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3 years ago

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Gambler is deciding whether or not to take a bet. she must pay $40 to take the bet, but if she wins, she willprofit$225.theproba

bility that she wins the bet is ¼. what is the player’s expected value in this situation

1 answer:

Vesnalui [34]3 years ago

3 0

Expected value of the bet is
the sum of the products of value of outcome and its probability,
less the amount paid to place the bet.

Outcomes value probability
win 225 1/4
lose 0 3/4
cost of bet = 40

So expected value of bet
E[X]=225*(1/4)+0*(3/4)-40
=56.25-40
=16.25

This means that in the long run, gambler will win, since the expected value is positive. (does NOT mean she will win in the next bet!)

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Solve for z<br> 4/z =<br> 12/5 <br> what is z

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Answer:

5/3 = z

Step-by-step explanation:

You can use proportions to figure this out.

Imma solve this as I work through it.

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4/z is equal to 12/5. So you can do something called the butterfly method (I have never used this before, but it works tho) and the method involves only multiplication and division.

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The butterfly method involves multiplying in a cross format on both sides, so the

4 12

__ = ______

z 5

becomes 4 times 5, and z times 12.

4 times 5 is 20, and z times 12 is 12z

so you now have 20 = 12z

Lets simplify the equation by dividing by 4s

20 divided by 4 is 5 and 12z divided by 4 is 3z

so

5 = 3z

You can divide again

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3

to get the unit rate of z.

It will be a fraction though

and it won't look pretty

but here it is:

5

__ = z

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5/3

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2 years ago

If you are able to save, $150 dollars per month-how many months will it take you to

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Answer:

16.66months

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There is a pair of x and y values that make each equation true in this system of equations

MAXImum [283]

Given Equations

5x+3y=8--(1)
4x+7y=34--(2)

Let it has solution (x,y)

Add both

$\\ \sf\longmapsto 5x+4x+3y+7y=8+34$

$\\ \sf\longmapsto 9x+10y=42$

It will also have same solution (x,y)

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2 years ago

Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a

svp [43]

Answer:

Step-by-step explanation:

n = sample size = 5

a) Let us determine the sum

$\sum x_i= 100+200+300+400+490=1490$

$\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100$

$\sum y_i = 237+350+419+465+507=1978$

$\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504$

$\sum x_i y_i=100 \times 237 + 200\times350+300 \times 419 + 400 \times 465 + 490 \times 507=653830$

Now we can determine $S_x_x, S_x_y, S_y_y$

$S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080$

$S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\$

$653830 - \frac{1490 \times 1978 }{5} = 64386$

$S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2$

The estimate b of the slope β is the ratio of $S_x_y$ and $S_x_x$

$b = \frac{S_x_y}{S_x_x}$

$\frac{64386}{96080} = 0.67$

The mean is the sum of all value divide by number of values

$\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298$

$\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6$

The estimate a of the intercept is

$a = \bar y - b \bar x$

$= 395.6 - 0.69 \times 298\\= 195.9$

General least square equation;

$\bar y = \alpha + \beta x$

replace alpha by a = 3 and beta by b = 0.67 in general least equation

y = a + bx

195.9 + 0.67x

b)

<em>Scatter plot is shown in the attached file</em>

x is on the horizontal axis

y is n the vertical axis

The degree of freedom of regression is 1

because we use one variable s predictor variable

$d_f_R = 1$

The degree of freedom of error is the sample size n decrease by 2

$d_f_E =n-2= 5 - 2=3$

Total df is equal to the sum of seperate degree of freedom dfR and dfE

total df = 1 +3 4

$SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296$

Total SS =Syy= 45007.2

SSE + Total SS = SSR

= 45007.2 - 43146.9296

= 1860.2705

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3 years ago

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Degger [83]

Answer:

(x+7)(x-7)

Step-by-step explanation:

x²-49

=x²-7²

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2 years ago

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