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balandron [24]
2 years ago
15

Ben and Alyssa play a game in which they earn the same number of points for each goal and lose the same number of points for eac

h penalty. Ben makes 7 goals and 2 penalties, ending the game with 21 points. Alyssa earns 10 goals and 8 penalties and ends the game with -6 points. How much does a penalty cost and how much does a goal give?
Mathematics
1 answer:
Nadya [2.5K]2 years ago
5 0

Answer:

Each goal gives 5 points and a penalty costs 7 points.

Step-by-step explanation:

Let a penalty cost = x points

And a goal gives = y points

Ben makes 7 goals and 2 penalties ending the game with 21 points,

7y - 2x = 21 --------(1)

Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,

10y - 8x = -6

5y - 4x = -3 --------(2)

Equation (1) multiplied by 2, then subtracted from equation (2),

(5y - 4x) - 2(7y - 2x) = -3 - 2(21)

5y - 4x - 14y + 4x = -3 - 42

-9y = -45

y = 5

From equation (1)

7(5) - 2x = 21

35 - 2x = 21

2x = 35 - 21

2x = 14

x = 7

Therefore, each goal gives 5 points and a penalty costs 7 points.

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A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation A pizza delivery company buys
zubka84 [21]

Answer:

z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028

z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441

An we can use the normal standard table and the following difference and we got this result:

P(-1.028

Step-by-step explanation:

Assuming this statement to complete the problem "with a standard deviation 5 mpg"

We have the following info given:

\mu = 34 represent the mean

\sigma= 5 represent the deviation

We have a sample size of n = 54 and we want to find this probability:

P(33.3 < \bar X< 34.3)

And for this case since the sample size is large enough >30 we can apply the central limit theorem and then we can use this distribution:

\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})

And we can use the z score formula given by:

z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028

z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441

An we can use the normal standard table and the following difference and we got this result:

P(-1.028

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3 years ago
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Answer:

Here is your answer:

5x + 2 < 32

solution:

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<em><u>Hope</u></em><em><u> </u></em><em><u>it</u></em><em><u> </u></em><em><u>will</u></em><em><u> </u></em><em><u>help</u></em><em><u> </u></em><em><u>you</u></em>

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