A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs

Answers

Answer 1

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

The total cost can be computed as:

[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]

[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]

At C'(x) = 0

[tex]\dfrac{12500}{x^2} = 20[/tex]

[tex]\dfrac{12500}{20} = x^2[/tex]

[tex]x^2= 625[/tex]

[tex]x = \sqrt{625}[/tex]

x = 25

[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]

[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]

where; x = 25

[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.


Related Questions

Find the value of y
A) 9.850
B) 18.610
C) 65.825
D) 125.365

Answers

Answer:

B) 18.610

Step-by-step explanation:

Using SOHCAHTOA (trig ratios), the tangent of 28° is the ratio of its opposite length to its adjacent.

in this scenario, the side opposite to 28°, and the side adjacent to it is 35°

tan 28° = y/35

Using inverse operations, multiply both sides by 35

y = 35 * tan 28

Solve your answer using your calculator.

I attached a picture that can help you later to recognize what function to use depending on the sides given.

the measure of an exterior angle of a triangle is greater than the measure of either of its remove interior angles​

Answers

Answer:

what do u want exactly or it us a theorem

Answer  

Step-by-step explanation:

The expression 1/2 bh gives the area of a triangle where
bis the base of the triangle and
H is the height of the triangle.

Answers

Answer:

yes that's correct

Step-by-step explanation:

let's say a question was given with the base of a triangle as 5cm and the height triangle as 8cm.

you will go by

solution

area = 1/2 * b * h

area = 1/2 (5 * 8)

area = 1/2 (40)

area = 20cm²

hope this helps

Which side lengths form a right angle?
Choose all answers that apply:

A) 3, square root 27, 6
B) 8, 15, 17
C) 5, 5, square root 50

Answers

Answer:

B and C

Step-by-step explanation:

Using the Pythagorean theorem a²+b²=c², those are the correct answers

There are four pairs of different types of shoes in a bag: a pair of boots a pair of sandals a pair of sneakers a pair of flip-flops If you pick shoes from that bag (in the darkness), what is the minimum number of shoes you should pick to be certain that you will have a pair of matching shoes

Answers

Answer:

5

Step-by-step explanation:

HELP !!!!

A circular pizza has been cut into five equal size pieces … how many degrees is the angle from one piece?

Answers

Answer:

72°

Step-by-step explanation:

360/5 = 72

Quantitative - Column chart


Quantitative - Line chart


Qualitative - Histogram


Qualitative - Pie chart

Answers

Answer:

A. Qualitative - Column chart

Step-by-step explanation:

Data could either be qualitative or quantitative. Quantitative data are usually given in a definite number, i.e it can be counted. While qualitative deals with characteristics, i.e it can be collected either by the use of questionnaires, or any similar method.

Therefore for the given question, the data survey is qualitative. And since the result would be presented as a graph showing the percentage users for each application, a column chart would be appropriate.

Thus for the data and its presentation, the answer is A. Quantitative - Column chart

six subtracted from one-half a number is 12.

Answers

Answer:

Number is 36

Step-by-step explanation:

Let the number be x

one half  of the number is  [tex]\frac{1}{2} x[/tex]

6 subtracted from one half is 12, That is,

                                                             [tex]\frac{1}{2} x - 6 = 12\\\\\frac{1}{2}x = 12 +6 \\\\x = 18 \times 2 = 36[/tex]

The number would be 36

my baby sister was born 2 ½ ago . how many months old is she​

Answers

It’s 30 months because 2.5 years old times 12 months in a year is 30

Each side of a square is (7 + 3x) units. Which is the perimeter of the square?

Answers

Answer:

28 + 12x

Step-by-step explanation:

Given,

Sides of a square is = 7 + 3x

Therefore,

Perimeter of a square = 4 × side

= 4 × (7 + 3x )

= 28 + 12x (Ans)

whats 926 divided by 30

Answers

[tex]30.87[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{926}{30} \\ = 30 \frac{26}{30} \\ ( \: or \: ) \\ = 30.8666 \\ = 30.87 [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

This table shows information about the number of
days of holiday taken last year by the employees at a
company.
Calculate the mean number of holiday days taken.
Give your answer to 1 d.p.
Holiday days taken 25
26
27
28
29
30
Frequency
6 9 7 7 3 0
2

Answers

Answer:

Mean number of holidays taken =26.6

Step-by-step explanation:

To find the mean,

We use Σfx/Σf

Σfx =150+234+189+84+0+60

=717

Σf= 6+9+7+3+0+2

=27

Σfx/Σf= 717/27

26.6

Find the function value f(-8)
f(x)=6x-1

Answers

Step-by-step explanation:

-8=6x-1

You will move the-8 to the right hand side which will become +8 and then you move+6x to the right hand side which will become -6x

-6x=-1+8

-6x=7

You will divide both sides by-6

-6x/-6=7/-6

x=7/-6

Determine the angles. There’s only two answers.
A. 90 clockwise
B. 90 counterclockwise
C. 180
D. 270 clockwise
E. 270 counterclockwise

Answers

Answer:

its would be a and d

Step-by-step explanation:

6 times 5

One pair of parallel sides proves a quadrilateral to be a parallelogram
True
False

Answers

The answer is true xxxxxx

A pupil dilates from 4.5 millimeters to 8 millimeters. What is the scale factor of the dilation?

