Math Answers

an=3an−1+n2−3,n≥,a0=1

limT(x-0){(a^x-1)/x then value of limit is

250 is invested at a discount rate of 18%p.a convertible monthly for the first 3 months followed by an interest rate of 20%p.a convertible quarterly for the first 9 months. Calculate the accumulated sum at the end of the year

a radio and cycle together cost ₹1200. if the price of the former rises by 20% and then latter by 25%,then two together would cost ₹1460.find the former prices

While putting, Kevin made 16 out of his last 21 putts. His friend Mike made 9 out of his last 14 putts. What is the probability that they both make their next putt? Leave answer as a simplified fraction.

Find the volume of the solid S enclosed by the cylinder x2 + y2 = 9 and the planes y + z = 5 and

 = 1. (Hint: Convert to Cylindrical/Polar Coordinates)

2.   The joint density function for random variables X, Y, and Z is

f (x,y,z) = {Cxyz, if 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2

0, otherwise

a)   Find the value of C.

b) Find P(X ≤ 1,Y ≤ 1, Z ≤ 1).

 A researcher is conducting a survey about the cellphones used by 50 employees. If 𝑋

represents the number of users of Brand X, what are the possible values of 𝑋? 

2.   Evaluate ∭_T  x²  dV where T is a solid tetrahedron with vertices  (0,0,0),(1,0,0),(0,1,0) and

(0,0,1).

Evaluate ∭_E  (𝑥z−y³)dV where E = { (x,y,z) ∣ -1 ≤ x ≤ 1,  0 ≤ y ≤ 2,  0 ≤ z ≤ 1 }.