The first two is wrong, the last two is one of the right ones, I think it’s c
Each coin has a head and a tail, therefore when you toss two coins, you have 4 possible outcomes. You have two heads in only one of these outcomes, while the other three have at least one tail.
The expected value of the game is the price paid/gained times the probability of loss/victory:
E = (1 / 4) · (-6) + (3 / 4) · (2)
= -3 / 2 + 3 / 2
= 0
Bob expects to tie with Will.
If you have multiple equations with multiple variables, you can either do clever substitutions, or turn it into a matrix on which you can perform linear combinations or multiplications (Gauss elimination)
1 1 1 1
2 1 -1 8
1 -1 1 -5
(note how the above 3 rows represent the 3 equations, just got rid of the variables, plus sign and equals sign)
subtract row1 from row3, that eliminates x and z from row 3.
1 1 1 1
2 1 -1 8
0 -2 0 -6
divide row3 by -2, that will give y a factor of 1
1 1 1 1
2 1 -1 8
0 1 0 3
The last row now says y=3
Solve for y:
y + 1 = -3/5x + 2.4 (multiply 4 by 3/5 no negatives because negative times a negative is a positive)
y = -3/5x + 1.4
Now graph the y-intercept of 1.4.
Then plot points using slope.
Hope this helps and let me know if you have more questions!
Answer:
1.) 8.09g ; 2) 206.7 years
Step-by-step explanation:
Given the following :
Half-life(t1/2) of Uranium-232 = 68.9 years
a) If you have a 100 gram sample, how much would be left after 250 years?
Initial quantity (No) = 100g
Time elapsed (t) = 250 years
Find the quantity of substance remaining (N(t))
Recall :
N(t) = No(0.5)^(t/t1/2)
N(250) = 100(0.5)^(250/68.9)
N(250) = 100(0.5)^3.6284470
N(250) = 100 × 0.0808590
= 8.0859045
= 8.09g
2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Using the relation :
N / No = (1/2)^n
Where N = Amount of remaining or left
No = Original quantity
n = number of half-lifes
N = 12.5g ; No = 100g
12.5 / 100 = (1/2)^n
0.125 = (1/2)^n
Converting 0.125 to fraction
(1/8) = 1/2^n
8 = 2^n
2^3 = 2^n
n = 3
Recall ;
Number of half life's (n) = t / t1/2
t = time elapsed ; t1/2 = half life
3 = t / 68.9
t = 3 × 68.9
t = 206.7 years
