Math Answers

You are getting engaged and your fiancée has hidden the engagement ring. If only one
statement is true, determine which statement is true? Where is the ring?
Statement 1: The ring is in this box --->A
Statement 2: The ring is not in this box --->B
Statement 3: The ring is not in box A --->C

Use truth table to show the answer.

a) In one sample of observations, the sum of the squares of the observations of the sample values from sample mean was 120 and in the other sample of 12 observations it was 314. Test whether the difference is significant at 5% level of significance.

a) In one sample of observations, the sum of the squares of the observations of the sample values from sample mean was 120 and in the other sample of 12 observations it was 314. Test whether the difference is significant at 5% level of significance

cos∝= √3/2 and 270°<∝<360°. Find: a) sin∝, b) tg∝, c) cotg∝

Find two numbers whose sum is 25 and one number is 10 more than twice the other.

Suppose the rate of savings in Malaysia is given by

dS/dt=5.1e^t+400t^2+6000


where t is the time in years, and S is the amount of money saved in billions of RM. Find the function S(t) which gives the total amount of money saved. You may assume that RM0 is saved at t = 0.

To fill an order for 100 units of a product, a firm wishes to distribute the production between its two plants, Plant 1 and Plant 2. The total cost function is given by

c=f(q_1,q_2 )=0.5q_1^2+2q_1+32q_2+500


where q_1 and q_2 are the number of units produced at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?

A manufacturer of furniture has determined that the weekly production function for p thousand furniture is

p=1000+20l^2 k^3-5l^3-3k^4

where l is the number of labor hours per week in thousands and k is the amount of capital in thousands of RM per week. Determine:

i) the marginal production function with respect to l

ii) the marginal production function with respect to k

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, conclusion in words)

using laws of logics how to show that
(∼p∧(∼q∧r))∨(q∧r)⋁(p∧r)↔r