Tag: business mathematics and statistics

Quizzes (14) Questions (285)

Questions Related to business mathematics and statistics

Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

Given the marginal cost function $\dfrac{2x}{3}+3-\dfrac{16}{x^2}$, find  average cost function.

  1. $\dfrac{1}{3}x^2+3x-7+\dfrac{16}{x}$
  2. $\dfrac{1}{2}x^2+3x-7+\dfrac{16}{x}$
  3. $\dfrac{1}{4}x^2+3x-7+\dfrac{16}{x}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have $MC=\dfrac{2x}{3}+3-\dfrac{16}{x^2}$


$\Rightarrow$  $Average\,\,cost=\int (MC)dx$ 


$\Rightarrow$   $Average\,\,cost=\int (\dfrac{2x}{3}+3-\dfrac{16}{x^2})dx$


$\therefore$   $Average\,\,cost=\dfrac{2x^2}{2\times 3}+3x-7+\dfrac{16}{x}$

$\Rightarrow$   $Average\,\,cost=\dfrac{1}{3}x^2+3x-7+\dfrac{16}{x}$

Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

The cost function of a firm $C(x)=3x^2-2x+3$. Find the average cost when $x=3$.

  1. 8

  2. 9

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $C(x)=3x^2-2x+3$

$\Rightarrow$  Average cost = $\dfrac{C(x)}{x}$

$\Rightarrow$  Average cost = $\dfrac{3x^2-2x+3}{x}$

$\Rightarrow$  Average cost = $3x-2+\dfrac{3}{x}$.

$\Rightarrow$  Substitute value of $x=3$,
$\Rightarrow$  Average cost = $3\times 3-2+\dfrac{3}{3}=9-2+1=8$
$\therefore$    $Average\, cost\,=8$. 

Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

If the demanding Law is given by $q = \dfrac{20}{p+1}$, find the elasticity of demand with respect to price at the point when $p = 3.$

  1. $\dfrac43$
  2. $-\dfrac34$
  3. $\dfrac23$
  4. $-\dfrac32$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Elasticity of demand $=\cfrac{\cfrac{dq}{q}}{\cfrac{dp}{p}}=-\cfrac{p}{(p+1)}$
When $p=3$
Elasticity of demand $=-\cfrac{3}{4}$
Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

If the total cost function for a manufacturer is given by $C =\dfrac{5x^2}{\sqrt(x^2+3)}+5000$, find marginal cost function.

  1. $\dfrac{3x(x^2+6)}{(x^2+3)^{(3/2)}}$
  2. $\dfrac{4x(x^2+6)}{(x^2+3)^{(3/2)}}$
  3. $\dfrac{5x(x^2+6)}{(x^2+3)^{(3/2)}}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given cost function $C\left(x\right)=\dfrac{5x^2}{\sqrt{\left(x^2+3\right)}}+5000$


Marginal cost function is given by $C'\left(x\right)$

$C'\left(x\right)=\dfrac{\left(\sqrt{x^2+3}\right)\left(10x\right)-\dfrac{5x^2}{2\sqrt{x^2+3}}\times\left({2x+10}\right)}{\left(\sqrt{x^2+3}\right)^2}$

$\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}$

$C'\left(x\right)=\dfrac{2\left(x^2+3\right)\left(10x\right)-5x^2\left(2x\right)}{2\left(\sqrt{x^2+3}\right)^3}=\dfrac{5x\left(x^2+6\right)}{\left(x^2+3\right)^\tfrac{3}{2}}$

Multiple choice business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

State, which of the following variables are continuous and which are discrete :


Sizes of shoes is discrete
If true then enter $1$ and if false then enter $0$

  1. $1$
  2. $0$

  3. Can't determine

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Size of a shoe can have integer values only. Hence, it is a discrete variable.

Multiple choice business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

Which one of the statement is discrete variable?

  1. weight of animals in zoo

  2. distance travelled between colleges

  3. number of heads by flipping a coins

  4. height of animals in park
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.

Multiple choice business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

The statement "number of heads when flipping a coin" is an example of ______ variable.

  1. continuous

  2. dependent

  3. discrete

  4. nominal
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.