Math Answers

Suppose we conduct a poll to estimate the proportion of voters who favor a major presidential candidate. Assuming that 50 percent of the electorate could be in favor of the candidate, determine the sample size needed so that we are 95 percent confident that , the sample proportion of voters who favor the candidate, is within a margin of error of .01 of p, the population proportion of all voters who are in favor of the candidate.

A new car is purchased for 17900 dollars. The value of the car depreciates at 13% per year. What will the value of the car be, to the nearest cent, after 7 years?

Find the coordinates of the foot of the perpendicular from (-2,6) on the line
2x+3y-1=0. �

Obtain the equation of the line passing through (1,-1,2) having direction ratios (2,0,1)

A CNC machine has been programmed to drill 10 blind holes in a piece of flat plate. Each hole has a
depth which increments from the previous one by an amount derived from an arithmetic progression
(AP).
Hole 1 has a depth of 2 mm.
Hole 10 has a depth of 29 mm.
 Calculate, using an analytical method, the common difference of the hole depths.
 Ignoring the pull back and repositioning times, calculate the total time spent cutting metal
if the spindle feed rate is set at 2 mm/sec.

Your manager asks you to work on the design of a 10-speed drilling machine which has a common
ratio of 1.38. The lowest speed is to be set at 200rev/min.
 Work out all the speeds.
 Plot them in a chart.
 Write down the general expression for the geometric progression (GP) which you have
used.
 If the design is changed to a 12 speed, calculate the highest speed using the GP formula.

the profit on a jacket can be found by the formula p=24x - 125, where x is the number of jackets sold. What is the profit if 15 jackets are sold?

A block of mass 1 kg is attached to a spring of force constant k = 25/4 N/m. It is pulled x = 0.3 m from its equilibrium position and released from rest. This spring‐block apparatus is submerged in a viscous fluid medium which exerts a damping force of – 4 v (where v is the instantaneous velocity of the block). Determine of the position x(t)
of the block at time t.

Solve the following ODE using the power series method:
(x + 2)y′′ + xy' − y = 0

using sin(0.1)= 0.09983 and sin(0.2)= 0.19867, find an approximate value of sin(0.15) by using Lagrange's interpolation. Obtain a bound on the truncation error.