The arclength of the curve r(t) = 2 cos³ (πt/2), 2 sin³ (πt/2), 1, between the points r = (2, 0, 1) and r = (0, 2, 1), is given by?

Use the First Derivative Test to find the exact location of all the relative extrema of the given function.

1. f(t) = t^3-3t^2, Domain [-1, +infinity)

2. f(x) = 3x^4-2x^3, Domain [1, +infinity)

3. f(x) = (x+1)^2/5. Domain [-2,0)

4. f(x) = √ x(x-1), Domain [0, infinity)

(4-4-6, From Example 4.4.2) Let X and Y have the joint pdf

f(x,y)=32x2(1−|y|),−1<x<1,−1<y<1

1. Calculate Var(X)
2. Calculate Var(Y)
3. P(−X≤Y)

Calculate the standard deviation of the following returns. Year Return 1 0.23 2 -0.08 3 0.03 4 -0.09 5 0.17 Enter the answer with 4 decimals, e.g. 0.1234.

Calculate the variance of the following returns.

Year Return

1 -0.2

2 -0.08

3   -0.08

4   0.19

5 0.21

Enter the answer with 4 decimals, e.g. 0.1234.

Given the following utility matrix, representing the ratings, on a 1–5 star scale, of eight items, a through h, by three users A, B, and C:

After we normalize the matrix by subtracting from each nonblank entry the average value for its user, what is the cosine distance between users A and C ?

1)
a.   Which of the following sets are the empty set?
i.   { x | x is a real number and x2 – 1 = 0 }
ii.   { x | x is a real number and x2 + 1 = 0 }
iii.   { x | x is a real number and x2 = -9 }
iv.   { x | x is a real number and x = 2x + 1 }

b.   Let A = {1, 2, 3, 4, 5}. Which of the following sets are equal to A?
i.   {4, 1, 2, 3, 5}
ii.   {2, 3, 4}
iii.   { x | x is an integer and x2 <= 25 }
iv.   { x | x is a positive rational number and x <= 5 }

Problem 1: The following data is in the following of Table. Education Expenditure data, Assuming there is unique variance in each region, using two stage approach weighted least square approach to estimate X1, X2 and X3 effect on Y.

（sas programming）

STATE   Y       X1      X2      X3      Region  

ME      189     2828    351     508     1 

NH      169     3259    346     564     1 

VT      230     3072    348     322     1 

MA      168     3835    335     846     1 

RI      180     3549    327     871     1 

CT      193     4256    341     774     1 

NY      261     4151    326     856     1 

NJ      214     3954    333     889     1 

PA      201     3419    326     715     1 

OH      172     3509    354     753     2 

IN      194     3412    359     649     2 

IL      189     3981    349     830     2 

MI      233     3675    369     738     2 

WI      209     3363    361     659     2 

MN      262     3341    365     664     2 

IA      234     3265    344     572     2 

MO      177     3257    336     701     2 

ND      177     2730    369     443     2 

SD      187     2876    369     446     2 

NB      148     3239    350     615     2 

KS      196     3303    340     661     2 

DE      248     3795    376     722     3 

MD      247     3742    364     766     3 

VA      180     3068    353     631     3 

WV      149     2470    329     390     3 

NC      155     2664    354     450     3 

SC      149     2380    377     476     3 

GA      156     2781    371     603     3 

FL      191     3191    336     805     3 

KY      140     2645    349     523     3 

TN      137     2579    343     588     3 

AL      112     2337    362     584     3 

MS      130     2081    385     445     3 

AR      134     2322    352     500     3 

LA      162     2634    390     661     3 

OK      135     2880    330     680     3 

TX      155     3029    369     797     3 

MT      238     2942    369     534     4 

ID      170     2668    368     541     4 

WY      238     3190    366     605     4 

CO      192     3340    358     785     4 

NM      227     2651    421     698     4 

AZ      207     3027    387     796     4 

UT      201     2790    412     804     4 

NV      225     3957    385     809     4 

WA      215     3688    342     726     4 

OR      233     3317    333     671     4 

CA      273     3968    348     909     4 

AK      372     4146    440     484     4 

HI      212     3513    383     831     4 

Question 1:

I believe that the population mean the amount of time millennials spend on social media. My findings consist of studying a group of 8 millennials for 24 hours.

I believe the population mean is less than 2.24

Question 2:

I am not certain that I am giving you the correct information so if not please let me know so I can get it correct so everyone can attempt to figure it out.

So I asked 8 people I work with how often they order for deliver to their home here are there answers

1-2

2-4

3-0

4-2

5-3

6-1

7-4

8-5

I will be using the .05 hypothesis significance level to compute my problem with a population mean.

Description

Inversion Count for an array indicates – how far (or close) the array is from being sorted. If array is already sorted then inversion count is 0. If array is sorted in reverse order that inversion count is the maximum. Formally speaking, two elements a[i] and a[j] form an inversion if a[i] > a[j] and i < j . Example: The sequence 2, 4, 1, 3, 5 has three inversions (2, 1), (4, 1), (4, 3).

Requirements:

• Design should be based on divide and conquer.

• Running time should NOT be worse than Θ (n log n).

• Must use recursion to subproblems

Input Specification

Your program should read from an input file, which starts with a line indicating the number of test cases. Each of the following lines indicates a test case, and each test case includes a sequence of numbers (separated by spaces) for which you need to count inversions.

Sample Input

3

2 4 1 3 5

1 2 4 8 9 3 5 6

1 20 6 4 5

Output Specification

For each test case, print one line with a format of The sequence has ? inversions in console.

Sample Output

Below is the correct output for the previous sample input.

The sequence has 3 inversions.

The sequence has 7 inversions.

The sequence has 5 inversions.

Hints:

The design can be based on merge sort.

How to get number of inversions in merge()?

Input file

input.txt

3

2 4 1 3 5

1. 2 4 8 9 3 5 6

1. 20 6 4 5

Please code in C++ thank you for your help and time!!