A company’s cash position, measured in millions of dollars, and denoted by (Xt) follows an arithmetic Brownian motion with dynamics dXₜ = αdt + σdWt along with the drift rate of α = 1.2 per annum and variance rate of σ2 = 1.92 per annum. The initial cash position is X₀ = 2.

(a) What are the probability distributions of the cash position at the end of 1 month, 1 year and 3 years?

(b) What are the probabilities of a negative cash position at the end of 1 month, 1 year and 3 years?

The ratio of rock songs to dance songs on jonathan’s mp3 player is 5: 6. the total number of rock and dance songs jonathan has is between 101 120. how many rock songs does he have?

State if the two triangles are congruent. if they are, state how you know?

Drag the tiles to the correct boxes to complete the pairs. match the exponential functions with their horizontal asymptotes and y-intercepts. f(x) = 7x − 4 f(x) = 3x+2 + 4 f(x) = 9x+1 − 4 f(x) = 2x + 4 horizontal asymptote and y-intercept exponential function horizontal asymptote: y = 4 y-intercept: (0, 5) arrowboth horizontal asymptote: y = -4 y-intercept: (0, 5) arrowboth horizontal asymptote: y = -4 y-intercept: (0, -3) arrowboth horizontal asymptote: y = 4 y-intercept: (0, 13) arrowboth