Math Answers

4. Bole cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Birr 5 and that from a shade is Birr 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit? (Solve by simplex model).

Show ((p ∨ q) ∧ ¬(¬p ∧ (¬q ∨ ¬r))) ∨ (¬p ∧ ¬q) ∨ (¬p ∧ ¬r) is tautology, by using replacement process.

brenda paid $462. For a cake mixer after a sales tax of 10% was added to the marked price . What was the price of the mixer before tax

A string of iength L is stretched and fastened to two fix points. Find the solution of

the r.{ave equatiorl (vibrating string) ytt = a^2.yxx, when initial displacernent

y(x,0) = f (x) = b sin (pi.x / t).

also find the Fourier cosine transformation of exp(-x^2)

22 Liam is trying to remember a 3-digit code.

He knows the rule that

the first digit is a cube number

the second digit is a factor of 16

the third digit is an odd number.

Liam tries at random a code that matches the rule.

Work out the probability that this is the correct code.

How many license plates can be made using either two or three letters followed by either two or three digits?

Find killing equations for spherical polar coordinates

Construct the discrete series. Count unbiased estimates of the general mean and general variance. Find the confidence interval for expectation with a confidence level of 0.05 5, 11, 13, 9, 11, 5, 7, 7, 5, 9, 13, 13, 11, 9, 5, 9, 11, 9, 5, 9, 11, 9, 9, 5.

The plant sent 2,000 thermometers to the pharmacy warehouse. The probability of damage to each thermometer along the way is 0.002. What is the probability that exactly 3 damaged thermometers will arrive at the pharmacy warehouse

1+4+7...+(3n-2)=n(3n-1)/2