Answer:
![x=4+-2\sqrt{7}](https://tex.z-dn.net/?f=x%3D4%2B-2%5Csqrt%7B7%7D)
Step-by-step explanation:
To solve, we need to take square root of both sides first:
![(x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}](https://tex.z-dn.net/?f=%28x-4%29%5E2%3D28%5C%5C%5Csqrt%7B%28x-4%29%5E2%7D%20%3D%2B-%5Csqrt%7B28%7D%20%5C%5Cx-4%3D%2B-%5Csqrt%7B28%7D)
Now we use the property of radical shown below to simplify square root of 28:
Property: ![\sqrt{x*y}=\sqrt{x} \sqrt{y}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2Ay%7D%3D%5Csqrt%7Bx%7D%20%5Csqrt%7By%7D)
Now, we have:
![x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}](https://tex.z-dn.net/?f=x-4%3D%2B-%5Csqrt%7B28%7D%5C%5Cx-4%3D%2B-%5Csqrt%7B4%2A7%7D%5C%5Cx-4%3D%2B-%5Csqrt%7B4%7D%5Csqrt%7B7%7D%5C%5Cx-4%3D%2B-2%5Csqrt%7B7%7D)
Now we take 4 to the other side and isolate x:
![x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}](https://tex.z-dn.net/?f=x-4%3D%2B-2%5Csqrt%7B7%7D%20%5C%5Cx%3D4%2B-2%5Csqrt%7B7%7D)
first answer choice is right.
Answer:
The difference is ![\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D)
Step-by-step explanation:
We must find the common denominator of the fractions.
The common denominator of
and
is
; therefore we have
![\frac{1}{2}=\frac{5}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B5%7D%7B10%7D)
![\frac{1}{5} =\frac{2}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%3D%5Cfrac%7B2%7D%7B10%7D)
now it is easy to subtract
using the number line: we have to move
units to the left in order to get to
.
Thus our answer is
![\boxed{\frac{1}{2} -\frac{1}{5}=\frac{3}{10} }](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B1%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B3%7D%7B10%7D%20%7D)
Answer:
0.5
Step-by-step explanation:
Answer:
Students
Step-by-step explanation:
Teachers: 13/20= 0.65 = 65%
Students: 37/50= 0.74 = 74%
74% > 65%
Students are more in favor of the new club than teachers
Answer: 37
Step-by-step explanation:
Given : Significance level : ![\alpha:1-0.98=0.02](https://tex.z-dn.net/?f=%5Calpha%3A1-0.98%3D0.02)
Critical value : ![z_{\alpha/2}=z_{0.01}=2.33](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.01%7D%3D2.33)
margin of error : E= 1 mile per gallon
Population standard deviation:
miles per gallon.
We know that when the population standard deviation is known then the formula to find the sample size is given by :
![n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2](https://tex.z-dn.net/?f=n%3D%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%5Ctimes%20%5Csigma%7D%7BE%7D%29%5E2)
[Round to the next whole number.]
Hence, the required number of automobiles should be used in the test = 37