Give equation of the line through given points (−1, 1) and (2, −1) in slope-intercept form.
First, we compute the slope using the familiar “rise-over-run” formula m = (y2 - y1)/(x2 - x1) (x1, y1) = (-1, 1) and (x2, y2) = (2, -1) m = ((-1-(1)) / (2-(-1)) = -2/3 The point-slope form (using the first point) is, y - y1 = m (x - x1) y − 1 = −2/3 (x - (-1)) y − 1 = -2/3 x - 2/3 and solving for y yields the slope-intercept form y = −2/3x + 1/3 .
Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT?
µ = 527 X = 500 σ = 112 Z = (X-µ)/σ Z = (500 - 527) / 112 = -0.24 Pr(X > 500) = Pr(Z > -0.24) = 1 – 0.4052 = 0.5948
You and two friends are considering buying a house in Chicagoland to live here together after you graduate. You can get a 15-year fixed-rate mortgage with a mortgage rate of 5% if you make a 20% down payment on the house. You will split the monthly mortgage payment equally among the three of you. Each of the three of you can afford to contribute up to $1,000 per month towards the mortgage payment. You each have $10,000 available towards the down payment. How expensive a house can you afford to buy?
The maximum monthly payment is $3000. Suppose you pay 180 months to pay off the debt. PV =A[1-1/(1+r)^n]/r = $379,365.73. This is the maximum principal you can pay. So the total cost of the house is $379,365.73/(1-0.2) = $474207.16 and the down payment is $474207.16 * 20% = $94,841.43 > $30,000. So the most expensive house you can afford is $30,000 / 20% = $150,000.