Extra Credit Algebra Homework?

Question

1) Of the following numbers, which has the most factors of nine?
a. 81
b. 999
c. 2727
d. 3333

2) Lee multiplied a number by its squre root and got a product of 64. What was Lee's original number?
a. 4
b. 8
c. 16
d. 32

3) Of the following numbers, which one is divisible by the greatest number of different primes?
a. 30
b. 36
c. 96
d. 128

4) (3989+3988+3987 . . . + 1998+1997+1996) - (1994+1993+1992+ . . . +3+2+1)

a. 1994 * 1994
b. 1994 * 1995
c. 1995 * 1995
d. 1994 + 1995

5) What is the remainder when the product of all the prime numbers between 1 and 100 is divided by 4?
a. 3
b. 2
c. 1
d. 0

6) At the Belltower school, 99% of the 100 students are girls, but only 98% of the students in grade 8 are girls. Which of the following could be the number of students in grade 8 who are girls.

a. 98
b. 97
c. 49
d. 48





If you can please show work and/or tell me how you did it.

Note: * = times or multiplied by

Thanks I really appreciate this!

Answer 1

1) Of the following numbers, which has the most factors of nine?
a. 81 = 9 * 9
b. 999 = 9 * 111 = 9 * 3 * 37
c. 2727 = 9 * 33 = 9 * 3 * 11
d. 3333 = 3 * 1111

so, a) is the right answer

2) Lee multiplied a number by its squre root and got a product of 64. What was Lee's original number?
a. 4
b. 8
c. 16
d. 32

c.16 * sqrt(16) = 16 * 4 = 64

3) Of the following numbers, which one is divisible by the greatest number of different primes?
a. 30 = 2 * 3 * 5
b. 36 = 2 * 2 *3 * 3
c. 96 = 2 * 2 * 2 * 2 * 2 * 3
d. 128 = 2 * 2 * 2 * 2 * 2 * 2 * 2

d.

4) (3989+3988+3987 . . . + 1998+1997+1996) - (1994+1993+1992+ . . . +3+2+1)

a. 1994 * 1994
b. 1994 * 1995
c. 1995 * 1995
d. 1994 + 1995

3989 - 1994 = 1995
3988 - 1993 = 1995
3987 - 1992 = 1995
...
1998 - 3 = 1995
1997 - 2 = 1995
1996 - 1 = 1995

1994 * 1995, which is b.

5) What is the remainder when the product of all the prime numbers between 1 and 100 is divided by 4?
a. 3
b. 2
c. 1
d. 0

(2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97) / 4 = 265, remainder zero (0), so d.

6) At the Belltower school, 99% of the 100 students are girls, but only 98% of the students in grade 8 are girls. Which of the following could be the number of students in grade 8 who are girls.

a. 98
b. 97
c. 49
d. 48

c. 49 is true, which means there are 50 students in grade 8.

Answer 2

turn the backside fraction and multiply. so (a+b)/xy circumstances xy/a the xy's cancel and you have (a+b)/a for you to go away like that or wreck up the fraction and get a million +b/a.