<u>Given</u>:
Given that in a game a player draws and replaces a card from a deck 2 times.
The possible outcomes and payouts are given.
We need to determine the expected value for someone playing the game.
<u>Expected value:</u>
The expected value for someone playing the game can be determined by
Simplifying the values, we have;
Dividing the terms, we get;
Adding, we have;
Thus, the expected value for someone playing the game is $8
Answer:
y=2x+5
Step-by-step explanation:
The equation of a line in slope intercept form is written as: y=mx +b where m is the slope and b is the y-intercept.
Taking point (-1,3) , m= 2 and imaginary point on the line, (x,y) then ;
m=change is y-coordinates/change in x-coordinate
m=Δy/Δx
m=y-3/x--1
2= y-3 / x+1
2(x+1) = y-3
2x +2 =y-3
2x=y-3-2
2x=y-5
<u>y=2x+5 is the equation.</u>
Answer:
the answer to this is -13
Answer:
45°, 45°, 90°
Step-by-step explanation:
Find the vectors to represent each sides
AB =<3-1, 6-0>=<2,6>
AC = < -1-1, 4 - 0 > = < -2, 4>
Magnitude of the vectors
AB = √(2²+6²) = 6.32
AC = √ ((-2)² + 4²) = 4.47
cosθ = vector of AB × vector AC / ( Product of the magnitude of AB and AC) = 2 × (-2) + (6×4)/ (6.32×4.47) = 20 / 28.2504
θ = arcos(20 / 28.2504 ) approx = 45°
Magnitude of the vectors
BA =<1-3,0-6>=<-2,-6>
BC =<-1-3,4-6>=<-4,-2>
Magnitude of the vectors equals
BA = √((-2)² + (-6)²) = 6.325
BC = √((-4)² + (-2)²) = 4.4721
cosθ = (-2×-4) + (-6 ×-2) / (6.325 × 4.4721) = 20 / 28.286
θ = arcos (20 / 28.286 ) = 45°
Magnitude of the vectors
CB =<3--1, 6-4>=<4,2>
CA=<1--1,0-4>=<2,-4>
Magnitude of the vector =
CB = √(4² + 2²) = 4.4721
CA = √(2² + (-4)²) = 4.4721
cosθ = (4×2) + (2×-4) / (4.4721×4.4721) = 0
θ = arcos 0 = 90°
Answer:
0.0001033058
Step-by-step explanation:
