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3 years ago

What is the simplified form of 3abc divided by abc when abc does not equal zero

Mathematics

1 answer:

melisa1 [442]3 years ago

4 0

3abc/abc = 3.
Simply put, the answer if you divide this equation by ABC, will quite literally transform into 3.

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What is the answer to 9x(6+x)

Anna11 [10]

$54x + x \\ \\ (constributive \: property)$

5 0

3 years ago

Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.

MrMuchimi

A random variable following a binomial distribution over $n$ trials with success probability $p$ has PMF

$f_X(x)=\dbinom nxp^x(1-p)^{n-x}$

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

$\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1$

The mean is given by the expected value of the distribution,

$\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}$

The remaining sum has a summand which is the PMF of yet another binomial distribution with $n-1$ trials and the same success probability, so the sum is 1 and you're left with

$\mathbb E(x)=np=126\times0.27=34.02$

You can similarly derive the variance by computing $\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$ , but I'll leave that as an exercise for you. You would find that $\mathbb V(X)=np(1-p)$ , so the variance here would be

$\mathbb V(X)=125\times0.27\times0.73=24.8346$

The standard deviation is just the square root of the variance, which is

$\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834$

7 0

3 years ago

You want to solve 11% of what number is 22. Explain how you can solve that by using a proportion

Doss [256]

Write the first ratio as 11/100 and set it equal to 22/n.

since 11 x 2=22 you can multiply 100 x 2 and you'll get 200.

*Check*: 11% of 200=22

3 0

3 years ago

Given the terms a10 = 3 / 512 and a15 = 3 / 16384 of a geometric sequence, find the exact value of the term a30 of the sequence.

GenaCL600 [577]

The answer is $\frac {3}{2^{29}}$

5 0

3 years ago

What are the solutions to the system of equations? y=2x^2−6x+3 y=2x+3

adoni [48]

Answer:

Step-by-step explanation:

y=2x²-6x+3

y=2x+3

2x²-6x+3=2x+3

2x²-6x+3-2x-3=0

2x²-8x=0

2x(x-4)=0

x=0,4

y=0+3=3

and y=2(4)+3=11

so solutions are (0,3) and (4,11)

5 0

2 years ago