{2\pi(x-B)}{P}=\dfrac{2\pi(x-0)}{\dfrac{4\pi}{3}}=\dfrac{3(2\pi)}{4\pi}x=\dfrac{3}{2}x[/tex]

The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and administrative support are $349,200 per year. Chimneysweep averages 200 service calls per month. What is the average cost per cleaning service call?

Answers

The average cost per cleaning service call charge by the company is $184.5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the total cost for x number of service calls in a year. Hence:

y = 39x + 349200

For 200 service call, in a year, x = 200 * 12 = 2400

y = 39(2400) + 349200 = $442800

Average cost = $442800 / 2400 = 184.5

The average cost per cleaning service call charge by the company is $184.5.

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A Bus begins its trip with R occupants (including the driver).At each of the 20 stops three people get on and no one leaves if there are three times as many boss occupants at the end of the 20th stop as there are at the end of the fourth stop how many occupants did the bus have immediately after the 10th stop?Pls explain for brainlest
A.12
B.24
C.30
D.42

Answers

Answer

D.42

Step-by-step explanation:

It's pretty easy and hard at the same time just do not overthink it. Obviously, the bus leaves with R occupants including the driver but that still means that there are occupants, to begin with. Now remembering that 3 people get on each stop you can take it to multiply 3*10  (3 people, ten stops) you would get thirty. Would this be the answer? NO! Remember that you began with R occupants to begin with and either using the process of elimination or common sense you can conclude that 12,24 are improbable answers because they are lower than thirty, and what about thirty? No, because you had thirty people in addition to the original occupants so that eliminates thirty. What's left?

                                                             42

                                              There Is Your Answer

Answer:

D. 42

================

Given

The bus has initially R occupants,At each stop the occupants increase by 3,After 20 stops there are 3 times more occupants than after 4 stops.

To find

The number of occupants after 10 stops

Solution

Let's find out the how many occupants are there after 20 and 4 stops, then compare:

After 20 stops:

R + 3*20 = R + 60

After 4 stops:

R + 3*4 = R + 12

Compare and solve for R:

R + 60 = 3(R + 12)R + 60 = 3R + 363R - R = 60 - 362R = 24R = 12

We found the number of initial occupants.

Use this  to find the number of occupants after 10 stops:

12 + 3*10 = 12 + 30 = 42

Correct answer choice is D.

Mr. Parks begins to fill a large container with water for the dunk tank at the school
fair before asking Brian to finish the job. The container has 25 gallons of water in it
before Brian uses a hose to finish filling it up. The container fills at a rate of 10
gallons per minute. Suppose that y is the amount of water in the tank after x
minutes. Which equation could be graphed to help Brian find out how much water is
in the tank at any time?
y = 25x + 10
y= 10x + 25
y= 10x - 25
y = 10x

Answers

Answer:

The answer is B / y= 10x+25

Step-by-step explanation:

your welcome

The population f(x), in millions, of State A of a country after x years is represented by the function shown below:

f(x) = 4(1.08)x

The graph shows the population g(x), in millions, of State B of the country after x years:

graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4

Which conclusion is correct about the populations of State A and State B?

Answers

Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

How to solve for the solution

The function in the question is given as

For A:

[tex]F(x) = 4*(1.08)^x[/tex]

For B

[tex]g(x) = 2*(1.08)^x[/tex]

The exponential growth equation that is used to solve this is

[tex]h(x) = A(r)^x[/tex]

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

Complete question:

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

2. The original population of State A was half of the original population of State B.

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.

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Answer:

Step-by-step explanation:

honestly thats what it is

Can someone help me with this step by step with explanation im confused need help

Answers

The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.

The given construction involves drawing a parallel line through a given point P to a given line AB.

From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.

Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1​

Answers

Answer:

6

Step-by-step explanation:

Which of the following shows the simplified form of sin x/1+cos x
O sin x- tan x
O sin x-cot x
O csc x-cot x
01

Answers

Answer:

csc x - cot x

Step-by-step explanation:

(sinx)/(1+cos x)

Multiplying the numerator and denominator by (1-cos x),

((sinx)(1-cos x))/(1-cos² x)

((sinx)(1-cosx))(sin²x)

(1-cosx)/(sinx)

cscx - cot x

Halfway through the season, a soccer player has made 12 penalty kicks in 18 attempts.
Based on her performance to date, what is the relative frequency probability that she will miss
her next penalty kick?

