Math Answers

find the set of values of x for which:

(a) x^2-3x>=10 and (x-5)^2<4

(b) x^2+4x-21<=0 and x^2-9x+8>0

(c) x^2+x-2>0 and x^2-2x-3>=0

Given the data below test the hypothesis that the mean of three populations are equal.let alpha=0.05

Sample-1 sample-2 sample-3

40 70 45

50 65 38

60 66 60

65 50 42

Let the number of car accidents be a Poisson R.V. If the rate of car accidents in a road is 3 accidents in a day , compute () the probability of having no accidents in the afternoon interval (12 pm, 18pm). ( ii) the average and standard deviation of accidents in a week.

1. which sets are a basis for the null space of [(1,1,-1,1),(2,1,1,4),(1,0,0,1)].
2. let T:R^3 to R^3 be defined as T(x,y,z)={x+y, x-y,x+2z). then the basis of range T is...?
3. let R^3 to R^3 defined as T(x,y,z)=(2x,x+y,x-z). then the adjoint operator T*(u,v,w) is (i) (2u+v+w,v,-w), (ii) (2u,v+w,u-w), (iii) (u,v,-w)

1. the square root of (2-i) is?

2. for a given ,matrix A=[(5,-6),(-3,2)] the matrix P that diagonalizes A is?

3. for a,b is an element of R, let S be a subset of R^2 defined as S={(x,y) is an element of R^3:x+y+axy=b}. Then S is a subspace of R^2 if...?

4. suppose U={(x,y,x+y,z,2y+z) is an element of F^5:x,y,z is an element of F}, then a subspace W of F^5 such that F^5=U denote W is...?

5. the vectors (1,-1,2),(2,3,1),(3,2,t) are not basis of R^3 if...?

1. in R3, let U span (1,0,0),(0,1/root2, 1/root2). then U is an element of U such that ||u-(2,4,6)|| is as small as possible.
2. for a given function f:R to R defined as f(x)=2x-1, the image of S={x is an element of R: x^2-4>/=0} is?
3. suppose T: R^2 to M22 is a linear defined by T(U,V)=[(U,U), (V,2U)]. Then ker(T) is?
4. suppose T:R^6 to R^4 is a linear map such that null T=U, where U is 2-dimensional subspace of R^6. Then dim range T is?

four items are taken at random from a box of12 item and inspected. the box is rejectwd if more than 1 item is found faulty. if there are 3 faulty item in the box. find the probablity

Determine the volume of the solid/ring obtained by the region bounded by

𝑦=2√𝑥−1and 𝑦=𝑥−1 about line x= -1 using shell method

solve the following recurrence relations

a. 𝑇(𝑛) = 𝑇( 𝑛/4) + 𝑇( 𝑛/2 ) + 𝑛^2

b. T(n) = T(n/5) + T(4n/5) + n

c. 𝑇(𝑛) = 3𝑇( n/4 ) + 𝑐𝑛^2 

f. 𝑇(𝑛) = (𝑛/𝑛−5) * 𝑇(𝑛 − 1) + 1

g. 𝑇(𝑛) = 𝑇(log 𝑛) + log 𝑛

h. 𝑇(𝑛) = 𝑇 (𝑛^ 1/ 4) + 1

i. 𝑇(𝑛) = 𝑛 + 7 √𝑛 ∙ 𝑇(√𝑛)

j. 𝑇(𝑛) = 𝑇 ( 3𝑛/4 ) + 1/root(n)

State TRUE or FALSE justifying your answer with proper reason.

a. 2𝑛^2 + 1 = 𝑂(𝑛^2 )

b. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 )

c. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 log 𝑛)

d. 3𝑛^2 + √𝑛 = 𝑂(𝑛 + 𝑛√𝑛 + √𝑛)

e. √𝑛 log 𝑛 = 𝑂(𝑛)