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maksim [4K]
1 year ago
10

The price that a company charged for a basketball hoop is given by the equation 50 - 5x^2 where x is the number of hoops that ar

e produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?
1.3 million hoops
1.4 million hoops
15 million hoops
30 million hoops
Mathematics
2 answers:
DiKsa [7]1 year ago
4 0

Answer: The correct option is first, the number of basketball hoops did the company previously produce to make the same profit is 1.3 million hoops.

Explanation:

Let the number of basketball hoops did the company previously produce to make the same profit be x.

Total Revenue = Price * Quantity

The total revenue in million dollars is,

\text{Total Revenue}=(50-5x^2)x

\text{Total Revenue}=50x-5x^3

The total cost in million dollars is,

Total Cost = One unit cost * Quantity

\text{Total Cost}=30x

Profit = Total Revenue - Total Cost

\text{Profit}=50x-5x^3-30x

The profit is 15 million.

15=20x-5x^3

5x^3-20x+15=0\\x^2-4x+3=0\\(x-1)(x^2+x-3)=0

The value of x is 1 and \frac{-1\pm \sqrt{13}}{2}.

The production is always positive therefore the value of x either 1 or 1.3. Since 1 million is not available in the options therefore the the correct optin is 1.3 million hoops.

uysha [10]1 year ago
4 0

Answer

A!!!!!

Step-by-step explanation:

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Answer:

w/2 = 7.5/5

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Step-by-step explanation:

Remaining question below:

Which proportion could Maddy use to model this situation?

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Equates the ratio

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Temperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit.
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Answer:

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F=32+1.8CF=32+1.8C

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1 year ago
A firm has a revenue function that can be represented by r (x)=700x-0.35x^2, where r (x) is the total revenue (in dollars) and x
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Answer:

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How many in dollars is the maximum revenue when the maximum of units are sold? $350,000

Step-by-step explanation:

We get max value of a function if we differentiate it and set it equal to 0.

We need to differentiate r(x) and set it equal to 0 and solve for x.

<u><em>That would be number of units sold to get max revenue.</em></u>

<u><em /></u>

<u>Then we take that "x" value and substitute into r(x) to get the max revenue amount.</u>

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Before differentiating, we see the rules shown below:

f(x)=ax^n\\f'(x)=n*ax^{n-1}

Where

f'(x) is the differentiated function

Now, let's do the process:

r (x)=700x-0.35x^2\\r(x)=700-2*0.35x\\r(x)=700-0.7x\\0=700-0.7x\\0.7x=700\\x=1000

So, 1000 units need to be sold for max revenue

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1 year ago
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?
zhuklara [117]

Answer:

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Explanation:

<u>1) </u><u>Vertex form</u><u> of the function that represents a parabola.</u>

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression  factor (in the case |A| < 1) factor.

<u>2) Find the vertex of the first function, f(x) = x²</u>

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

<u>3) Find teh vertex of the second function, g(x) = x² -10x + 2</u>

The method is transforming the form of the function by completing squares:

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That is the searched vertex form: g(x) = (x - 5)² - 23.

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1 year ago
A small coffee shop sells freshly squeezed juices in a refrigerated unit with slots where juice is displayed. These slots are ca
lianna [129]

Answer: kindly check attached picture

Step-by-step explanation:

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In other to make the proportion of facing visible on the graph we multiply by 100; Hence,

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Hence, from the plot, it could be clearly seen that the distribution of facing is different or not equal to the number of juice sold.

The barchart produced is attached below.

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