A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)
B. Determine if each of the following numbers is a prime or composite.
6. 828
7. 1666
8. 1781
9. 1125
10. 107
C. Find the greatest common divisor of each of the following pairs of integers.
11. 60 and 100
12. 45 and 33
13. 34 and 58
14. 77 and 128
15. 98 and 273
D. Find the least common multiple of each of the following pairs of integers.
16. 72 and 108
17. 175 and 245
18. 150 and 70
19. 32 and 27
20. 540 and 504
Define the multiplicative inverse in modular arithmetic and identify the multiplicative inverse of 6 mod 13 while explaining the algorithm used.
Find the remainder when 7^21+49^21+343^21+2401^21 is divided by 7^20+1
In horse racing, a trifeta is a type of bet. To win a trifeta bet, you need to specify the horses that finish in the top three spots in the exact order in which they finish. If eight horses enter the race, how many different ways can they finish in the top three spots?
Polya described four steps in the solving of a mathematics problem. Here is a problem: A classroom has 2 rows, each with 8 seats. Of 14 students, 5 always sit in the front row, and 4 always sit in the back row, and the rest sit in either row. In how many ways can the students be seated?
6.1.1 Use three different types of representations to model the problem
6.1.2 Now use the steps of Polya to solve this problem. You must explain in detailwhat you are doing in each step
Coach Tab will select 3 girls and 3 boys for
the mix volleyball games. If he has 7 girls
and 8 boys on the pool, how many different
combinations can he have?
How many different rectangles can be made, whose side lengths in centimeters are counting numbers and whose area is 1159 cm2.?
Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?
A={1,2,3,4} and R={(1,2),(3,4),(2,1)}.find transitive closure of R
Consider the simple problem of placing four coloured balls: red, blue, green and white in 15
boxes. What are the numbers of distinct ways in which the balls can be placed in these
boxes, if each box can hold only one ball? Also write the generalized formula of this
numerical result.