Math Answers

Is there a continuous function f:[0,1]~>[0,1] that is not constant in any nontrivial interval such that f^-1{0} is uncountable?

suppose that $f:[0,1]\rightarrow r$ is continous on [0,1] and differentiable on (0,1) with f(0)=0 anf f(1)=10.prove that there exist 100 distinct points x_k belonging to (0,1) such that summation from k=1 to 100 of 1/f'(x k)=1000

Find the first partial derivative of

f(w, x, y, z) = w ^ 2 * x * y ^ 2 + x * y ^ 3 * z ^ 2

Find the first partial derivative of

h(x, y, z) = cos(x+y+z)

Find the first partial derivative of

s(y, z) = z ^ 2 * tan yz

Does number of goof friends depend on happiness? 

(GSS Data)

Very happy                Pretty happy                         Not too happy

Mean              10.4                                        7.4                                          8.3                  

Std. dev.        17.8                                        13.6                                        15.6

N                    27.6                                        468                                         87

                                   Sum of                       Mean

Source                       squares         df        square           F         Sig

Between-groups      1627               2         813                 3.47    0.032

Within-groups          193901           828     234

Total                          195528           830

The percentage X of a particular compound contained in a rocket

fuel follows the normal distribution with mean 33 and SD of 3,

though the specification for X is that it should lie between 30

and 35. The manufacturer will get a net profit ( per unit of the

fuel) of Rs. 100, if 30<X<35 ; Rs.50, if 25<X≤30 or 35≤X<40

and incur a loss of Rs. 60 per unit of the fuel otherwise.

Calculate the expected profit of the manufacturer.

The Manufacture of television tubes knows from the past experience that the average life of tube is 2000hrs with a s.d. of 200 hrs. A sample of 100 tubes has average life of 1950 hrs. Test at the 0.01 level of significance to see if this sample came from a normal population of mean 2000 hrs.

The length of a rectangular garden is 4m greater than the width. The area of the garden is 20m squared. Find the dimensions of the garden.

A Dell company manufactures computers. For quality control,two sets of laptops were tested. In the first group, 32 out of 500 were found to contain some sort of defect. In the second group,30 out of 500 were found to have a defect. Is the difference between the groups significant?(use a significance level of 0.05.