Response:
the expected value of this raffle if you purchase 1 ticket = -0.65
Breakdown of the calculation:
Details:
5,000 tickets are sold at $1 each for a charitable raffle
Winners will be chosen at random with cash prizes as follows: 1 prize of $500, 3 prizes of $300, 5 prizes of $50, and 20 prizes of $5.
Therefore, the value and its respective probability can be calculated as follows:
Value Probability
$500 - $1 = $499 1/5000
$300 - $1 = $299 3/5000
$50 - $1 = $49 5/5000
$5 - $1 = $4 20/5000
-$1 1 - 29/5000 = 4971/5000
The expected value of the raffle when buying 1 ticket is computed as follows:
So, the expected value of this raffle when one ticket is purchased = -0.65
a. The point estimate for the population mean is b. The confidence interval at 80% is c. This means there is an 80% probability that the true mean of the population lies within the given confidence interval.
A) The independent variable in this scenario is the quantity of books purchased.
C) The overall cost for the year hinges on the number of books obtained.
E) The output of this function is the total yearly cost.
Given:
Triangle ABC is rotated 90 degrees counterclockwise and then translated vertically by 3 units to form triangle A'B'C'.
To determine:
The transformation rule necessary to map each point (x,y) on Triangle ABC to its equivalent point on Triangle A'B'C'.
Solution:
For a figure that undergoes a 90-degree counterclockwise rotation, the transformation will be defined as:
To translate a figure upward by 3 units, the appropriate transformation will be applied afterwards.
Hence, when triangle ABC experiences a rotation of 90 degrees counterclockwise followed by a translation of 3 units upward to create triangle A'B'C', the transformation rule will be established accordingly.
The provided function is:
P = 0.04x + 0.05y + 0.06(16-x-y)
To determine the function's value at each vertex, simply plug in the respective x and y coordinates into the equation to find the value of P as shown below:
1- For (8,1):
P = 0.04x + 0.05y + 0.06(16-x-y)
P = 0.04(8) + 0.05(1) + 0.06(16-8-1)
P = 0.79
2- For (14,1):
P = 0.04x + 0.05y + 0.06(16-x-y)
P = 0.04(14) + 0.05(1) + 0.06(16-14-1)
P = 0.67
3- For (3,6):
P = 0.04x + 0.05y + 0.06(16-x-y)
P = 0.04(3) + 0.05(6) + 0.06(16-3-6)
P = 0.84
4- For (5,10):
P = 0.04x + 0.05y + 0.06(16-x-y)
P = 0.04(5) + 0.05(10) + 0.06(16-5-10)
P = 0.76
I hope this is useful:)
