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Suppose a coin is tossed two times. Let T be the random variable representing the number of tails that occur. Find the values of the random variable T and construct its probability distributions.
1. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a rate of p 3 ft s, how fast is the bottom of the ladder sliding away from the building when the top of the ladder is 10 ft above the ground?
2. A sphere is growing in such a manner that its volume increases at 0:2 m³ s(cubic meter per second). How fast is its radius increasing when it is 7 m long?
Two balanced dice are rolled. Let X be the sum of two dice. Obtain the probability distribution of X
let the random variable x represent the number of boys in the family construct the probability distribution for the family of two children
find the value(s) of t so that the distance from P(3,4) to R(t,8) is 4√2
What is the probability that the number of pants sold is more than 3
9.) Look up what is meant by a system of linear equations.
A known fact of solutions of systems of linear equations is that only one the following options can hold :
(i) No solution possible
(ii) A unique solution can be found
(iii) The system has infinite solutions.
Consider that two straight lines form a linear system.
Interpret what happens geometrically to the straight lines to get each case of the solution types given
abo
Which of the following linear systems is homogeneous. [just give the answer I) or II) or III) : no motivation
is required.]
I) 3x + 14y = 0 & 2x − 3y = 7
II) 7x + 2y = 10 & 11x − 0y = 7
III) 4x − 23y = 0 & 7x − 3y = 0
Let X =
1 2
3 4
; E =
a
b
Find each of the following.
If the operation cannot be done : state undefined operation.
a) XE
b) EX
c) XT X where XT
stands for the transpose of X
Consider the linear equation 2a + 3b = 4
Is (a; b) = (1; 1
2
) a solution to the equation? Motivate your answer.
