Math Answers

The height of 40 students were measured and recorded as follows;

38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7
39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2
44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3
49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9
55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5

Using classes of 35-39, 40-44,- - - calculate;
i. The arithmetic mean
ii. The standard deviation

From the frequency distribution table below calculate;
i. The harmonic mean
ii. The geometric mean
iii. The mode
Class 25-29 30-34 35-39 40-44 45-49 50-54
Frequency 3 9 13 10 7 2

The masses of packages from a particular machine are normally distributed with a mean of 200g and a standard deviation of 2g. Find the probability that a randomly selected package from the machine weighs
(i) Less than 196g
(iii) Between 198.5g and 199.5g

The table below shows discrete frequency distribution data. Use it to answer the questions that follow.
Class 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39
Frequency 5 8 10 12 7 6 3 2

Compute;
(i) Mode of the distribution
(ii) The 7th decile
(iii)The third quartile

If α and β are the roots of the equation x2+2x+p=0 and if 1- α / α and 1- β/ β are the root s of the equation 4x2-3x+q=0 find p and q

The exponential distribution with rate parameter μ > 0 is a continuous distribution on [0, ∞) with density

f(t) = μ exp(−μt), t > 0

1. Compute the cumulative distribution function defined by

F(t) := P(X ∈ [0,t]).

2. Compute P(s < X ≤ t).

3) Find P( X∈ [1,2] ∪[3,4] ).

4) Compute the conditional probability P (X ∈ [3, 4] | X ∈ [1, 4] )

5) Compute the conditional probability P (X > t + s | X > s ) for s, t ≥ 0.

6) Find the mean of the exponential distribution with rate parameter μ > 0.

A recent article in the Myrtle Beach Sun Times reported that the mean labor cost to repair a color television is $90.00 with a standard deviation of $22.00. Monte's TV sales and service completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. Compute the z values for each and comment on your findings.

1 If
ϕ=2xz4−x2y
ϕ=2xz4−x2y
, find
|▽ϕ|

2 If
ϕ(x,y,z)=3x2y−y3z2
ϕ(x,y,z)=3x2y−y3z2
, find
▽ϕ
▽ϕ
at point (1,-2,-1)

3 Find a unit normal to the surface
x2y+2xz=4
x2y+2xz=4
at point (2,-2,3)
4 Let
ϕ(x,y,z)=xy2z
ϕ(x,y,z)=xy2z
and
A=xzi−xy2j+yz2k
A=xzi−xy2j+yz2k

,find
∂3∂x2∂z(ϕA)
5 Given that
ϕ=2x2y−xz3
ϕ=2x2y−xz3

find
▽2ϕ
6 If
A=xz3i−2x2yzj+2yz4
A=xz3i−2x2yzj+2yz4
, find
▽×A
▽×A

at point (1,-1,1).

7 Given that
A=A1i+A2j+A3k
A=A1i+A2j+A3k
and
r=xi+yj+zk
r=xi+yj+zk
, evaluate
▽⋅(A×r)
▽⋅(A×r)

if
▽×A=0
8 Let A=x2yi−2xzj+2yzk
A=x2yi−2xzj+2yzk

, find Curl curl A.
9 Given A=2x2i−3yzj+xz2k
A=2x2i−3yzj+xz2k
and
ϕ=2z−x3y
ϕ=2z−x3y
, find

10 Find the directional derivative of
ϕ=x2yz+4xz2
ϕ=x2yz+4xz2
at (1,-2,-1) in the direction
2i−j−2k
A⋅▽ϕ
A⋅▽ϕ
at point (1,-1,1)

1 Find the angle between
A=2x+2j−k
A=2x+2j−k
and
B=6i−3j+2k
2 Determine the value of a so that
A=2i+aj+k
A=2i+aj+k
and
B=4i−2j−2k
B=4i−2j−2k
are perpendicular
3 Determine a unit vector perpendicular to the plane of
A=2i−6j−3k
A=2i−6j−3k
and
B=4i+3j−k
4 Find the work done in moving an object along a vector
r=3i+2j−5k
5 Given that
A=2i−j+3k
A=2i−j+3k
and
B=3i+2j−k
B=3i+2j−k

, find
A⋅B
6 If
A=2i−3j−k
A=2i−3j−k
and
B=i+4j−2k
B=i+4j−2k
, find
(A+B+×(A−B)
7 If
A=3i−j+2k
A=3i−j+2k
,
B=2i+j−k
B=2i+j−k
and
C=i−2j+2k
C=i−2j+2k
, find
(A×B)×C
8 Determine a unit vector perpendicular to the plane of
A=2i−6j−3k
A=2i−6j−3k
and
B=4i+3j−k
9 Evaluate
(2i−3j)⋅[(i+j−k)×(3i−k)]
10 If
A=i−2j−3k
A=i−2j−3k
,
B=2i+j−k
B=2i+j−k
and
C=i+3j−2k
C=i+3j−2k

,evaluate
(A×B)⋅C

7 If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj
. evaluate
ddt(A⋅A)
8 If
A=sinui+cosuj+uk
A=sin⁡ui+cos⁡uj+uk
,
B=cosui−sinuj−3k
B=cosui−sinuj−3k
and
C=2i+3j−k
C=2i+3j−k
, evaluate
ddu(A×(B×C))
ddu(A×(B×C))

at u=0
9 Let
A=x2yzi−2xz3j−xz2
A=x2yzi−2xz3j−xz2
and
B=4zi+yj+4x2k
B=4zi+yj+4x2k
, find
∂2∂x∂y(A×B)
∂2∂x∂y(A×B)

at (1,0,-2)

10 solve
d2Adt2−4dAdt−5A=0