Answer:
x = 1.4 (or 21/15)
Step-by-step explanation:
12x - 15 = 6 - 3x
+3x +3x
-----------------------
15x - 15 = 6
+15 +15
-----------------------
15x = 21
/15 /15
----------------------
x = 21/15 or
x = 1.4
Answer:
![y=3x-3](https://tex.z-dn.net/?f=y%3D3x-3)
Step-by-step explanation:
The equation of the line with the slope
and passing through the point
is
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=y-y_0%3Dm%28x-x_0%29)
In your case,
![m=3\\ \\x_0=3\\ \\y_0=6](https://tex.z-dn.net/?f=m%3D3%5C%5C%20%5C%5Cx_0%3D3%5C%5C%20%5C%5Cy_0%3D6)
Hence, the equation of the line is
![y-6=3(x-3)\\ \\y-6=3x-9\\ \\y=3x-9+6\\ \\y=3x-3](https://tex.z-dn.net/?f=y-6%3D3%28x-3%29%5C%5C%20%5C%5Cy-6%3D3x-9%5C%5C%20%5C%5Cy%3D3x-9%2B6%5C%5C%20%5C%5Cy%3D3x-3)
So what you do is (2/3)x-9=7. Add 9 to both sides (2/3)x=16. Multiply by reciprocal on both sides 16 x (3/2). 16 x 3 = 48. 48/2=24
Answer:
The standard deviation of the sample mean is
Step-by-step explanation:
From the question we are told that
The mean is ![\= x = 60](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%2060)
The standard deviation is ![\sigma = 21](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%2021)
The sample size is ![n = 60](https://tex.z-dn.net/?f=n%20%20%3D%20%2060)
Generally the standard deviation of the sample mean is mathematically represented as
![\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }](https://tex.z-dn.net/?f=%5Csigma%20_%20%7B%5C%3D%20%20x%20%7D%20%3D%20%20%5Cfrac%7B%5Csigma%20%20%7D%7B%5Csqrt%7Bn%7D%20%7D)
substituting values
![\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }](https://tex.z-dn.net/?f=%5Csigma%20_%20%7B%5C%3D%20%20x%20%7D%20%3D%20%20%5Cfrac%7B%2021%20%7D%7B%5Csqrt%7B60%7D%20%7D)
![\sigma _ {\= x } = 2.711](https://tex.z-dn.net/?f=%5Csigma%20_%20%7B%5C%3D%20%20x%20%7D%20%3D%202.711)
Answer:
The 80% confidence interval for the mean number of words a third grader can read per minute is between 40.4 wpm and 40.8 wpm.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.8}{2} = 0.1](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.8%7D%7B2%7D%20%3D%200.1)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.28](https://tex.z-dn.net/?f=z%20%3D%201.28)
Now, find M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
![M = 1.28*\frac{4.1}{\sqrt{840}} = 0.2](https://tex.z-dn.net/?f=M%20%3D%201.28%2A%5Cfrac%7B4.1%7D%7B%5Csqrt%7B840%7D%7D%20%3D%200.2)
The lower end of the interval is the sample mean subtracted by M. So it is 40.6 - 0.2 = 40.4 words per minute.
The upper end of the interval is the sample mean added to M. So it is 40.6 + 0.2 = 40.8 words per minute.
The 80% confidence interval for the mean number of words a third grader can read per minute is between 40.4 wpm and 40.8 wpm.