Math Answers

The following contingency table represents the voters’ opinion concerning a new tax

reform bill and their level of income.

Levels of Income

Opinion Low Medium High

For 213 203 182

Against 138 110 154

Apply chi-square (χ2

) test to examine whether the opinion of people on new tax bill is

independent from their income level. [Table value of chi- square (χ2

) at 5% level of

significance and for 2 degrees of freedom is 5.99]

The distribution of height of adult male of a particular race is normally distributed with

mean 165 cm and variance 36 cm. find the probability of an adult male to have height

between 150 cm and 180 cm. [given that 0 ≤ Z ≤ 2.5 = 0.4938]

The distribution of height of adult male of a particular race is normally distributed with

mean 165 cm and variance 36 cm. find the probability of an adult male to have height

between 150 cm and 180 cm. [given that 0 ≤ Z ≤ 2.5 = 0.4938]

The average age of bank managers is 35 years. Assume the variable is normally distributed. If the standard deviation is 5 years, find the probability that the age of a randomly selected bank manager will be in the range between 25 and 40 years old.

For the following functions:

(a) f(x)=(x+2)²(x-1)

(b) f(x)= (x²)/(x²-9)

(c) f(x)= (x²-2x+1)/(x+1)

i. Find the critical numbers off (if any);

ii.Find the open interval(s) on which the function. increasing or decreasing

iii. Apply the first derivative test to identify all relative extrema;

iv. Use graphing utility to confirm your results.

Consider the function f(x)=sin x cos x+5 on the interval (0, 2pi).

(a) find the open interval(s) on which the function increasing or decreasing, and

(b) apply the first derivative test to identify the relative extrema.

Determine the open intervals on which the graph of f(x)= (x²)/(x²+1) is concave upward or concave downward

Answer these questions for the poset ({3, 5, 9, 15, 24, 45}, |).

a) Find the maximal elements.

b) Find the minimal elements.

c) Is there a greatest element?

d) Is there a least element?

e) Find all upper bounds of {3, 5}.

f) Find the least upper bound of {3, 5}, if it exists.

g) Find all lower bounds of {15, 45}.

h) Find the greatest lower bound of {15, 45}, if it exists.

Find the points of inflection and discuss the concavity of the graph of the function

f(x)= (x+1)/√x

Find all relative extrema. Use the second derivative test where applicable.

(a) f(x)=√x2+1

(b) f(x)=cos x -x