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2 years ago

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A bag contains 1 gold marbles, 6 silver marbles, and 29 black marbles. Someone offers to play this game: You randomly select one

marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?

2 answers:

pentagon [3]2 years ago

7 0

Answer:

the expected value is -$1

algol [13]2 years ago

4 0

Answer:

7$ it is

Step-by-step explanation:

You might be interested in

Find the measurement of ∠DOC Round your answer to the nearest whole number.

polet [3.4K]

Answer:

61.2 degrees

Step-by-step explanation:

You want to isolate x on one side of the equation and the numbers on the other side

3x + 2x + 27 = 180

3x + 2x +27 - 27 = 180-27

5x = 153

x = 153/5

x = 30.6

<DOC = 2x

2x = 30.6 x 2

61.2 degrees

7 0

3 years ago

Read 2 more answers

josh has a job mowing lawns. He charges$25 for each yard. He needs at least $400 for the new game system that he wants. write an

Murljashka [212]

25x $\geq$ 400

x $\geq$ 16

Hope Your Thanksgiving Went Well, Here's Some Help Cleaning Up

-TheKoolKid1O1

5 0

3 years ago

A regional planner employed by a public university is studying the demographics of nine counties in the eastern region of an Atl

Brilliant_brown [7]

Answer:

Step-by-step explanation:

Hello!

Given the variables:

X₁: Median Age

X₂: Median Income

b) Considering it from a logical point of view, income changes with age, for example, the more experienced the worker is you would think he would get a better paying job than a younger worker who is just starting. Then the dependent variable will be the median income and the independent variable will be the median age.

a) and c)

To see if there is a linear regression between the median income and median age you have to conduct a hypothesis test for the slope. If the slope is equal to zero, there is no linear regression between the two variables, if it is different to zero, there is a regression between the two of them:

H₀: β=0

H₁: β≠0

α: 0.05

$t= \frac{b-\beta }{Sb} ~~t_{n-2}$

The estimated regression equation for this regression ^Yi= 20.01 + 0.50X

The standard deviation for the slope is Sb= 0.11

$t_{H_0}= \frac{0.50-0}{0.11} = 4.545$

And the p-value for the test is 0.0022

The p-value is less than the level of significance I choose, so the decision is to reject the null hypothesis. You can conclude that there is a linear regression between these two variables.

The correlation coefficient between the median income and the median age is r= 0.87 ⇒ This means you could expect a positive and strong linear correlation between the two variables.

d)

The slope represents how much the variable Y is modified whenever the variable X increases one unit.

In this example: Is the modification of the population mean of the median income, when the median age increases one year.

5 0

3 years ago

Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

Then with $x(t)=y(t)=z(t)=1-t$ , we have

$\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r$

$=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt$

Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt$

$\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du$

Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

$\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv$

$\displaystyle=-(2e-1)+(e-1)=-e$

So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

$\implies f(1,1,1)=2-e$

3 0

3 years ago

Find the distance between the points ?<br><br>

tatuchka [14]

Answer:

4

Step-by-step explanation:

The distance between the two points is (-1,-4) - (-5,-4)

5 0

3 years ago