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2 years ago

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Mathematics

1 answer:

Sati [7]2 years ago

8 0

The correct answer is option b which is the break-even quantity will be 20217 units.

<h3>What is the break-even point?</h3>

The point at which the company will not have any profit and loss on the products they manufactured they only get the amount they invested in manufacturing the product is called the break-even point.

Given that:-

If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400.

The formula for calculating break-even quantity will be given as:-

$BEQ = \dfrac{FC}{SP-VC}$

Here,

FC = Fixed cost = $281000

SP = Selling price = $33

VC = Variable cost = $21

The fixed cost is reduced by $38400 so the fixed cost now:-

FC = $281000 - $38400

FC = $242600

$BEQ = \dfrac{242600}{33-21}$

BEQ = 20217 units

Therefore the correct answer is option b which is the break-even quantity will be 20217 units.

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The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .1

snow_lady [41]

We assumed in this answer that the question b is, Are the events V and M independent?

Answer:

(a). The probability that a student has either a Visa card or a MasterCard is<em> </em> $\\ P(V \cup M) = 0.88$ . (b). The events V and M are not independent.

Step-by-step explanation:

The key factor to solve these questions is to know that:

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

We already know from the question the following probabilities:

$\\ P(V) = 0.73$

$\\ P(M) = 0.18$

The probability that a student has both cards is 0.03. It means that the events V AND M occur at the same time. So

$\\ P(V \cap M) = 0.03$

The probability that a student has either a Visa card or a MasterCard

We can interpret this probability as $\\ P(V \cup M)$ or the sum of both events; that is, the probability that one event occurs OR the other.

Thus, having all this information, we can conclude that

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

$\\ P(V \cup M) = 0.73 + 0.18 - 0.03$

$\\ P(V \cup M) = 0.88$

Then, <em>the probability that a student has either a Visa card </em><em>or</em><em> a MasterCard is </em> $\\ P(V \cup M) = 0.88$ .<em> </em>

Are the events V and M independent?

A way to solve this question is by using the concept of <em>conditional probabilities</em>.

In Probability, two events are <em>independent</em> when we conclude that

$\\ P(A|B) = P(A)$ [1]

The general formula for a <em>conditional probability</em> or the probability that event A given (or assuming) the event B is as follows:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

If we use the previous formula to find conditional probabilities of event M given event V or vice-versa, we can conclude that

$\\ P(M|V) = \frac{P(M \cap V)}{P(V)}$

$\\ P(M|V) = \frac{0.03}{0.73}$

$\\ P(M|V) \approx 0.041$

If M were independent from V (according to [1]), we have

$\\ P(M|V) = P(M) = 0.18$

Which is different from we obtained previously;

That is,

$\\ P(M|V) \approx 0.041$

So, the events V and M are not independent.

We can conclude the same if we calculate the probability

$\\ P(V|M)$ , as follows:

$\\ P(V|M) = \frac{P(V \cap M)}{P(M)}$

$\\ P(V|M) = \frac{0.03}{0.18}$

$\\ P(V|M) = 0.1666.....\approx 0.17$

Which is different from

$\\ P(V|M) = P(V) = 0.73$

In the case that both events <em>were independent</em>.

Notice that

$\\ P(V|M)*P(M) = P(M|V)*P(V) = P(V \cap M) = P(M \cap V)$

$\\ \frac{0.03}{0.18}*0.18 = \frac{0.03}{0.73}*0.73 = 0.03 = 0.03$

$\\ 0.03 = 0.03 = 0.03 = 0.03$

3 0

4 years ago

What is 1/7 divided by 1/3

KiRa [710]

Answer:

Step-by-step explanation:

0.428

(.43)

7 0

3 years ago

Select ALL of the choices that are equal to (-2) - (-5)

saveliy_v [14]

(-2)+(-5) ok ok have a good day

5 0

3 years ago

to solve the equation |x-9|=0.5x, kiana graphed the functions f(x)=|x-9| and g(x)=0.5x on the same set of coordinate axes. She t

Pani-rosa [81]

Answer:

The answer is the option D

$f(6)=g(6)$ and $f(18)=g(18)$

Step-by-step explanation:

we have

$f\left(x\right)=\left|x-9\right|$

$g(x)=0.5x$

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

see the attached figure

The solution are the points $(6,3)$ and $(18,9)$

therefore

The solution of the equation $\left|x-9\right|=0.5x$ are

$x=6, x=18$

For $x=6$

$f\left(6\right)=\left|6-9\right|=3$

$g(6)=0.5(6)=3$

$f(6)=g(6)$

For $x=18$

$f\left(18\right)=\left|18-9\right|=9$

$g(18)=0.5(18)=9$

$f(18)=g(18)$

therefore

$f(6)=g(6)$ and $f(18)=g(18)$ because the intersection points are common points for both graphs

5 0

3 years ago

Read 2 more answers

Which pair of statements describes the end behavior of the graphed function

Alex777 [14]

The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

<h3>What is polynomial?</h3>

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

$\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n$

We have a polynomial function:

$\rm f(x) = x^{3}+2x^{2}-5x-6$

The function is a cubic function and the graph of the cubic function will be a curve.

As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.

Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

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6 0

2 years ago