9514 1404 393
Answer:
y = 2x +5
Step-by-step explanation:
"Gradient" is another word for "slope." The given point (with x-coordinate equal to zero) is the y-intercept. So, it is easy to write the equation in slope-intercept form:
y = mx + b . . . . . . line with slope m and y-intercept b
y = 2x + 5
36-4.5x+36=102-7.5x-60
72-4.5x=42-7.5x
72+3.5x=42
3.5x=-30
x=8.57
Answer:
A 47.1 in
Step-by-step explanation:
This is a pretty simple Java (though probably applicable to all programming) question:
Math. Random() returns a number between zero and one.
If I want to return an integer between zero and hundred, I will do:
(int) Math. Floor(Math. Random() * 101)
Between one and hundred, I would do:
(int) Math. Ceil(Math. Random() * 100)
But what if I wanted to get a number between three and five? Will it be like following statement:
Since h represents the height of the ball at any given time, t, let h = 25, such that the ball will be 25m high at t.
Now, we have 25 = 20t - 5t²
5t² - 20t + 25 = 0
t² - 4t + 5 = 0
![\frac{4 +- \sqrt{16 - 20}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%2B-%20%5Csqrt%7B16%20-%2020%7D%7D%7B2%7D)
Since the discriminant is less than zero, there are no solutions.
Hence, the ball will never be 25m high.
Using the normal distribution, it is found that the 10.56% of fire station response times are under 3 minutes.
<h3>How to get the z scores?</h3>
If we've got a normal distribution, then we can convert it to a standard normal distribution and its values will give us the z score.
If we have
![X \sim N(\mu, \sigma)](https://tex.z-dn.net/?f=X%20%5Csim%20N%28%5Cmu%2C%20%5Csigma%29)
(X is following a normal distribution with mean
and standard deviation
)
then it can be converted to a standard normal distribution as
![Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D%2C%20%5C%5C%5C%5CZ%20%5Csim%20N%280%2C1%29)
The mean is of 4.5 minutes,
The standard deviation is of 1.2 minutes,
The proportion of fire station response times are under 3 minutes is the p-value of Z when X = 3, hence:
![Z = \dfrac{X - \mu}{\sigma}, \\\\Z = \dfrac{3 - 4.5}{1.2}, \\\\Z = -1.25](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D%2C%20%5C%5C%5C%5CZ%20%3D%20%5Cdfrac%7B3%20-%204.5%7D%7B1.2%7D%2C%20%5C%5C%5C%5CZ%20%3D%20-1.25)
-1.25 has a p-value of 0.1056.
0.1056 x 100% = 10.56%
10.56% of fire station response times are under 3 minutes.
To learn more about the normal distribution, brainly.com/question/24663213
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