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Kagiso wants to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Kagiso to have R40 000 available is
- For what values of h the vectors
⟶ [ 1 ⟶ [ -1 ⟶ [ 5
u = -3 u2 = 9 u3 = -7 <--- u1, u2, and u3 are vectors
-2] -6] h]
are linearly independent?
1.Consider the plane ℿ1 : 3z + 2y + x = 2.
a.) If ℿ2 : 2z - 3y = 1 is another plane. Are the planes ℿ1 and ℿ2 orthogonal?
b.) Consider the line L that passes through the point P0(0, 1, 1) and is parallel to the vector
⟶
u = [ 1
1 Find the point of intersection of the plane ℿ1 and the line L.
1]
Experiment: Tossing two coins. Random variable 𝑋 = number of heads a) List all possible sample space. b) Find the random variable values. c) Find the probabilities for the random variable values.
If you invest $500 today in an account that pays 6 percent interest compounded annually, how much will be in your account after two years?
You play a game with two six-sided dice. If you roll a sum of 5 or 7, you win ₱400. If you
roll a sum of 6 or 8, you win ₱300. If you roll a sum of 11 or 12, you win ₱200. However,
you lose ₱250 for anything else. If you continue to play the game, how much do you
expect to win or lose in the game? Will you encourage your friend to play that kind of
game? Why or why not?
The officers of the Mathematics Club are planning to sell 280 tickets to be raffled during
the school’s foundation day. One ticket will win ₱5,000, two tickets will win ₱3,000, three
tickets will win ₱2,000 and the other tickets will win nothing. If you will buy one ticket,
what will be your expected value and variance of his gain?
A. Identify if the equation f(x)=x⁵-2x⁴+x³-3x²-x+5 has a solution on each given closed interval. Show your proof using the intermediate value theorem.
1.[-2,1]
2.[-1,0]
3.[0,1]
4.[1,2]
5.[2,4]
B. Sketch the graph of f(x)=4-x² and then find the absolute extreme values of the interval [-3,1]
Show the graph and determine if the given function is continuous on each of the given intervals.
1. f(x)=4x²-x+6; (-infinite, 0)
2.f(x)=4/x-5;(-5,5)
3.f(x)=√x-1;(1,+infinite)
4.f(x)=-|-5x|;(-1,+infinite)
A manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 120
hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is less than 900
hours?
