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astra-53 [7]
4 years ago
14

Owen receives $10 and puts it into his savings account. He adds $0.50 to the account each day for a number of days, dd, after th

at. He writes the expression 10+0.5(d−1) to find the amount of money in his account after dd days. Which statement about his expression is true?
A.) It is the product of the initial amount and the additional amount after d days.


B.) It is the sum of the initial amount and the number of days, d.


C.)It is the difference between the initial amount and the additional amount after d days.


D.)It is the sum of the initial amount and the additional amount after d days.
Mathematics
2 answers:
Nady [450]4 years ago
7 0

Answer:

Option (d) is correct.

It is the sum of the initial amount and the additional amount after d days.

Step-by-step explanation:

Given :  Owen receives $10 and puts it into his savings account. He adds $0.50 to the account each day for a number of days, d, after that.  

He writes the expression 10+0.5(d−1) to find the amount of money in his account after d days.

We have to choose the statement from the given options that is correct about the given expression.

Since, The given expression is 10+0.5(d−1)

Where 10 is the initial amount and 0.5(d−1) is the additional amount after d days.

So, in statement , It is the sum of the initial amount and the additional amount after d days.

Option (d) is correct.

                   

tankabanditka [31]4 years ago
6 0

It is the sum of the initial amount and the additional amount after d days



HOPE THIS HELPS!


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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
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Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

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