Math Answers

Find the vector C of magnitude c that is perpendicular to vectors A=a1i + a2j + a3k and B=b1i + b2j + b3k

Find the unit vector that is perpendicular to vectors A=2i + j + k and B= -1 + 2j + k

Given that A(2,3,-1) and B(1,2,4) are points in space. Find the unit vector along the direction of AB and the one along BA. Also find the position vector of the point C which is on the mid-point of AB

Let W = {(x, y, z): y² = x + z}, Is W a subspace of R³

Find the Cartesian product A × B × C where A = (0, 1), B = (1, 2) and C= (0, 1, 2)

A random sample of 40 households has an average water consumption of 29 cubic meters per month with a standard deviation of 8 cubic meters. Give the 90% confidence interval for the mean usage of water per month.

Solve the recurrence relation of an=3an-3an-2-an-3 n>=3 a0=1 a1=-2 a2=-1

Find the area between 𝑧 = 0 and each of the following.(used z-table).

1. z = 0.85

2. z = 1.27

3. z = 2.86

4. z = −1.05

5. z = −2.96

A parabola given by x = ay2 + by + c passes through points (1,2) , (-3,2) and (-2,4) .

1. Find the equation ?

2. Determine whether the line x + 2y + 3 = 0 is tangent to the parabola in (1)

3. Show that each point P(x,y) on the parabola is equidistant from (-2,2) and the line x= -4

A.     Using the t-table, give the confidence coefficients for each of the following:

a. _n=21, 95% confidence

b. _n=26, 99% confidence

B.     Compute the population proportion interval estimate given , and the confidence level.

a. _{n=420;p-hat=0.61}, 95% confidence

b. _{n=960;p-hat=0.17}, 99% confidence

C.     Estimate the interval for the population proportion from each of the following. Then, interpret the results.

a. x=_{610, n=1050}, 95% confidence

b. x=_{734, n=1540}, 99% confidence