Math Answers

Find a function y of x such that

9yy'=x and y(9)=10

Solve the separable differential equation for.

dy/dx= [1+x] divided by [xy^15]

Use the following initial condition: y(1)=5

y^16=?

.

Solve the separable differential equation

10x-8ysqrt(x^2 +1) * dy/dx =0

Subject to the initial condition: .y(0)=9

y=??

On average 20% of the calculators produced in a factory are faulty. Samples of 10 calculators are to be selected at a random each day. Each calculator will be selected and replaced in the set of calculators which have been produced on that day. Calculate the probability that in any one sample, two calculators or less will be faulty. 

The differential equation

dy/dx= cos(x)(y^2 +6y+8)/(6y+16)

has an implicit general solution of the form F(x,y)=K

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form

F(x,y)=G(x)+H(y)=K

Find such a solution and then give the related functions requested.

F(x,y)=G(x)+H(y)=

Solve the following differential equation:

(7x+8y)dx+(8x-2)dy=0

The differential equation dy/dx = 25+20x+40y+32xy

has an implicit general solution of the form F(x,y)=K

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form of F(x,y)=G(x)+H(y)=K

Find such a solution and then give the related functions requested for

F(x,y)=G(x)+H(y)=

A random sample of size 36 was taken from a population distributed as Nμ,3.92.The value of the sample x was 15.6. i. Find a 90% confidence interval for μ. (5mks)

It is believed that value of μ is 17. Use your confidence interval to comment on this belief.(2mks)

In the year 1918 a flu like disease occurred in Spain and spread to the rest of the world. This year 2020 another similar flu like disease has occurred in china and is spreading in the whole world. Researchers have found that the likelihood of the disease occurring again is 0.01.Determine the average number of flus in the next 300 years and the likelihood that in the next 300 years, the disease will occur at most five times.       

Two judges in a beauty contest rank the ten competitors in the following order.

x 6 4 3 9 2 7 1 5 10 8

y 4 1 6 7 5 8 2 3 9 10

Do the two judges appear to agree in their standards? (6mks)