(i) John has 5 toy cars and 4 toy buses that are all different from each other. John arranges these 9 toys in a line. Find the number of possible arrangements if: (a) (a) the cars and buses are arranged alternately. (B) the buses are all next to each other. (b) John randomly chooses 4 toys to take on holiday with him. Find (a) in how many ways John can choose the 4 toys. (B) the probability that his choices will include both his favourite car and his favourite bus.
(i) John has 5 toy cars and 4 toy buses that are all different from each other. John arranges these 9 toys in a line. Find the number of possible arrangements if: (a) (a) the cars and buses are arranged alternately. (B) the buses are all next to each other. (b) John randomly chooses 4 toys to take on holiday with him. Find (a) in how many ways John can choose the 4 toys. (B) the probability that his choices will include both his favourite car and his favourite bus.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:"Question 3 (MaC)".
(i)
John has 5 toy cars and 4 toy buses that are all different from each other.
John arranges these 9 toys in a line. Find the number of possible
arrangements if:
(a)
(a)
the cars and buses are arranged alternately.
(B)
the buses are all next to each other.
(b)
John randomly chooses 4 toys to take on holiday with him. Find
(a)
in how many ways John can choose the 4 toys.
(B)
the probability that his choices will include both his favourite car and
his favourite bus.
|
(ii)
Consider the function f(x) =
x" +1
(a)
Evaluate lim
x→® x* +1
(b)
Find the stationary point of the curve y = f(x) and determine its nature.
(c)
Find the point(s) of inflection of the curve y = f(x).
(d)
Sketch the curve y = f(x) showing all the features found above.
Using your graph, find all values of k for which the equation kx² = 1-k has
exactly one solution.
(e)
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