Answers

Answer:

21

Step-by-step explanation:

18÷6=3 attemps

13÷6=2 makes

she will probably missed I next 3rd pe alty kick

21st attempts

Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x​

Answers

The answer to this question is choice B

The actual length of the ship is 575 feet. The scale of the model is 1 inch: 25 feet. What will be the length of the model?

Answers

The length of the model as described in the task content would be; 23 inches.

What is the length of the model?

According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.

On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.

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What is the equation of the graph below?

Answers

Answer:

A

Step-by-step explanation:

Write the number in numerical form-twenty-six thousandths

Answers

The answer is 0.026 in numerical form
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A satellite orbits the earth at a speed of 8.0x 10^3m/s . Calculate the period of orbit of the satellite if the distance between the centre of the earth and the satellite is 6400km? The graph shows the cube root parent function.Which statement is true?A. (0, 0) is the x- and y-intercept of the function.B. The function has no intercepts.C. (0, 1) is the x- and y-intercept of the function.D. (1, 1) is the x- and y-intercept of the function. The indictment is the section of the Declaration of Independence where thegrievances against the king are listed. What is the main purpose of the indictment?TO to suggest a new form of governmentto describe the kind of country America should beto document the offenses of Great Britain against the American peopleOto justify the cruelty of the colonists against Native Americans When a phased-in change in rates is scheduled to occur in the future years in which a temporary difference is expected to reverse, the ___. Multiple Choice currently enacted tax rate is multiplied by the temporary amounts reversing in each of those years and the total is the deferred tax liability or asset. differences between the currently enacted rate and the future tax rates are multiplied by the temporary amounts reversing in each of those years and the difference is the deferred tax liability or asset. specific tax rates of each future year are multiplied by the temporary amounts reversing in each of those years and the total is the deferred tax liability or asset. specific tax rates of each future year are multiplied by the temporary amounts reversing in each of those years to determine the change in the deferred tax liability or asset. 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Include the calculations to show the probability.Determine the type of prize a winner would deserve and the cost of playing your game. A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.Trigonometric area formula: Area = One-half a b sine (C)To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin? 16 square centimeters30 square centimeters56 square centimeters60 square centimeters Which statement best completes the table?Structure of the Federal GovernmentThere are three branches of government.All branches of government have equal power.?Power is separated between three branches of government.1 of 7 QUESTIONSCongress has total control over every branch of government.All branches of government can create new laws.Each branch of government can check the power of the other two.Only the legislative branch is described in the U.S. Constitution.SUBMIT Solve for the remaining angles help me please!!!!!!!! 20 points what are the properties of most transition metals What do argentines generally eat more of per capita than any other people in the world?. As time went on, how did the Northern English colonies begin to differ from theSouthern English colonies by 1750 in terms of government, social structure, labor andeconomics? A company issues 7%, 7-year bonds with a par value of $170,000 on January 1 at a price of $179,602, when the market rate of interest was 6%. The bonds pay interest semiannually. The amount of each semiannual interest payment is: The sum of two numbers is 32. One number is 3 times as large as the other. What are the numbers? Why was the bond among the states in the Articles of Confederation a loose league of friendship?A) because the state capitals were far apartB) because the states were not very friendlyC) because they wanted to avoid the tight controls of the monarchyD) because a league means a strong allianceE) because they knew their friendship would grow without the monarchy A chief receives yams from members of the chiefdom and then gives those yams back to other people within the chiefdom. This form of exchange is known as: Who encouraged African Americans to escape race-based discrimination inthe United States by moving to Africa?A. W. E. B. Du BoisB. Booker T. WashingtonC. Frederick DouglassD. Marcus Garvey What lesson does American born learn from immigrants? Keep in mind unhomeliness and how the journey affects them.