What is Normal, Binomial, Poisson and Exponential Distributions with examples.

What is Continuous Distributions and Density Functions.

What is Normal density and Standardizing: Z-Values

Suppose we restrict the domain of the Post correspondence problem to include only alphabets with exactly two symbols. Is the resulting correspondence problem decidable?

Prove or disprove that the union of two subspaces is a subspace. If it is not true, what is the smallest subspace containing the union of the two subspaces.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$110,000 loan.

Option​ 1: a​ 30-year loan at an APR of 7.25​%.

Option​ 2: a​ 15-year loan at an APR of 6.8%.

1.) Find the monthly payment for each option.

The monthly payment for option 1 is what?

The monthly payment for option 2 is​ what?.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

2.) Find the total payment for each option.

The total payment for option 1 is what?

The total payment for option 2 is what?

​(Round to the nearest cent as​ needed.)

Compare the two options. Which appears to be the better​ option?

A.Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B.Option 1 will always be the better option.

C.Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

D.Option 2 will always be the better option

11.

Give a 95% confidence interval, for μ1−μ2μ1-μ2 given the following information.

n1=25n1=25, ¯x1=2.65x¯1=2.65, s1=0.91s1=0.91
n2=45n2=45, ¯x2=2.45x¯2=2.45, s2=0.83

---------- ± -----------  Use Technology Rounded to 2 decimal places.

13.

Two samples are taken with the following numbers of successes and sample sizes
r1r1 = 36 r2r2 = 33
n1n1 = 60 n2n2 = 100

Find a 99% confidence interval, round answers to the nearest thousandth.
---------- < p1−p2p1-p2 < ------------

14.

Two samples are taken with the following sample means, sizes, and standard deviations
¯x1x¯1 = 40 ¯x2x¯2 = 27
n1n1 = 50 n2n2 = 45
s1s1 = 5 s2s2 = 3

Estimate the difference in population means using a 94% confidence level. Use a calculator, and do NOT pool the sample variances. Round answers to the nearest hundredth.
---------- < μ1−μ2μ1-μ2 < ------------

16.

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:p1=p2Ho:p1=p2
      Ha:p1>p2Ha:p1>p2

You obtain 29.1% successes in a sample of size n1=508n1=508 from the first population. You obtain 24.6% successes in a sample of size n2=783n2=783 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The original toy of Edouard Lucas had 8 disks. Suppose you were to carry out the moves to transfer the disks from one post (A) to another post (B) on this toy. At least how many moves are required?

gives the gold medal times for every other Summer Olympics for the women’s 100-meter freestyle (swimming). ^^^

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the data.

c. Does it appear from inspection that there is a relationship between the variables? Why or why not?

d. Calculate the least squares line. Put the equation in the form of: ŷ = a + bx.

e. Find the correlation coefficient. Is the decrease in times significant? Find the estimated gold medal time for 1932.

f. Find the estimated time for 1984.

g. Why are the answers from part f different from the chart values?

h. Does it appear that a line is the best way to fit the data? Why or why not?

i. Use the least-squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your answer is reasonable? Why or why not?

True or False: Profitability index is the PV of future cash flows divided by the initial investment. A result of greater than .9 is desired.

In financial terms, what is the biggest downfall to using payback rather than discounted payback when analyzing a project? The first choice always seems to be best. It does not account for time value of money. The WACC isn't accurate. It is more difficult to calculate than discounted payback.

Theorem: Let K/F be a field extension and let a ∈ K be algebraic over F. If deg(mF,a(x)) = n, then

1. F[a] = F(a).

2. [F(a) : F] = n, and

3. {1, a, a2 , ..., an−1} is a basis for F(a).

Please answer with a solution. Thank You!

1) Given a differential equation (1−2x²−2y)dy−(4x³+4xy)dx = 0. Is it an exact equation? Justify your answer. Solve the equation.

2) Given a differential equation (y³ − y² sinx − x)dx + (3xy² + 2y cos x)dy = 0. Is it an exact equation? Justify your answer. Solve the equation.

3) Solve the linear equation of order one: dy/dx + (1 + 2/x)y = x^-2e^x

4) Solve the linear equation of order one: xdy/dx − 2y = x⁴e^{x^2}

1. Answer the following questions regarding permutations and combinations.

How many different 5-digit octal numbers are there which do not contain the digit 0?

How many different 5-digit octal numbers are there which do not contain the digit 0 and in which all digits are different?

How many 5-digit octal numbers are there which do not contain the digit 0 and where the third digit is an odd number and the last digit and even number?

How many different combinations of three 5-digit octal numbers and two 3-digit hexadecimal numbers are there where, in all numbers, all digits are odd and where all 5 numbers are different? (for a hexadecimal number, consider 1,3,5,7,9,B,D,F to be odd)

Describe what happens to the graph of ?(?) = ?(? − ℎ)2 + ? when each of the variables has the following changes:

k: positive:

k: negative:

h: positive:

h: negative

a: negative

|?|>1:

|?|<1:

The discriminant tells you how many and what type of solutions a quadratic equation has. How many and what type of solutions do the following discriminants have?

Positive:

Negative:

Zero:

What is the formula for finding the discriminant?


Describe what the vertex of a quadratic equation is?


How do you find the vertex of the quadratic equation when it’s in standard form?


How do you find the vertex of the quadratic equation when it’s in vertex form