A decreasing sequence of numbers is a sequence of integers where every integer in the sequence is smaller than all other previous integers in that sequence. For example, • 35, 16, 7, 2, 0, -3, -9 is a decreasing sequence of numbers. The length of this sequence is 7 (total numbers in the sequence) and the difference of this sequence is 35 (-9) = 44. • 5 is a decreasing sequence of numbers with length 1 and difference 5-5 = 0 • 99, -99 is a decreasing sequence of numbers with length 2 and difference 99-(-99) = 198 17, 23, 11, 8, -5, -3 is not a decreasing sequence of numbers. Write a program that contains a main() function. The maint function repeatedly asks the user to enter an integer if the previously entered integers form a decreasing sequence of numbers. This process stops as soon as the latest user input breaks the decreasing sequence. Then your function should print the length and difference of the decreasing sequence. Finally, call the main() function such that the call will be executed if and only if the program is run as a stand alone program. Note: your function must not use any data structures like list.

= =×ばつ2 and 6 = (a) A composite number is a positive integer that has at least one divisor other than 1 and itself. For example, 2 ×ばつ2 is not a composite number but 4 2 ×ばつ 3 are composite numbers. A logic circuit has four binary input variables, A, B, C and D. The output Z of the logic circuit is 1 if the unsigned integer represented by the binary number ABCD is a composite number. Using variables A and B for the select inputs S1 and S0 of a 4-to-1 multiplexer, implement the logic function Z(A, B, C, D) using this multiplexor and other logic gates.

A typical roulette wheel used in a casino has 38 slots that are numbered 1,2,3,....,36,0,00, respectively. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls. (a)Define the Sample space S. (b)Let A = {0,00}. Give the value of P(A). (c) Let B = {14,15,17 18}. Give the value of P(B). (d) Let D = {x:x is odd}. Give the value of P(D).

Computer science

let n = 1*3*5*....*197*199 (the product of first 100 odd numbers) find the last 2 digits of n

3. Two 7-digit integers (leading zeros allowed) are considered to be equivalent if one can be obtained from the other by rearranging its digits. For example, 0012234, 0312042, 3220014 and 2100243 are all considered equivalent, whereas 0012234 and 0001234 are not equivalent. How many nonequivalent 7-digit integers are there in which the digits 0, 2, 4 and 6 can each appear at most once?

Start with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.