If jake has 3 boxes and he put 7 toys in it what does that mean

You select every tenth student on an alphabetical list of the students in your school. You survey the selected students in their

GalinKa [24]

Answer:

no it is not biased because it is randomly selected although in alphabetical order.

Step-by-step explanation:

7 0

3 years ago

You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your a

Troyanec [42]

Answer:

E(X)=3.125

Step-by-step explanation:

We are given that two four sided dice.

Then , the sample space

{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

Total number of outcomes=16

Let the random variable X represent the maximum value of the two dice

Outcomes X P(X)

(1,1) 1 1/16

(1,2),(2,1),(2,2) 2 3/16

(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16

(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16

Using the probability formula

$P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}$

Now,

$E(X)=\sum_{i=1}^{n}x_iP(x_i)$

$E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)$

$E(x)=\frac{1+6+15+28}{16}$

$E(x)=\frac{50}{16}=3.125$

7 0

3 years ago

A(n)=-6-4(n-1) find the 4th term

egoroff_w [7]

Answer:67738373783

Step-by-step explanation:

3 0

3 years ago

You are building a flower bed with a perimeter of 16 feet. The length of the bed is 4 feet longer than the width. What are the d

kykrilka [37]

Answer:

Step-by-step explanation:

The perimeter is basically the outline of the shape. The perimeter of a rectangle is given by P=2l+2w, where l is the length and w is the width. Thus, the perimeter of the flower bed would be given by P=2(3n5o)+2(5n5o).

6 0

2 years ago

For <img src="https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7D" id="TexFormula1" title="e^{-x^2/2}" alt="e^{-x^2/2}" align="absmiddl

nevsk [136]

I'm assuming you're talking about the indefinite integral

$\displaystyle\int e^{-x^2/2}\,\mathrm dx$

and that your question is whether the substitution $u=\dfrac x{\sqrt2}$ would work. Well, let's check it out:

$u=\dfrac x{\sqrt2}\implies\mathrm du=\dfrac{\mathrm dx}{\sqrt2}$
$\implies\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt2\int e^{-(\sqrt2\,u)^2/2}\,\mathrm du$
$=\displaystyle\sqrt2\int e^{-u^2}\,\mathrm du$

which essentially brings us to back to where we started. (The substitution only served to remove the scale factor in the exponent.)

What if we tried $u=\sqrt t$ next? Then $\mathrm du=\dfrac{\mathrm dt}{2\sqrt t}$ , giving

$=\displaystyle\frac1{\sqrt2}\int \frac{e^{-(\sqrt t)^2}}{\sqrt t}\,\mathrm dt=\frac1{\sqrt2}\int\frac{e^{-t}}{\sqrt t}\,\mathrm dt$

Next you may be tempted to try to integrate this by parts, but that will get you nowhere.

So how to deal with this integral? The answer lies in what's called the "error function" defined as

$\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt$

By the fundamental theorem of calculus, taking the derivative of both sides yields

$\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}$

and so the antiderivative would be

$\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt{\frac\pi2}\mathrm{erf}\left(\frac x{\sqrt2}\right)$

The takeaway here is that a new function (i.e. not some combination of simpler functions like regular exponential, logarithmic, periodic, or polynomial functions) is needed to capture the antiderivative.

3 0

3 years ago