How to solve math equation

a retangular pool is filled with 18.75 cubic meters of water. If the pool is 5 meters long and 2.5 meters wide, what is the dept

BigorU [14]

The volume of a rectangular prism is given by length x width x height.

Now in the question the volume is given, length is given, and width is given.

7 0

3 years ago

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What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? C

charle [14.2K]

Answer:

$(D)E[ X ] =np.$

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success p,

$f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n$

$E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}$

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

$E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}$

Now,

$x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)$

Substituting,

$E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}$

Factoring out the n and one p from the above expression:

$E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}$

Representing k=x-1 in the above gives us:

$E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}$

This can then be written by the Binomial Formula as:

$E[ X ] = (np) (p +(1 - p))^{n -1 }= np.$

5 0

3 years ago

Fill in the table using this function rule. y = 10x-3 X - 0

dexar [7]

Answer:

Step-by-step explanation:

y = 10(- 1) - 3 = - 13

y = 10(0) - 3 = - 3 

y = 10(1) - 3 = 7 

y = 10(5) - 3 = 47

5 0

3 years ago

3/4 (x - 3) - 5 = 1/8 ( x - 1 )

KonstantinChe [14]

Answer:

x = - $\frac{57}{5}$

Step-by-step explanation:

$\frac{3}{4}$ (x - 3) - 5 = $\frac{1}{8}$ (x - 1)

Multiply through by 8 to clear the fractions

6(x - 3) - 40 = x - 1 ← distribute parenthesis and simplify left side

6x - 18 - 40 = x - 1

6x - 58 = x - 1 ( subtract x from both sides )

5x - 58 = - 1 ( add 58 to both sides )

5x = - 57 ( divide both sides by 5 )

x = - $\frac{57}{5}$

3 0

3 years ago

Leah is writing an equivalent equation which solves for y. What should be her next step? 3x+4y=8 Add 4y to both sides of the equ

ratelena [41]

The given equation is

$3x+4y=8$

And we have to solve for y.

Solving for y, means isolating y . And to isolate y, we need to get rid of 4 that is with y .

It means we have to separate 4 from y, and for separation , we have to perform division. That is, we have to divide both sides by 4, and that will be the next step .

So out of the four options, correct option is the last option .

4 0

3 years ago

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