Problem 6. Find (with proof) the least positive integer m with the following properties: • The last digit (units digit) of m is 6. • By deleting the last digit 6 and replacing it in front of the remaining digits one obtains a number four times greater than the given number.

Graph letter e X = 10 Y = 19

Hello, any help for this problem would be great, thank you!

Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number.  Show all your work.

Serial numbers for a product are made using 3 letters followed by 2 numbers. If the letters are taken from the first 8 letters of the alphabet with no repeats and the numbers are taken from the 10 digits (0 − 9) with no repeats, how many serial numbers are possible?

please answer question 16 and 18 by using combination

3. In this problem, you may use the following formulae without further justification: 2 ^²³ − ( ² - - (n(n + ¹)) ². 2 £* k k=1 n(n+1) 2 12 k=1 k² (a) Find a formula in n for each of (b) Find a formula in n for each of Σ(2k) and Σ(2k - 1). k=1 k=1 n n(n+1)(2n +1) 6 (c) Find a formula in n for each of n Σ(2k)² and Σ(2k-1)². TL k=1 TL (d) Only use the formulae above, to compute Σ(2k)³ and Σ(2k-1)³. 1³22 +33 4²+ +99³-100², which is the sum of cubes of all odd integers no greater than 100, minus the sum of squares of all even integers no greater than 100.

ERCISES 5.1.7. Solve the following problems. 1) Find the number of 5-lists of the form (21, 22, 23, 24, 25), where each , is a nonnegative integer and x₁ + x₂ + x3 + x4 + 3x5 = 12. 2) We will buy 3 pies (not necessarily all different) from a store that sells 4 kinds of pie. different ord possible? List all of the possibilities (using A for apple