Math Answers

What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

1. A machine produces metal pieces that are cylindrical in shape. A random sample of 12 metal pieces from the machine shows a mean diameter of 1.3 cm and a standard deviation of 0.05 cm. Compute a 98% confidence interval for the true average mean diameter for the metal pieces produced by the machine.

A Manufacturer produces two products, the Klunk and the Klick. Klunk has a contribution

to profit of $3, and the Klick $4 per unit. The manufacturer wishes to establish the weekly

production plan that maximizes profit. Production of these products is limited to machine,

labor and material constraints. Each Klunk requires four hours machining, four hours labor

and one kilogram of material, where as each Klick requires two hours machining, six hours

labor and one kilogram of material. Machining and labor has a maximum of one hundred

and one hundred and eighty hours available, and total material available is forty kilograms.

Because of a trade agreement, sales of Klunk are limited to a weekly maximum of twenty

units and to honor an agreement with an old established customer at least ten units of Klick

must be sold each week.

i. Determine graphically using linear programming a suitable production mix of Klunk

and Klick. [12]

ii. What will be the company’s maximum profit?

Survey of 300 households that bought large screen TVs as type of purchase and whether satisfied with the equipment produced the table below:

SATISFIED WITH PURCHASE?

TYPE OF TV Yes No Total

Plasma screen 64 16 80

Not plasma screen 176 44 220

Total 240 60 300

You are required to identify, calculate

and interpret the meaning of the following :

a. P(Plasma)

b. P(Satisfied ∩ Plasma screen)

c. P(Satisfied│Plasma screen)

d. If P(Satisfied│Plasma screen) = P(Satisfied) , what conclusion would you make?

Give an example of a function of two variables such that f(0,0) = 0 but f is NOT continuous at (0,0). Explain why the function f is NOT continuous at (0,0).

It's time to tidy up your work desk. you are given 27cm^2 of cardboard to build a rectangular box without a lid to store small electronic components. By using the knowledge of partial derivative, determine the maximum volume of this box

Two ideal dice are thrown . Let X₁ be the score on the first die and X₂ be the score on the second die. Let Y = max(X₁, X₂) then

(i) Evaluate Corr(Y, X₁).

(ii) Evaluate Corr(Y, X₂).

Use generating functions to solve the recurrence relation an = 4a_n−1 − 4a_n−2 +n²

, where a₀ = 2, a₁ = 5.

Plot the following points:

P1 (-3, 135°)

P2 (2, )

P3 (4, 405°)

Graph

Sketch the graph of r = 3 − 2cosθ.

The present value of obligation of rs.7000 due in small n year at rate if discount of 7% cover table continuasly is rs.5290.46 find the value of n