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Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one?
Solution: There are 10 ways to choose a returning player and 4 ways to choose a new one. Thus, there are 10 x 4 = 40 ways to choose one of each.
Example: Suppose we pick 2 numbers from 1, 2, 3, 4, 5 with replacement. Find the probability that one number is even.
Solution: Note that we want only one number to be even, not both, so we can rephrase this as: The first number is even AND the second number is odd OR the first number is odd AND the second number is even.
Use the addition and multiplication rules to calculate that there are (2 x 3) + (3 x 2) = 12 ways for this event to occur. Since there are 5 ways of choosing the first number AND 5 ways of choosing the second, S contains 5 x 5= 25 points.
The probability that one number is even is:
P(one number is even) = 12/25
Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second
1/2+1/2
Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative later shows that there
Explain Pie Charts ? If the frequencies are written as percentages, they can be easily compared using a pie chart. The following is an example of a pie chart using the data fr
A door height is 6 feet and 6 inches and 36 inches wide. What is the widest piece of sheetrock that will ?t through the door? Round to the nearest inch. a. 114 in b. 86 in
Consider the system of linear equations X + ay = 1 2x + 8y = b Where a and b are real numbers. (a) Write out the augmented matrix for this system of linear equations.
When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years. Find their present
Five cards - the ten, jack, queen, king and ace, are well shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is
what are these all about and could i have some examples of them please
Components of the Vector We should indicate that vectors are not restricted to two dimensional (2D) or three dimensional space (3D). Vectors can exist generally n-dimensional s
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