Math Answers

There are 7 boys and 5 girls in a youngsters’ club. A committee of 3 boys and 2 girls is to be chosen. How many different possibilities are there?

Evaluate the cube root of z=27cis(240^ \circ) . Then raise them to the cube. Show the steps of your reasoning.

2. Evaluate [ \sqrt[5]{3} ( \frac{ \sqrt{3}}{2}+ \frac{i}{2} ) ]^{10} .

3. Find \frac{z_1}{z_2} in polar form:

z_1=21cis(135^ \circ) z_2=3cis(75^ \circ)

The average weight of ten bulls is 500kg and the standard deviation of the weight is 30kg. What would be the weight of a bull that is 6 standard deviation above the mean weight?

A committee of 4 men and 6 women is to be selected from 7 men and 8 women. If there is a married couple among the 15 people, in how many ways can the committee be selected so that the couple are automatically in the committee?

The following attributes are measured for members of a herd of Asian elephants:

weight, height, tusk length, trunk length, and ear area. Based on these

measurements, what sort of similarity measure from Section 2.4 would you use

to compare or group these elephants? Justify your answer and explain any

special circumstances.

A firm's average revenue function 

𝐴𝑅=−18−7,5𝑄+𝑄

2

.

AR=−18−7,5Q+Q2.

Find the TR and 𝑀𝑅 functions.

a.

=−18𝑄−7,5𝑄2+𝑄3=−18Q−7,5Q2+Q3

b.=−18𝑄−7,5𝑄2+𝑄3=−18Q−7,5Q2+Q3

c.=−18−7,5𝑄+𝑄2=−18−7,5Q+Q2

d.=−18−7,5𝑄+𝑄2=−18−7,5Q+Q2

A lot consists of 10 good articles, 4 with minor defects and 2 with major defects.

i. One article is chosen at random. Find the probability that

a. It has no defects, c) It is either good or has major defects.

b. It has no major defects,

A firm's average revenue function 

𝐴𝑅=−18−7,5𝑄+𝑄

2

.

AR=−18−7,5Q+Q2.

Determine the number of units to be produced and sold to maximise revenue.

a.−1

b.6

c.3,75

d.0