Answer:
20
Step-by-step explanation:
This sequence follows a pattern of doubling then subtracting by two. The last action was 12 to 10, which is subtracting by two, so the next must be multiplying by 2.
Note that 
Answer:
Mary's risk premium is $0.9375
Step-by-step explanation:
Mary's utility function,
Mary's initial wealth = $100
The gamble has a 50% probability of raising her wealth to $115 and a 50% probability of lowering it to $77
Expected wealth of Mary, 
= (0.5 * $115) + (0.5 * $77)
= 57.5 + 38.5
= $96
The expected value of Mary's wealth is $96
Calculate the expected utility (EU) of Mary:-
![E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75](https://tex.z-dn.net/?f=E_u%20%3D%20%5B0.5%20%2A%20U%28115%29%5D%20%2B%20%5B0.5%20%2A%20U%2877%29%5D%5C%5CE_u%20%3D%20%5B0.5%20%2A%20115%5E%7B0.5%7D%5D%20%2B%20%5B0.5%20%2A%2077%5E%7B0.5%7D%5D%5C%5CE_u%20%3D%205.36%20%2B%204.39%5C%5CE_u%20%3D%20%5C%24%209.75)
The expected utility of Mary is $9.75
Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where
U(EW - P) is equal to Mary's expected utility from the risky gamble.
U(EW - P) = EU
U(94 - P) = 9.63
Square root (94 - P) = 9.63
If Mary's risk premium is P, the expected utility will be given by the formula:
Mary's risk premium is $0.9375
Answer:
The equation of the line in the slope-intercept form is y = -5x + 79
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept
∵ The slope of the line is -5
∴ m = -5
∵ The form of the equation is y = m x + b
→ Substitute the values of m in the form of the equation
∴ y = -5x + b
→ To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The line passes through the point (18, -11)
∴ x = 18 and y = -11
∵ -11 = -5(18) + b
∴ -11 = -90 + b
→ Add 90 to both sides to find b
∵ -11 + 90 = -90 + 90 + b
∴ 79 = b
→ Substitute it in the equation
∴ y = -5x + 79
∴ The equation of the line in the slope-intercept form is y = -5x + 79
Answer:
second picture
Step-by-step explanation:
The rule to rotate a point counterclockwise about the origin is:
Or in words, we switch the coordinates of the point and change the sign of the y-coordinate.
We know from the first picture that the coordinates of our quadrilateral ABCD are A = (-1, 0), B = (0, -1), C = (-2, -3), and D = (-3 , -2), so let's apply the rotation rule to each one of those points:
Now we know that the coordinates of the quadrilateral after a rotation of 90° are A' = (0, 1), B' = (1, 0), C' = (3, -2), and D' = (2, -3), which corresponds to the second picture
