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2 years ago

Which one should I choose

Mathematics

1 answer:

SIZIF [17.4K]2 years ago

5 0

Answer:

I think 9 is correct

if answer is correct then please mark me as brainlist

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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 researcher is interested in estimating the mean weight of a semi trailer truck to determine the potential load capacity. She t

Kaylis [27]

Answer: 95% confidence interval = 20,000 ± 2.12 $\times$ $\frac{1500}{\sqrt{17} }$

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

Step-by-step explanation:

Given :

Sample size(n) = 17

Sample mean = 20000

Sample standard deviation = 1,500

5% confidence

∴ $\frac{\alpha}{2}$ = 0.025

Degree of freedom ( $d_{f}$ ) = n-1 = 16

∵ Critical value at ( 0.025 , 16 ) = 2.12

∴ 95% confidence interval = mean ± $Z_{c}$ $\times$ $\frac{\sigma}{\sqrt{n} }$

Critical value at 95% confidence interval = 20,000 ± 2.12 $\times$ $\frac{1500}{\sqrt{17} }$

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

3 0

3 years ago

Please someone help me: Complete the reasons for the proof.

dimulka [17.4K]

Step-by-step explanation:

1) given

2) 2 non - common sides in 1 ray

3) supplemental

5) opposite angles are congruent

5 0

2 years ago

Read 2 more answers

Michael sold his painting for $50. He sold his painting for $10 less than its original price. At what price did Michael buy the

netineya [11]

It would be 60. He sold his painting for 50 which was 10 less that the original price. So 50+10=60

7 0

3 years ago

Read 2 more answers

1/(x+4)(x-2)(x-5) excluded values

UNO [17]

Answer:

see explanation

Step-by-step explanation:

The excluded values are any values of x that make the function undefined

Given

$\frac{1}{(x+4)(x-2)(x-5)}$

The denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the values that x cannot be.

(x + 4)(x - 2)(x - 5) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x - 5 = 0 ⇒ x = 5

x = - 4, x = 2, x = 5 are the excluded values

4 0

2 years ago