Fill in the blank distributive property

A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plate

yulyashka [42]

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:

$\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}$

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:

$C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)$

$C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)$

At C'(x) = 0

$\dfrac{12500}{x^2} = 20$

$\dfrac{12500}{20} = x^2$

$x^2= 625$

$x = \sqrt{625}$

x = 25

$C'' (x) = -12500 \times \dfrac{-2}{x^3} +0$

$C'' (x) = \dfrac{25000}{x^3}$

where; x = 25

$C'' (x) = \dfrac{25000}{25^3}$

C''(x) = 1.6

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

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

4 0

3 years ago

Jaymie wants to construct congruent angles with a compass and straightedge, while Annie wants to construct congruent segments wi

SashulF [63]

Jaymie will measure the segment and then place the point just across from the line's beginning point to create a congruent segment that shows the similarity between them.

<h3>What are the conditions of the congruent triangle?</h3>

Triangles that are equivalent in terms of size and form are known as a congruent triangle.

Segments will be built using the straightedge, and measurements will be taken using the compass. They will pick a starting point and draw a line using the straightedge, then use the compass to finish the job.

To make the congruent segment, Jaymie will measure the segment and then position the point that is opposite from the line's starting point.

Jaymie, on the other hand, will have to work a bit harder with the compass since she will need to draw a semi-circle in the original angle and transfer this measurement to the new line in order to create congruent angles.

To learn more about the congruent triangle refer;

brainly.com/question/12413243

#SPJ1

6 0

2 years ago

A group of five people are all working on the same mathematics problem. On the night before it is due, they call each other to d

UkoKoshka [18]

Answer:

Minimum number of calls = 10

Step-by-step explanation:

Lets name the five people as A,B,C,D and E.

<u>On the night before ,each person talks to every other person atleast once that means A would talk to B,C,D and E atleast once.</u>

Lets start with A. He would talk to other 4 people which means there would be 4 phone calls made.

Now lets take B. He can talk to A,C,D and E. But A has already talked to C therefore to get minimum number of phone calls , B need not call A again. So he calls only C,D and E.

In case of C using similar logic he need to talk to only D and E.

For D , he talks to E alone.

E does not have to talk to anyone as he has already talked to everyone atleast once.

Total calls = 4 + 3 + 2 + 1

= 10

5 0

3 years ago

A land developer is splitting up 1.19 hectares of land to form 9 identical properties. To the nearest tenth of a hectare, what s

OlgaM077 [116]

In this question , it is given that the land is 1.19 hectares. And the land developer splitting it into 9 identical properties . So to find the size of each property, we need to divide 1.19 by 9 and on doing that, we will get 0.13 hectares .

So the size of each property is 0.13 hectares .

4 0

3 years ago

What is the surface area of this rectangular prism?

dybincka [34]

Answer:

256 ft²

Step-by-step explanation:

4 lateral faces + 2 bases

The total area

$=2 \times (12 \times 4) + 2 \times (12 \times 5) + 2 \times (5 \times 4)$