Answer:
110 IQ too!
Step-by-step explanation:
For statistical problems, especially for ones with large enough sample sizes like this one (n = sample size = 100), the means for various samples is usually equal to the population mean.
It is the standard deviation of sample that differs from the standard deviation of the population through
σₓ = σ/√n
But, The mean of the sample = The population mean
μₓ = μ = 110 IQ
Answer:
- a) x+y
- b) 2x+y
- c) -x
- d) x+y+1
- e) y-x
- f) x/2
Step-by-step explanation:
The applicable rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a^b) = b·log(a)
__
![\text{a) }\log{6}=\log{(2\cdot 3)}=\log{2}+\log{{3}=\boxed{x+y}](https://tex.z-dn.net/?f=%5Ctext%7Ba%29%20%20%7D%5Clog%7B6%7D%3D%5Clog%7B%282%5Ccdot%203%29%7D%3D%5Clog%7B2%7D%2B%5Clog%7B%7B3%7D%3D%5Cboxed%7Bx%2By%7D)
![\text{b) }\log{12}=\log{(2^23)}=2\log{2}+\log{3}=\boxed{2x+y}](https://tex.z-dn.net/?f=%5Ctext%7Bb%29%20%20%7D%5Clog%7B12%7D%3D%5Clog%7B%282%5E23%29%7D%3D2%5Clog%7B2%7D%2B%5Clog%7B3%7D%3D%5Cboxed%7B2x%2By%7D)
![\text{c) }\log{(1/2)}=\log{2^{-1}}=-\log{2}=\boxed{-x}](https://tex.z-dn.net/?f=%5Ctext%7Bc%29%20%20%7D%5Clog%7B%281%2F2%29%7D%3D%5Clog%7B2%5E%7B-1%7D%7D%3D-%5Clog%7B2%7D%3D%5Cboxed%7B-x%7D)
![\text{d) }\log{60}=\log{(2\cdot 3\cdot 10)}=\log{2}+\log{3}+\log{10}=\boxed{x+y+1}](https://tex.z-dn.net/?f=%5Ctext%7Bd%29%20%20%7D%5Clog%7B60%7D%3D%5Clog%7B%282%5Ccdot%203%5Ccdot%2010%29%7D%3D%5Clog%7B2%7D%2B%5Clog%7B3%7D%2B%5Clog%7B10%7D%3D%5Cboxed%7Bx%2By%2B1%7D)
![\text{e) }\log{1.5}=\log{3\cdot2^{-1}}=\log{3}-\log{2}=\boxed{y-x}](https://tex.z-dn.net/?f=%5Ctext%7Be%29%20%20%7D%5Clog%7B1.5%7D%3D%5Clog%7B3%5Ccdot2%5E%7B-1%7D%7D%3D%5Clog%7B3%7D-%5Clog%7B2%7D%3D%5Cboxed%7By-x%7D)
![\text{f) }\log{\sqrt{2}}=\log{2^{\frac{1}{2}}}=\dfrac{1}{2}\log{2}=\boxed{\dfrac{x}{2}}](https://tex.z-dn.net/?f=%5Ctext%7Bf%29%20%20%7D%5Clog%7B%5Csqrt%7B2%7D%7D%3D%5Clog%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Clog%7B2%7D%3D%5Cboxed%7B%5Cdfrac%7Bx%7D%7B2%7D%7D)
Horizontal line has a slope of zero because does not rise vertically.
The form that we have to use in this case is y=b because the slope is zero.
So I would say that the answer for this one is
Y=-1
And a vertical line has a undefined slope because it will go up infinitely.
And in this one we have to put the x-intercept.
So I would say that the answer for this one is x=-9
I hope you get it right :D
x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Step-by-step explanation:
We need to solve the equation
and find values of x.
Solving:
Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)
Multiply the entire equation with x(x-1)
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D%5C%5C%5Cfrac%7B1%7D%7Bx-1%7D%2Ax%28x-1%29%2B%5Cfrac%7B2%7D%7Bx%7D%2Ax%28x-1%29%3D%5Cfrac%7Bx%7D%7Bx-1%7D%2Ax%28x-1%29%5C%5CCancelling%5C%2C%5C%2Cout%5C%2C%5C%2Cthe%5C%2C%5C%2Csame%5C%2C%5C%2Cterms%3A%5C%5Cx%2B2%28x-1%29%3Dx%5E2%5C%5Cx%2B2x-2%3Dx%5E2%5C%5C3x-2%3Dx%5E2%5C%5Cx%5E2-3x%2B2%3D0)
Now, factoring the term:
![x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2](https://tex.z-dn.net/?f=x%5E2-2x-x%2B2%3D0%5C%5Cx%28x-2%29-1%28x-2%29%3D0%5C%5C%28x-1%29%28x-2%29%3D0%5C%5Cx-1%3D0%5C%2C%5C%2Cand%5C%2C%5C%2C%20x-2%3D0%5C%5Cx%3D1%5C%2C%5C%2Cand%5C%2C%5C%2C%20x%3D2)
The values of x are x=1 and x=2
Checking for extraneous roots:
Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.
If we put x=1 in the equation,
the denominator becomes zero i.e
which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.
If we put x=2 in the equation,
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D)
![\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2-1%7D%2B%5Cfrac%7B2%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2-1%7D%5C%5C%5Cfrac%7B1%7D%7B1%7D%2B1%3D%5Cfrac%7B2%7D%7B1%7D%5C%5C1%2B1%3D2%5C%5C2%3D2)
So, x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Keywords: Solving Equations and checking extraneous solution
Learn more about Solving Equations and checking extraneous solution at:
#learnwithBrainly
Distributive property: <em>a(b + c) = ab + ac</em>.
We have 18 + 24
18 = 6 · 3
24 = 6 · 4
Therefore
18 + 24 = 6 · 3 + 6 · 4 = 6 · (3 + 4)
<h3>Answer: 18 + 24 = 6 · (3 + 4)</h3>