Answer:
z=-8 and z=8
Step-by-step explanation:
A rational expression is undefined when its denominator is equal to zero, so our expression is undefined when
. Solving for z, we get
![z^2=64\\\sqrt{z^2}=\pm\sqrt{64}\\ z=\pm8](https://tex.z-dn.net/?f=z%5E2%3D64%5C%5C%5Csqrt%7Bz%5E2%7D%3D%5Cpm%5Csqrt%7B64%7D%5C%5C%20z%3D%5Cpm8)
Pahelp pi,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
lilavasa [31]
Step-by-step explanation:
Angles 4, 5, 8, 9 12, 13 and 16 are 48°, The rest of the angles will have 132°
Answer:
![\bar x = 82](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2082)
![\sigma = 9.64](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%209.64)
Step-by-step explanation:
Given
![n = 12](https://tex.z-dn.net/?f=n%20%3D%2012)
![87\ 91\ 86\ 82\ 72\ 91\ 60\ 77\ 80\ 79\ 83\ 96](https://tex.z-dn.net/?f=87%5C%2091%5C%2086%5C%2082%5C%2072%5C%2091%5C%2060%5C%2077%5C%2080%5C%2079%5C%2083%5C%2096)
Solving (a); Point estimate of mean
To do this, we simply calculate the sample mean
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\bar x = \frac{87+ 91+ 86+ 82+72+91+60+77+80+79+83+96}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B87%2B%2091%2B%2086%2B%2082%2B72%2B91%2B60%2B77%2B80%2B79%2B83%2B96%7D%7B12%7D)
![\bar x = \frac{984}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B984%7D%7B12%7D)
![\bar x = 82](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2082)
Solving (b); Point estimate of standard deviation
To do this, we simply calculate the sample standard deviation
![\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n - 1}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%28x-%5Cbar%20x%29%5E2%7D%7Bn%20-%201%7D)
![\sigma = \sqrt\frac{(87-82)^2+ (91-82)^2+ ....+ (79-82)^2+ (83-82)^2+ (96-82)^2}{12-1}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%5Cfrac%7B%2887-82%29%5E2%2B%20%2891-82%29%5E2%2B%20....%2B%20%2879-82%29%5E2%2B%20%2883-82%29%5E2%2B%20%2896-82%29%5E2%7D%7B12-1%7D)
![\sigma = \sqrt\frac{1022}{11}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%5Cfrac%7B1022%7D%7B11%7D)
![\sigma = \sqrt{92.91}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B92.91%7D)
![\sigma = 9.64](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%209.64)
<em>Note that: The sample mean and the sample standard deviation are the best point estimators for the mean and the standard deviation, respectively.</em>
<em>Hence, the need to solve for sample mean and sample standard deviation</em>
Answer:
Ex 1: f(2)-f(1)+f(1÷2)=9÷4
Step-by-step explanation:
f(2)=2²-2×2+2=4-4+2=2
f(1)=1²-2×1+2=1-2+2=1
f(1÷2)=(1÷2)²-2×(1÷2)+2=5÷4