Consider the following expression.

Mathematics

1 answer:

Maksim231197 [3]2 years ago

8 0

7b and 6b are like terms, thats all i know of!

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According to a certain website, wine critics generally use a wine-scoring scale to communicate their opinions on the relative qu

const2013 [10]

Answer:

$\bar x = 82$

$\sigma = 9.64$

Step-by-step explanation:

Given

$n = 12$

$87\ 91\ 86\ 82\ 72\ 91\ 60\ 77\ 80\ 79\ 83\ 96$

Solving (a); Point estimate of mean

To do this, we simply calculate the sample mean

$\bar x = \frac{\sum x}{n}$

$\bar x = \frac{87+ 91+ 86+ 82+72+91+60+77+80+79+83+96}{12}$

$\bar x = \frac{984}{12}$

$\bar x = 82$

Solving (b); Point estimate of standard deviation

To do this, we simply calculate the sample standard deviation

$\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n - 1}$

$\sigma = \sqrt\frac{(87-82)^2+ (91-82)^2+ ....+ (79-82)^2+ (83-82)^2+ (96-82)^2}{12-1}$

$\sigma = \sqrt\frac{1022}{11}$

$\sigma = \sqrt{92.91}$

$\sigma = 9.64$

<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>

3 0

3 years ago

D -e/3d + e= e, for d

navik [9.2K]

Answer:

$\large\boxed{d=\dfrac{e^2+e}{1-3e}}$

Step-by-step explanation:

$\dfrac{d-e}{3d+e}=e\\\\\dfrac{d-e}{3d+e}=\dfrac{e}{1}\qquad\text{cross multiply}\\\\(1)(d-e)=(e)(3d+e)\qquad\text{use the distributive property}\\\\d-e=3de+e^2\qquad\text{add}\ e\ \text{to both sides}\\\\d=3de+e+e^2\qquad\text{subtract}\ 3de\ \text{from both sides}\\\\d-3de=e^2+e\qquad\text{distribute}\\\\d(1-3e)=e^2+e\qquad\text{divide both sides by}\ (1-3e)\\\\d=\dfrac{e^2+e}{1-3e}$