Solution:
Number of times a die is rolled = 20
1 - 3=A
2 - 5=B
3 - 4=C
4 - 2=D
5 - 3=E
6 - 3=F
Total number of arrangements of outcomes , when a dice is rolled 20 times given that 1 appear 3 times, 2 appears 5 times, 3 appear 4 times, 4 appear 2 times , 5 appear three times, and 6 appear 3 times
= Arrangement of 6 numbers (A,B,C,D,E,F) in 6! ways and then arranging outcomes
= 6! × [ 3! × 5! × 4!×2!×3!×3!]
= 720 × 6×120×24×72→→[Keep in Mind →n!= n (n-1)(n-2)(n-3)........1]
= 895795200 Ways
We have to find the expected value for the PlayBall lottery.
The price of the ticket = $1
Prize amount = $250
If a player wins, he will be winning $249 as the price is not paid back along with the prize amount. He is spending $1, getting back $250, so the net amount he is getting back is $249.
Now we have to find the probability of winning and losing.
Number of letters from A to T = 20
Number of digits from 0 to 9 = 10
Probability of picking up the same letter that was picked on that day = 1/20
Probability of picking up the same number that was picked on that day = 1/10
Thus, the Probability of picking up the same letter and same number that was picked on that day =

Thus, the probability of winning = 1/200
The probability of losing =

The expected value E for the PlayBall lottery will be:
Thus, the option C gives the correct answer
Answer:

Step-by-step explanation:
Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.
The equation becomes
.
Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.
The equation of a line given the slope and y-intercept is given as;
m(x-x₁) = (y-y₁)
∴equation of line with m = 2 and y-intercept = (0,3) =
2(x - 0) = (y - 3)
= 2x - 0 = y - 3
making y the subject obtains y = 2x + 3.
so, equation of the line: y = 2x + 3.
This is a geometric sequence with a common ratio of -4:
-9*-4=36
36*-4=-144
-144*-4=576
Thus, the 9th term would be equal to:
(-4)^5*576 which is -589824
The exponent 5 comes from the fact that 4 terms have already been displayed and we need 9-4 more terms to get to the 9th term. Since we are multiplying by -4 only, the 5 remains an exponent