Using racket software

Q$1(15$ pts$).$ Write scheme code to calculate the following equations:

a$.24+315-\frac{7}{2}$

b$.\frac{23}{4}-\frac{4}{56}$

c$.(24+\sqrt[\phantom{2}]{3})\frac{15-7}{2}$

Q$2(15$ pts$).$ Write a scheme function named number Type that takes one number parameter

and returns one of the following strings using an if statement: "Positive odd", "Positive even",

"Negative odd", "Negative even", "Zero". Define a list L having numbers $9,-4,0,12,-5,7,-12$

and apply your function to each element of your list. The output should be

$("$Positive odd" "Negative even" "Zero" "Positive even" "Negative odd"

"Positive odd" "Negative even"$)$

Q$3(10$ pts$).$ Define $a,b,$ and c as $2,(471),12$ using let and change the first element of b with

$a+c$ by getting the tail of b and adding $a+c$ as new head. Your code should print $(1471).$

Q$4(10$ pts$).$ Write a scheme function named Multiple$3$or $4?$ that returns true if the number

is divisible by $3$ or $4,$ false otherwise. Filter all numbers divisible by $3$ or $4$ in a list containing $5,$

$9,15,20,22,34,24,14,4.$

Q$5(10$ pts$).$ Write scheme expressions with car's and cdr$\text{'}$s to access symbol D for each of the

following lists. Note that you can combine at most $4$ car's or cdr$\text{'}$s using shorter notation such as

$($cdadar L$).$ If you need to use more, you can write it separately such as $($cadar $($cdadar L$)).$

a$.(ABCDEF)$

b$.(($ABC$)($DEF$))$

c$.(($AB$)($CD$)(EF)$

d$.(A(BCD)EF)$

e$.(AB((CD)E)F)$

Q$6(10$ pts$).$ Write a non$-$tail recursive scheme function countStrings that returns the

number of strings in a list. You can use string? function to check each list element. For instance,

$($countStrings $\text{'}($P $"123"0$ #t $-57$ "abc"$))$ should return $2.$

Q$7(10$ pts$).$ Write a tail recursive version of the same function named countStrings T that

returns the number of strings in a list. Your function should get a second argument to store

accumulated result. For instance, $($countStringsT $\text{'}($P $"123"0$ #t $-57$ "abc"$)$

$0$ should return $2.$

Q$8(10$ pts$).$ Write a tail recursive scheme function named difference that takes two lists

$\text{'}([6,3,11])0)$ should return $9$ as the sum of differences of elements

$|7-11|).$ Assume that the lists only contain numbers. So$,$ you don't need to check the types.

Your function should stop when it reaches the end of any list. For instance, $($difference

Q$9(10$ pts$).$ Write a scheme function named sequence that takes two number parameters I

and $u,$ and returns a list that contains the sequence of numbers $($by a difference of $1)$ from I to

u$.$ You can write your function tail recursive or non$-$tail recursive. For instance, $($sequence $3$

should return $(\{$:$[3,4,6,7,9,10]),($sequence $66)$ should return $(6),$

$($sequence $75)$ should return $().$