University of Southern California

Statistics

Statistics Solutions

Consider the following table. xi 0.2 0.3 0.6 0.9 0.11 0.13 0.14 0.16 Y₁ 0.050 0.098 0.332 0.726 1.097 1.5698 1.848 2.501 a) Construct the least squares polynomial of degree 4 and compute the error. b) Construct the least squares approximation of the form beᵃˣ, and compute the error.

Calculus

Application of derivatives Solutions

By using the delta method, show that V[In(Ĥ(t))]=V^1/2 [Ŝ(t)]/ Ĥ(t)s(t)

Statistics

Statistics Solutions

Calculate the standard deviation, median and mode of the following data. Age Frequency 12 4 14 15 16 1 18 13 20 14

Math

Basic Math Solutions

Solve the system of equations: x + y/5 = 51/5 x + y/11 = 11 – x a. (11.10) b. (-10,-1) c. infinite solutions d. no solutions e. (10, 1)

Math

3D Geometry Solutions

Solve the system of equations: (x/3) = 3 - (2/30 y x + 2y = 13 a. (9,0) b. (0,0) c. (0, 13/2) d. infinite solutions e. no solutions

Algebra

Complex numbers Solutions

Consider the matrix 1 2 4 -3 A = 2 4 3 1 1 0 2 -6 0 1 1 2 Form the augmented matrix [A | I ] , where I is the 4 x 4 identity matrix .Use matlab to reduce [ A | I ] to reduced row echelon form . Write A^-1

Math

Linear Programming Solutions

Maximize P subject to the given constraints. P = 3x + 8y constraints x ≥ 0 y ≥ 0 x + y ≤ 2 a. P = 16 at (0, 2) b. P = 6 at (2,0) c. none of these d. P = 0 at (0,0) e. P = 22 at (3,8)

Math

Linear Programming Solutions

Maximize P subject to the given constraints. P= 14y – x constraints x ≤ 7 y ≥ 0 -x + 7y ≤ 6 x +y ≥ 5 a. none of these b. P = 26 at (13/7, 14) c. P = 19 at (7, 13/7) d. P = 70 at (0,5)

Math

Linear Programming Solutions

Maximize P subject to the given constraints. P = x – 10y constraints. x ≤ 10 y ≤ 4 x ≥ 0 y ≥ 0 x +y ≤ 14 a. P=26 at (10, 4) b. none of these c. P=14 at (14, 0) d. P=10 at (10, 0)

Math

Linear Programming Solutions

Minimize P subject to the given constraints. P= 9x + y constraints x ≥ 0 y ≥ 0 -x + 3y ≤ 8 -3x + y ≥ -3 a. P=0 at (0, 0) b. P=9 at (1, 0) c. P=-3 at (0, -3) d. none of these

Math - Others

Trigonometry Solutions

Give the rectangular coordinates for each of the following points in the polar coordinate system. (5, 30°) (-3,-π/4) (33, 217°)

Math

Quadratic equations Solutions

A ball is thrown downward from the top of a 220-foot building with an initial velocity of 12 feet per second. The height of the ball h in feet after t seconds is given by the equation h= - 16t² - 12t + 220. How long after the ball is thrown will it strike the ground?