# Mr. Alexander

Popular questions and responses by Mr. Alexander
1. ## Algebra

Find the largest three-digit number that can be written in the form 3^m + 2^n, where m and n are positive integers.

2. ## Number Theory

Express $3.\overline{4}_{13}$ as a base 10 fraction in reduced form.

3. ## Algebra

Suppose $A$ and $B$ are digits for which the product of the two-digit numbers $\underline{2A}$ and $\underline{AB}$ is 1971. Find the sum of $A$ and $B$. Note: This is LaTeX, so if you need to render it, then go ahead

4. ## Algebra

The Master Chief collects spiders and starfish. If his spiders have 8 legs and his starfish have 5 legs, how many starfish must he have given that his spider/starfish collection totals 19 creatures and 116 legs?

5. ## Number Theory

What is $1000000_{16} - 8D6A7B_{16}$ in base 16? (You do not need to include the subscript 16 in your answer.)

6. ## Algebra

Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays

7. ## Counting and Probability

Suppose I have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them. How many 4's do I have to add before the expected value is at least 3.5?

8. ## Number Theory

Find a base 7 three-digit number which has its digits reversed when expressed in base 9. (You do not need to indicate the base with a subscript for this answer.)

9. ## Counting and Probability

(a) A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. How many of the small cubes are painted red on exactly one side? (b) A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. How many of the

10. ## Algebra (Percentages)

Annie loves giving away puppies. When her friend Bobby walks by, she instantly gives him 50% of her puppy stash. Bobby, stunned with this shower of puppies, gives back 20% of his total. Annie counters by giving Bobby 50% of her new puppy total. Bobby

11. ## Counting and Probability

What is the difference between the sum of the first 400 even counting numbers and the sum of the first 400 odd counting numbers?

12. ## Algebra

Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays

13. ## Counting and Probability

How many 3-digit numbers have the units digit larger than the tens digit?

14. ## Counting and Probability

Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them. What is the expected value of the number shown if we add two additional 4's (instead of just one) to the bag?

15. ## Counting and Probability

One member of the debate team is going to be chosen President. Each member is equally likely to be chosen. The probability that a boy is chosen is 2/3 the probability that a girl is chosen. Girls make up what fraction of the debate team?

16. ## Counting Numbers

A prime number less than 100 is selected randomly. What is the probability that its square has units digit 7?

17. ## Algebra

Agents J and K work in a long hallway with 4000 equally-spaced, consecutive offices. The agents decide to walk toward each other so they can meet and have lunch together. Agent J has recently been relocated from office 2013 to office 1. His former office

18. ## Algebra

Tom took five math tests and got an integer score on each of them. He never scored higher than 90, and his lowest score was the fourth test. If his average score, rounded to the nearest integer, was 82, what is the lowest possible score he could have

19. ## Counting and Probability

Hi! I need urgent help for these questions here. They have a deadline for today and I have no idea how to solve them (a). Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them. What is the

20. ## Counting and Probability

(a) A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. How many of the small cubes are painted red on exactly one side? (b) A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. How many of the

21. ## Counting and Probability

The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?

22. ## Algebra

A wooden plank is 5 feet long and 1 1/2 inches thick. To make the plank 1 1/8 inches thick, a carpenter removes the same thickness of wood from the top and bottom of the plank. How many inches does the carpenter remove from the top of the plank? Express

23. ## Algebra

Find the largest three-digit number that can be written in the form $3^m + 2^n$, where $m$ and $n$ are positive integers.

24. ## Geometry

One leg of a right triangle has a length of 15 m. The other sides have lengths that are consecutive integers. Find the number of meters in the perimeter.

1. ## Algebra

Cause I tried entering the problem, it was wrong :(

posted on July 18, 2015
2. ## Algebra

I do not know very well. Help me~

posted on July 18, 2015