Answers

Answer:

[tex]\frac{80}{45} =k[/tex]

Step-by-step explanation:

image/actual=  8/4.5

8(10)/4.5(10)= 80/45

What is the volume of a cylinder, in cubic feet, with a height of 3 feet and a base diameter of 18 feet?

Answers

Answer:

763.41 ft

Step-by-step explanation:

V=π(d/ 2)2*huse formula

help me pls pls pls plsss​

Answers

A) Angle WEB is actute angle

B) angle DEB is a obtuse angle

C) mEM is a striagle angle

D) yBE is angle of vertex B
E) M is angle

G) MEx and xEW are adjacent angles
H) EBy and yBx are supplementary angles

Which of the following logarithmic expressions have been evaluated correctly, to the nearest hundedth? Select all that apply.
A. log3 8 = 0.43
B. log3 6 = 1.63
C. log4 5 = 1.16
D. log2 32 = 1.51

Answers

Answer:

b

Step-by-step explanation:

ive done it before

Solve 2x2 + 8 = 0 by graphing the related function.
There are no real number solutions.
There are two solutions: V8.
There is one solution: 2
There are two solutions: 2 and -2.

Answers

Answer:

there are no real number solutions

Step-by-step explanation:

2x² + 8 = 0

x² + 4 = 0

x² = -4

these solutions all involve "i", the imaginary or complex numbers, as normally the square of any number has to be positive (and cannot be negative).

An auto repair shop charged a customer $170 to repair a car. The bill listed $50 for parts and the
remainder for labor. If the cost of labor is $30 per hour, how many hours of labor did it take to repair
the car?

Answers

The answer is attached. I hope this helps answer your question!

The fencing William chooses costs $29.53 per foot, including installation. What will the fencing cost? Show your work.

Answers

Answer:

[tex]C = 29.53x[/tex]

Step-by-step explanation:

Given

[tex]Unit\ cost = \$29.53[/tex]

Required

The cost of fencing (C)

The cost is calculated as:

[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]

Let:

[tex]x \to Perimeter\ of fencing[/tex]

So, we have:

[tex]C = Unit\ Cost * x[/tex]

[tex]C = 29.53 * x[/tex]

[tex]C = 29.53x[/tex]

The question cannot be solved further since the dimension of the fence is not given

If you know the dimension, calculate the fence perimeter and substitute the value for x


What's 60 in the ratio 1 : 4

Answers

Answer:

15/240 = 5/80= 1:16. helpful answer

Answer:

1+4=60

5=60

60/5

12#

Step-by-step explanation:

or,let it be X

1x+4x=60

5x=60

X=60/5

there fore

X=12#

I need help please someone help me

Answers

Answer:

We know that the height equation is given by:

H(t) = -16*t^2 + 108*t + 28

in ft.

First, we want to find the maximum height of the ball.

The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.

We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).

To get the velocity equation we need to derivate the above equation, we will get:

V(t) = 2*(-16)*t + 1*108

V(t) = -32*t + 108

We need to find the value of t such that this is zero, we will get:

V(t) = 0 =  -32*t + 108

        32*t = 108

             t = 108/32 = 3.375

So the ball reaches its maximum height after 3.375 seconds.

Then the maximum height is given by the height equation evaluated in that time, we will get:

H(3.375) =  -16*(3.375)^2 + 108*3.375 + 28 = 210.25

Then the maximum height of the ball is 210.25 ft

The ball will hit the ground when:

H(t) = 0

Then we just need to solve:

0 =  -16*t^2 + 108*t + 28

Using the Bhaskara's equation we can find that the two solutions for t are:

[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]

So the two solutions are:

t = (-108 + 116)/-32 = -0.25

t = (-108 - 116)/-32 = 7

Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).

Then we can conclude that the ball hits the ground after 7 seconds.


The yearbook staff receive 75 submissions for yearbook articles. Paul will acceptſ of all submissions. Currently, Paul plans for the yearbook to have 156
pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.

Answers

Answer:

The correct answer is - 332 pages.

Step-by-step explanation:

Given:

number of articles submissions - 75

number of pages in the yearbook on current plan = 156

pages required for two articles = 13 pages.

The number of pages to add = ?

Solution:

1 article takes pages in the yearbook = 13/2

= 6.5

the number of pages required for 75 articles = 75*6.5

= 487.5

The number of pages to add in the yearbook = 487.5 - 156

= 331.5 or 332.

Thus, the correct answer is - 332 pages.

I’ll mark brainliest

Answers

Answer:

B

Step-by-step explanation:

they said 2 hours for each final

Find the volume of the figure shown below.

A)42 1/2 units^3
B)11 1/4 units^3
C)14 1/4 units^3
D)80 1/4 units^3
E)None of these answers are correct

Answers

Answer:

A. 42½ units

Step-by-step explanation:

the volume = 5×2×4¼ = 10×4¼ = 42½

HELP PLEASE!! I WILL MARK BRAINLIST

Answers

Answer:

D

Step-by-step explanation:

Have a nice day :)

If any of the graphs below have a Hamiltonian circuit, list the vertices of the complete circuit. There may be many possibilities. For full credit, just list one for each graph, if the circuit exists

Answers

9514 1404 393

Answer:

ABHGEFDCAdoes not existECBADFE

Step-by-step explanation:

A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.

__

For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.

__

For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. ​

Answers

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.

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