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3 years ago

A shirt originally costing $20 is marked as 15% off. What is the sale price?

Mathematics

1 answer:

tester [92]3 years ago

7 0

Answer:

Step-by-step explanation:

Set up a proportion ?/20=15/100

cross multiply and divide 15x20=300

divide 300÷100=3

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QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

Part A

Price Function $= 580 - 10x$

The revenue function

$R(x)=x\cdot (580-10x)\\R(x)=580x-x^2$

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

Part B

(Fixed Cost)

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

Marginal Cost Function

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

Part C

Profit Function

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

The number of cakes that maximizes profit is 4.

6 0

3 years ago

A large city has a population of 8,000,000 and an area of 20.5 square miles. what is the city's approximate population density?

gayaneshka [121]

Answer: Approximately 390,244 people per square mile

Work Shown:

Density = population/area

Density = (8 million people)/(20.5 square miles)

Density = 390,243.9024 approximately

This rounds to 390,244 since we're talking about the number of people.

3 0

3 years ago

Please answer this correctly

Fantom [35]

Answer:

4 weeks 5 days

Step-by-step explanation:

3 0

4 years ago

What is the range of F(x)=72x-x^2

Marianna [84]

Answer:

Range of F(x) = (-∞ ,72).

Step-by-step explanation:

Range of the function F(x) means the set of values which are taken by the function along its domain.

F(x) = 72 - $x^{2}$

Since coefficient of $x^{2}$ is negative on the right side ,

Maximum value of F(x) will come at x = 0.

Which is, F(0) = 72.

Now, as x increases , F(x) decreases , when x will reach infinity ,

F(x) will be reaching negative of infinity .

Thus, F(x) is ranging from -∞ to 72 .

Range of F(x) = (-∞ ,72).

3 0

3 years ago

Find the value of n, correct to 4 significant figures.

Law Incorporation [45]

Answer:

6.708

Step-by-step explanation:

Y varies directly as the square of x (Given)

$\implies y\:\alpha \:x^2$ ......(1)

Y varies inversely as the square root of z (Given)
$\implies y\:\alpha\: \frac{1}{\sqrt z}$ ......(2)

Combining (1) & (2), we find:

$y\:\alpha \:\frac{x^2}{\sqrt z}$

$\implies y=\frac{kx^2}{\sqrt z}$ (Where k is constant of proportionality).....(3)

Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.

$2=\frac{k(3)^2}{\sqrt 4}$

$\implies 2=\frac{k(9)}{2}$

$\implies k =\frac{4}{9}$

Plugging the value of k in (3), we find:

$y=\frac{4x^2}{9\sqrt z}$ ....(4)

Next, in equation (4), plug y = 5, x = n and z = 16 and obtain the value of n by solving it.

$5=\frac{4(n)^2}{9\sqrt {16}}$

$\implies 5=\frac{4(n)^2}{9(4)}$

$\implies 5=\frac{(n)^2}{9}$

$\implies 5(9)=(n)^2$

$\implies 45=(n)^2$

$\implies n=\sqrt{45}$

$\implies n=6.70820393$

$\implies n\approx 6.708$

7 0

2 years ago