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Sever21 [200]
2 years ago
7

In the game of roulette, a player can place a $4 bet on the number 10 and have a 1/38 probability of winning. If the metal ball

lands on 10, the player gets to keep the $4 paid to play the game and the player is awarded an additional $140. Otherwise, the player is awarded nothing and the casino takes the player’s $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
Mathematics
1 answer:
Ahat [919]2 years ago
5 0

this one is kinda Hard ill do sum research and help

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7.5 x 18.74 show your work
FinnZ [79.3K]
7.5x18.74= 140.55 is the correct answer
7 0
2 years ago
Consider the product (x + y + z)2. If the expression is multiplied out and like terms collected, the result is: x2 + y2 + z2 + 2
VLD [36.1K]

Answer:

Part a: The coefficient of v^9w^2x^5y^7z^2 is 1.766 \times 10^{13}

Part b: The number of terms are 23751.

Step-by-step explanation:

part a

From the given equation the

(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx

So the coefficient of any term x^ny^nz^n is given as  

\dfrac{2!}{n!n!n!}

Similarly for the generic equation of coefficient of the term x_1^{r_1}x_2^{r_2}x_3^{r_3}......x_k^{r_k} in the equation of form (x_1+x_2+x_3+x_4......x_k)^n is given as  

\dfrac{n!}{r_1!r_2!r_3!....r_k!}

So now the coefficient of v^9w^2x^5y^7z^2  is given as

=\dfrac{25!}{9!2!5!7!2!}\\=1.766 \times 10^{13}

The coefficient of v^9w^2x^5y^7z^2 is 1.766 \times 10^{13}

Part b:

The number of terms is given as \left (\ {{m+n-1} \atop {n}}  \right )

where m is the number of variables which are 5 here

n is the power which is 25 so the number of variables is given as

\left (\ {{5+25-1} \atop {25}}  \right )\\\left (\ {{29} \atop {25}}  \right )\\\dfrac{29!}{25!4!}=23751

So the number of terms are 23751.

3 0
2 years ago
The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, for a sample of 8 families.
marishachu [46]

Answer:

a. Scatterplot is attached.

b. Positive Correlation

c. Correlation coefficient=0.9219

Step-by-step explanation:

a.

The following procedure will be used to obtain the scatter plot

  •    Open an Google Sheets file online or excel sheet on your computer.
  •    In column B and C, enter  the Income and Vacation data  as provided above.
  •    Select the data > click on insert CHART.
  •    Chose Scatter Chart option
  •    Click OK.

A scatter plot visualizing your data should be displayed as attached.

b.

  • On your computer, open a spreadsheet in Google Sheets.
  • Double-click on your scatter plot.
  • At the right, click on Customize  tab and then Series.
  • Scroll down and check the Trend line box

-From the trend line, your notice that your variables have a positive correlation.

-As the income increases, so does vacation expenditure.

c. The correlation coefficient can be calculated as follows.

  • Click on any empty cell in the sheet and enter the formula
  • "=CORREL((y-axis range),(x-axis range))"
  • ENTER

-From our Google Sheets calculation our variables have a positive correlation and the correlation coefficient is 0.9219

-The correlation coefficient,r can also be calculated manually:

-let x be income, and y be vacation and divide all the values by 100 to make the smaller and easier to manipulate:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219

4 0
2 years ago
A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost.
yKpoI14uk [10]

Answer:

a)

We know that the total cost for the 150 shirts (plus a flat-rate of $25) is $1,825.

First, let's find how much costs each shirt.

First, the total cost of the shirts alone (neglecting the flat-rate) is:

$1,825 - $25 = $1,800

Then each shirt costs equal to the quotient of the cost and the number of shirts:

$1,800/150 = $12

Each shirt costs $12.

Then if you order T shirts, the total cost will be the flat-rate of $25 plus T times $12. The equation is:

C(T) = $25 + T*$12

b) C represents the cost

   T represents the number of shirts ordered.

c) The initial value is the constant value, in this case, is $25

The rate of change is the coefficient that multiplies the independent variable (T), in the equation the rate of change is $12.

7 0
2 years ago
Three times the sum of half Carlita's age and 3 is at least 12. What values represent Carlita's possible age?
cestrela7 [59]

Answer:

at least 6

Step-by-step explanation:

3(.5x+3)>12

1.5x+9>12

1.5>9

x>6

5 0
2 years ago
Read 2 more answers
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