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kiruha [24]
3 years ago
10

Kim's softball team is playing in the championship game. They are losing by a score of 1 7 1717 to 6 66. There are 4 44 innings

to go. Kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (Each run is worth 1 11 point.) Let r rr represent the number of runs per inning. Assume that the team scores the same number of runs per inning, and write an inequality to determine the number of runs per inning needed to win the game.
Mathematics
2 answers:
Furkat [3]3 years ago
7 0

Answer:

4r+6 > 17, and they would need at least 3 runs per inning.

Step-by-step explanation:

Letting r represent the number of runs per inning, for 4 innings, we have 4r.

The team already has 6 runs; this means we add the additional runs to this:

4r+6

The team wants to score more than the other team; this means they need more than 17:

4r+6 > 17

To solve this, subtract 6 from each side:

4r+6-6 > 17-6

4r > 11

Divide both sides by 4:

4r/4 > 11/4

r > 2.75

We can't have a portion of a run, so this means there will be at least 3 runs per inning.

irga5000 [103]3 years ago
6 0
The inequality is
6+4r>17
The miminum number of runs per inning is
3.
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Answer:

The required function is: P(x)=-3x^2+78x-360

The price for each feeder to maximize profit should be $13.

The maximum weekly profit is $147

Step-by-step explanation:

Consider the provided information.

Part (A)

The materials for each feeder cost $6, and the society sells an average of 30 per week at a price of $10 each.

Let x be the price per feeder.

Profit = Revenue - cost

So the profit per feeder is x-6

If we increase then for every dollar increase, it loses 3 sales per week.

This can be written as:

30-3(x-10)

30-3x+30

-3x+60

Where x-10 represents the increase in price and 3  represents the decrease in sales per week.

Thus the profit will be:

P(x)=(x-6)(-3x+60)

P(x)=-3x^2+78x-360

Hence, the required function is: P(x)=-3x^2+78x-360

Part (B) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

The above function is a downward parabola so the maximum will occur at vertex.

The x coordinate of the vertex of parabola is: x=\frac{-b}{2a}

Substitute a=-3, b=78 and c=-360 in above.

x=\frac{-78}{2(-3)}=13

Hence, the price for each feeder to maximize profit should be $13.

Now substitute the value of x in P(x)=-3x^2+78x-360

P(x)=-3(13)^2+78(13)-360=$147

Hence, the maximum weekly profit is $147

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BigorU [14]

Answer:

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Step-by-step explanation:

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A method you could use to do this more easily or check your answers would be to graph the fuctions used on a website like desmos

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