c(t) = t/72 represents the number of cases the coach will
need to purchase to have a total of t tennis balls.
I am hoping that this answer has
satisfied your query and it will be able to help you in your endeavor, and if
you would like, feel free to ask another question.
The domain is the set of feasible inputs, i.e. the x-coordinates in which you can evaluate the function.
We can see that this function is defined only for x values between -1 and 3 (included), so this is your domain.
Answer:
![Leg\ 1 = 8](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%208)
![Leg\ 2 = 15](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2015)
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
![Hyp^2 = Adj^2 + Opp^2](https://tex.z-dn.net/?f=Hyp%5E2%20%3D%20Adj%5E2%20%2B%20Opp%5E2)
In this case:
![17^2 = x^2 + (2x- 1)^2](https://tex.z-dn.net/?f=17%5E2%20%3D%20x%5E2%20%2B%20%282x-%201%29%5E2)
Open Bracket
![17^2 = x^2 + 4x^2- 2x-2x + 1](https://tex.z-dn.net/?f=17%5E2%20%3D%20x%5E2%20%2B%204x%5E2-%202x-2x%20%2B%201)
![17^2 = 5x^2 - 4x + 1](https://tex.z-dn.net/?f=17%5E2%20%3D%205x%5E2%20-%204x%20%2B%201)
![289= 5x^2 - 4x + 1](https://tex.z-dn.net/?f=289%3D%205x%5E2%20-%204x%20%2B%201)
Collect Like Terms
![5x^2 - 4x + 1 - 289 = 0](https://tex.z-dn.net/?f=5x%5E2%20-%204x%20%2B%201%20-%20289%20%3D%200)
![5x^2 - 4x - 288 = 0](https://tex.z-dn.net/?f=5x%5E2%20-%204x%20-%20288%20%3D%200)
Solving using quadratic formula:
![x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
So:
or ![x = -7.2](https://tex.z-dn.net/?f=x%20%3D%20-7.2)
Since, x can't be negative, then:
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
One of the leg is:
![Leg\ 1 = x](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%20x)
![Leg\ 1 = 8](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%208)
![Leg\ 2 = 2x - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%202x%20-%201)
![Leg\ 2 = 2*8 - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%202%2A8%20-%201)
![Leg\ 2 = 16 - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2016%20-%201)
![Leg\ 2 = 15](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2015)
Using the Empirical Rule, it is found that there is a 68% probability that a student scored between 66 and 82.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, considering the mean of 74 and the standard deviation of 8, we have that:
74 - 8 = 66
74 + 8 = 82.
Hence, there is a 68% probability that a student scored between 66 and 82.
More can be learned about the Empirical Rule at brainly.com/question/24537145