WLHS Math Team

4.  If x⁵ - 3x²=6y and 2x³=4y+6, find all possible real values for x.

5. If a, b, and c are distinct prime numbers less than 10, and the quadratic ax²+bx+c=0, what real numbers could be roots of the equation?

1. Bill knows how many blue and red marbles are in a jar. Jill removes marbles from the jar one at a time. Using his knowledge of probability and his knowledge of what is in the jar, bill bets which color she will remove. Bill bets 27 times that Jill will draw a blue marble. He is correct 18 times. For the next draw, Bill refuses to bet, saying that the odds are “even.” If there were 101 marbles in the jar when they began this game, how many blue marbles were there initially?

2. If the 5th term in the binomial expansion of (2x-3)¹⁰ has a numeric value of 128, what are the real values of x to the nearest hundredth?

3. A gaggle is worth 10 giggles, and 12 giggles are worth 50 gurgles. If a giggle and two gaggles are worth a gurgle plus $50, how much would it cost (to the nearest cent) to purchase a giggle, a gaggle, and a gurgle?

5. If x is real, what is the minimum possible value of:
| 2 x 1 |
| 1 0 1 |
| x 1 2 |
(that is supposed to be one matrix with one line going down each side [meaning you take the determinant] but that’s too complicated to do so I just typed it like that)

6. There are 10 bells in the bell tower. Starting at noon, Quasimodo randomly selects a bell and rings it on the hour. At n o’clock, the probability that Quasimodo will ring a bell that he has already rung is greater than 0.5. What is the minimum value for n?

3. Mr. X uses light bulb Brand A, which last 1000 hours and costs $4.00 for a box of six bulbs. Mrs. Y uses light bulb Brand B, which lasts 1200 hours and costs $6.00 for a dozen bulbs. If it takes 2 Brand A bulbs to provide as much light as 3 Brand B bulbs for the same amount of time, what is the ratio of money spent by Mr. X on light bulbs to the amount of money spent by Mrs. Y on light bulbs?

4. A semicircle is placed on a 3-4-5 right triangle so its diameter lies along the hypotenuse and it is tangent to the legs. What is the area of the semicircle?

1. Solve for n if (2^-n-1)^(1/n) x (2⁴ⁿ⁺⁶)^(1/2n)=4

2. a1, a2, and a3 are in geometric sequence with a1 not equal to 0. b1, b2, and b3 are in arithmetic sequence. a1+b1, a2+2b2, a3+3b3 are in arithmetic sequence. If a1=(b1-b3)/6, what is the common ration of the geometric sequence a1, a2, a3?

Basically, we have this randomly scheduled math meet NEXT WEEK!…Wed Nov 12 @ Hammond.

So remind your friends to sign up for the meet throughout the end of this week and the beginning of next!

2nd, 3rd,  & 4th year Mathletes Only. I will buy a T-shirt from the Mathlete who posts the correct solutions first. (You may wish to print and mark up the pages) The Pancake Mistake

First Year Mathletes Only! I will buy a T-shirt from the first “First Year Mathlete” to post the correct solutions. (you may wish to print the pages to mark up)Hang on, Harry!

4.    Water is poured from a full cylinder into a sphere, until the sphere is 1/2 full, at which point the cylinder is 2/3 full.  The remainder of the water is poured into a 5 foot cube, which is then filled to capacity by pouring 5 cubic feet of water from the sphere to the cube.  If the sphere and the cylinder have the same radius, what is the height of the cylinder, to the nearest 1/100 of a foot?

5.    A container holds 31 tiles.  Each of the first 26 tiles has a different letter of the alphabet printed on the surface.  The remaining 5 tiles show the 5 vowels (A, E, I, O, U).  If James takes four tiles from the container, what is the probability that the four letters, in the order drawn, spell one of the following words: DOPE, HOPE, MOPE, POPE, OR ROPE?

1.    A set of 5 numbers is in arithmetic progression.  Their sum is 50.  If the next two numbers in the progression are added, the new sum will be 91.  What is the fifth number in the sequence?

2.    The sum of an infinite geometric series is 3/r, where r is the common ratio.  What is the third term of the series, in terms of r?

3.    What is the fourth term in teh binomial expansion of (3x-k)¹⁰?