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Anvisha [2.4K]
2 years ago
14

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as ed

iting) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $57,077 , and the variable costs will be $11.75 per book. With the other method, the one-time fixed costs will total $22,459, and the variable costs will be $21.25 per book. For how many books produced will the costs from the two methods be the same?
Mathematics
1 answer:
Lady_Fox [76]2 years ago
4 0

Answer:

for 3644 produced books the costs will be the same.

Step-by-step explanation:

x = number of books

f(x) = production method 1 costs

g(x) = production method 2 costs

f(x) = 11.75x + 57077

g(x) = 21.25x + 22459

for what number of books (x) will that be the same ?

11.75x + 57077 = 21.25x + 22459

34618 = 9.5x

x = 34618 / 9.5 = 3644

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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters o
ladessa [460]
X = amount of the 18% solution

y = amount of the 40% solution

we know the 18% solution has only 18% of alcohol, the rest is maybe water or something, now, how many liters is 18%?  well, 18% of anything is just (18/100) * anything, so, 18% of x is just (18/100) *x or 0.18x, and that's how many liters are there.

likewise, how many liters are there in the 40% solution?  well, (40/100) * y, or 0.4y, that many.

we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that?  well, (20/100) * 10, or 2 liters.

\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}

\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
x=\cfrac{-2}{-0.22}\implies x=\cfrac{100}{11}\implies x=9\frac{1}{11}

how much of the 40% solution?  well y = 10 - x
3 0
3 years ago
23/50 of Zanders friends prefer to stay home on Friday night what percent of Xander's friends prefer to stay home on Friday nigh
koban [17]

Answer:

46%  of Xander's friends prefer to stay home on Friday nights.

Step-by-step explanation:

Formula

Percentage = \frac{Part\ value\times 100}{Total\ value}

As given

\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.

i.e

Zanders friends prefer to stay home on Friday night = 23

Total numbers of Zanders friends are 50.

Part value = 23

Total value = 50

Put in the formula

Percentage = \frac{23\times 100}{50}

Percentage = \frac{2300}{50}

Percentage = 46%

Therefore 46%  of Xander's friends prefer to stay home on Friday nights.

3 0
3 years ago
A plumber charges $52.50 per hour plus a $75.00 service charge. Your father's firm hired him to fix some leaky pipes.
Setler79 [48]
Cost as a function of hours is:

c(h)=52.5h+75
4 0
3 years ago
Hello everyone, I have this question. Please help me.
kobusy [5.1K]

Answer:

7 reservoirs

Step-by-step explanation:

1 yards = 3 feet => 3.5 yards = 10.5 feet

To determine how many numbers of reservoirs to reserve 90000, we first need to determine the capacity of each reservoirs (how much liquid one reservoir can contain) - which is equal to the volume.

The formula to calculate the volume of a circular cylinder is:

  - <em>Volume of cylinder = Area of base x Height </em>

<em />

The base of this cylinder is a circle with radius equal to 4 feet. (\pi = 3.14)

=> The are of the base is = \pi *radius^{2} = 3.14 x 4^2 = 50.24 feet square

=> The volume of cylinder = Area of base x Height

=> The volume of one cylinder = 50.24 x 10.5 = 527.52 Cubic foot

We have: 1 cubic foot = 28.317 liters

=> 1 liter = 1/28.317 cubic foot

=> 90000 liters equal to: 90000/28.317 = 3,178.303 cubic foot

The number of reservoirs needed to contain 90000 liters of liquid is:

3,178.303/527.52 = 6.025

=> So that it needs 7 reservoirs to store all 90000 liters of liquid.

5 0
2 years ago
A jar contains six blue marbles and five red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you ch
TEA [102]

The jar has 6+5=11 marbles.

We have to find the probability of the following event:

1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red

2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)

The probability of the first event is:

P_1=\frac{5}{11}

The probability of the second event is:

P_2=\frac{4}{10}=\frac{2}{5}

The probability of the both events to happen is:

P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818

3 0
3 years ago
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