What are two factors of -72 that add up to 6

Is 3pi/4pi a rational number?

Natali5045456 [20]

Answer:No

Step-by-step explanation:

Pi is irrational

4 0

3 years ago

If XX is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

Liula [17]

Answer:

(a) The mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b) The mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c) The mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d) The mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameters n and p.

The mean, variance and standard deviation of X are:

$\mu=np\\\sigma^{2}=np(1-p)\\\sigma=\sqrt{np(1-p)}$

(a)

For n = 4 and p = 0.40 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.40=1.60\\\sigma^{2}=np(1-p)=4\times0.40\times(1-0.40)=0.96\\\sigma=\sqrt{np(1-p)}=\sqrt{0.96}=0.98$

Thus, the mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b)

For n = 4 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.80=3.20\\\sigma^{2}=np(1-p)=4\times0.80\times(1-0.80)=0.64\\\sigma=\sqrt{np(1-p)}=\sqrt{0.64}=0.80$

Thus, the mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c)

For n = 3 and p = 0.50 compute the mean, variance and standard deviation of X as follows:

$\mu=np=3\times0.50=1.50\\\sigma^{2}=np(1-p)=3\times0.50\times(1-0.50)=0.75\\\sigma=\sqrt{np(1-p)}=\sqrt{0.75}=0.87$

Thus, the mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d)

For n = 5 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=5\times0.80=4.00\\\sigma^{2}=np(1-p)=5\times0.80\times(1-0.80)=0.80\\\sigma=\sqrt{np(1-p)}=\sqrt{0.80}=0.89$

Thus, the mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

6 0

3 years ago

how many quarts of pure antifreeze must be added to 6 quarts of a 10% antifreeze solution to obtain a 40% antifreeze solution

saveliy_v [14]

First off, let's change the percentage amounts to decimal format, thus, a pure antifreeze is 100% antifreeze, so it has a 100% concentration, thus if we were to add an amount of "x", then the amount on antifreeze in that will then be (100/100) * x, or 1x, or just "x".

the mixture will be say, "y" amount of 40% antifreeze, thus, the concentrated amount in it will be (40/100) * y or 0.4y.

thus

$\bf \begin{array}{lccclll}
&amount(quarts)&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&------&------&------\\
\textit{pure antifreeze}&x&1.00&1x\\
\textit{10\% solution}&6&0.10&0.6\\
------&------&------&------\\
mixture&y&0.40&0.4y
\end{array}$

now, bear in mind that, whatever "x" is,
x + 6 = y <--- the amounts added must yield the amount of the mixture

and x + 0.6 = 0.4y <--- the contrated amounts sum will also add up to the mixture's

$\bf \begin{cases}
x+6=\boxed{y}\\
x+0.6=0.4y\\
----------\\
x+0.6=0.4\left( \boxed{x+6} \right)
\end{cases}
\\\\\\
x+0.6=0.4x+2.4\implies 0.6x=1.8\implies x=\cfrac{1.8}{0.6}$

4 0

3 years ago

Read 2 more answers

State the degree and leading coefficient of each polynomial in one variable -12-8x^2+5x-21x^7

leonid [27]

Answer:

The degree is 7 and the leading coefficient is -21.

Step-by-step explanation:

The degree of an equation is found using the highest exponent on the variable in the equation.

-12-8x^2+5x-21x^7 has the term x^7 so its degree is 7

The leading coefficient is the coefficient of the term with the highest degree. The coefficient of x^7 is -21.

4 0