Referring to the above question, use the quick formula to compute Pnj$=1$ j for all values of n

between $1$ and $100.$ Store the $100$ values in a vector.

$4.$ The volume V of a sphere of radius r is given by

V $=43\backslash$pi r $3.$

Use R to calculate the approximate volume of Earth, assuming a radius of $6378$ km$.$ Assign

the result to an object named volumeEarth.

$5.$ The breakdown of music preferences for a class of university students is: $40\%$ prefer rock, $10\%$ prefer country, $15\%$ prefer hip$-$hop and the rest prefer alternative. Construct a pie chart and a bar plot to display these data.

$6.$ Calculatethe the quotient, without remainder after dividing $31079$ into $170166719.$

$7.$ Calculate the remainder after dividing $31079$ into $170166719.$

$8.$ Provide the R codes for creating a function named MEAN$()$ which calculates the average of square root of all integer numbers between $1$ and $100.$ Assign the reslt to an object named mymath.

$9.$ Display the first $5$ observations in rivers as a bar plot. Have the observations in rivers been recorded in decreasing order?

$10.$ The area of a rectangle can be calculated by multiplying the length by the width. You have $5$ rectangles with lengths $3,7,12,15$ and $20.$ The corresponding widths are $2,5,8,11$ and $15.$ Construct appropriate vectors called reclength and recwidth, and use R to calculate all of the areas of these rectangles.

$11.$ Download a file called rain.txt that comes with lab assignment question. Then read the data in the file into a data frame called rain.df using the read.table$()$ function. Use theheader $=$ FALSEoption.