Answer:
The sample size to obtain the desired margin of error is 160.
Step-by-step explanation:
The Margin of Error is given as
Rearranging this equation in terms of n gives
![n=\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2](https://tex.z-dn.net/?f=n%3D%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7BM%7D%5Cright%5D%5E2)
Now the Margin of Error is reduced by 2 so the new M_2 is given as M/2 so the value of n_2 is calculated as
![n_2=\left[z_{crit}\times \dfrac{\sigma}{M_2}\right]^2\\n_2=\left[z_{crit}\times \dfrac{\sigma}{M/2}\right]^2\\n_2=\left[z_{crit}\times \dfrac{2\sigma}{M}\right]^2\\n_2=2^2\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2\\n_2=4\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2\\n_2=4n](https://tex.z-dn.net/?f=n_2%3D%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7BM_2%7D%5Cright%5D%5E2%5C%5Cn_2%3D%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7BM%2F2%7D%5Cright%5D%5E2%5C%5Cn_2%3D%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B2%5Csigma%7D%7BM%7D%5Cright%5D%5E2%5C%5Cn_2%3D2%5E2%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7BM%7D%5Cright%5D%5E2%5C%5Cn_2%3D4%5Cleft%5Bz_%7Bcrit%7D%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7BM%7D%5Cright%5D%5E2%5C%5Cn_2%3D4n)
As n is given as 40 so the new sample size is given as
So the sample size to obtain the desired margin of error is 160.
Answer:
x = 3
Step-by-step explanation:
Given the linear equation :
1/4(x-5)+4=1/3(2x+7)-5/6
(x-5)/4 + 4 = (2x+7)/3 - 5/6
Take the lcm and sum
(x-5+16)/4 = (4x+14-5)/6
(x+11)/4 = (4x+9)/6
Cross multiply
6(x+11) = 4(4x+9)
6x + 66 = 16x + 36
Collect like terms
6x - 16x = 36 - 66
-10x = - 30
x = 30/10
x = 3
Answer:
3
Step-by-step explanation:
Since the parabola is connecting the points, it means that the points given are on the parabola or that the points are solutions of the parabola. Thus, when we substitute the points into the function, we should end up with the correct y-value.
To find the correct choice, let's test a point. An easy point to test I believe would be (-3, 0) because we should be getting 0 as a y-value. Let's test:
We can see that Choice B is the correct function, because it produces 0 when we substitute 
. Thus, Choice B, or (x + 3)(x - 4) is the answer.
#1 first we need to solve for slope which is y2-y1/x2-x1
plug in the coordinates and get 1-6/5-(-2) which makes our slope -5/7
then use the equation for point slope form which is:
y-y1=m(x-x1)
then plug in one of the coordinates, I'll use (-2,6), now we have
y-6=-5/7(x+2)
now to make this slope intercept, we just have to solve
y-6=-5/7x-10/7
y=-5/7x+4 4/7
repeat all these steps for 2 and 3
#2: slope = -13/5
plug it in to point slope and get: y+8=-13/5(x-3)
slope intercept:
y+8= -13/5x + 39/5
y= -13/5x -1/5
#3: slope = 3/4
point slope form: y-2=3/4(x-3)
slope intercept: y-2=3/4x-9/4 --> y=3/4x-1/4
