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bobbym wrote:

A picture is worth 1000 words - pappym

Yes your father taught you much wisdom that must be used greatly.

**MatheMelgocart**- Replies: 3

1. Solve for x in

2. A circle is inscribed in a equilateral triangle, touching all 3 sides. Then another equilateral triangle is inscribed in the aforementioned circle. What is the ratio of the large triangle to the small triangle?

3.

4. if x^2017 = 2019, find the value of this expression.

5. x + 10 / x+2 = (x-3/2x+5)^2, find x.

6. cos(1) + cos(2) + cos(3) + cos(4) + cos(5) + cos(6) ..... up to cos(90) - (sin(1) + sin(2) + sin(3)..... up to sin(90)) = x. Find x.

bobbym wrote:

Did you check my answers yet?

Yes, they seem to be all correct. How did you solve no12?

thickhead wrote:

(2) 8 and 9 will do? I have assumed the SAME means equal. If you mean consecutive then it is different.

I meant this

2) If the 1st day of a certain month is a Monday, then the xth day cannot fall on a Monday. Find x.

thickhead wrote:

I have both 15 or 16 as choices.

bobbym wrote:

Hi;

3) Find the smallest sum of consecutive numbers that the sum of the divisors are the SAME.

12) Marcie has 3 sets of lights, One stays lit for 11 secs and goes off for 1 second, a 2nd light stays lit for 7 secs and goes off for 1 second.A 3rd light stays lit for 4 secs and goes off for 1 sec,

If they are all lit together, beginning the lit cycle, how many seconds will it be until ALL 3 turn off?15) There are 5 boys who play checkers. Each boy played 4 games of checkers against the other boys. How many games are played altogether?

19) A clock shows 3 or 4 digits at a time. What time is it when the digits have the same sum?

Same sum as what?

20) How many multiples of 7 are between 250 and 500?

21)

A = 1,2,3,4,5

B= 6,9,11,16

How many different way to choose exactly one number from both sets A and B that one is prime and the other is a perfect square?

1 is not a prime.

Sorry bobbym, I meant for 19, the largest sum.

**MatheMelgocart**- Replies: 15

Hello people, could anyone help me with these problems?

2) If the 1st day of a certain month is a Monday, then the xth day cannot fall on a Monday. Find x.

3) Find the smallest sum of consecutive numbers that the sum of the divisors are the SAME

My thoughts: None of the two can be prime. semi-brute forcing it led me to no avail.

12) Marcie has 3 sets of lights, One stays lit for 11 secs and goes off for 1 second, a 2nd light stays lit for 7 secs and goes off for 1 second.A 3rd light stays lit for 4 secs and goes off for 1 sec,

If they are all lit together, beginning the lit cycle, how many seconds will it be until ALL 3 turn off?

15) There are 5 boys who play checkers. Each boy played 4 games of checkers against the other boys. How many games are played altogether?

18) Michelle and Audrey begin walking at noon. Michelle walks from P to Q, back and forth at a constant speed of 3mph. Audrey walks from Q to P, at 2mph, back and forth at a constant speed. They meet each other for the first time at 1 PM. When will they be at POINT Q at the same time?

[---]---]---]---]--]

^ 5 miles, each segment is 1 mile.

19) A clock shows 3 or 4 digits at a time. What time is it when the digits have the same sum?

20) How many multiples of 7 are between 250 and 500

21) A = 1,2,3,4,5

B= 6,9,11,16

How many different way to choose exactly one number from both sets A and B that one is prime and the other is a perfect square?

1 is not a prime.

Thank you, I must have ignored the small sections when I drew the diagram. thanks.

**MatheMelgocart**- Replies: 4

1) A rectangle is split using 4 lines. What is the greatest number of area sections that can be made from the seperation?

I'm thinking 9, can anyone confirm this?

**MatheMelgocart**- Replies: 2

We connect dots with toothpicks in a grid as shown below. For example, the grid below has 7 horizontal toothpicks in each row and 5 vertical toothpicks in each column.

(a) Suppose we instead have a grid of dots that requires 10 horizontal toothpicks in each row and 20 vertical ones in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?

Me: What I tried to do was find a pattern:

a 2 x 2 square has 12 toothpicks. 4 of the "sides" are shared and 8 are not shared. A 1 vert x 2 horiz has 1 shared side and 6 n.s sides(7). A 3 x 3 square has 8 shared sides and 12 unshared sides. 20. I gave up after this

(b) Can you generalize your answer? Suppose we have a grid that requires $h$ horizontal toothpicks in each row and $v$ vertical toothpicks in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?

???? I have no clue on how to start this?

clarification: Slime guy starts the fight.

bobbym wrote:

Hi;

Bobbym, can you explain why it is 9/9

There are 9 total balls and you can pick anyone of the 9 first so 9 / 9. Once you have picked anyone of them there are only 2 left of that color.

Hey bobbym, how did you find the 3 exponents that add up to 400? Guess and check?

A simple program would have been fastest but I used generating functions instead. This will seem like overkill but it is more in keeping with the Teakettle Principle.

Bobbym, my teacher said not to use a computer on the powers problem. Is there a reasonably easy and simple way?

Bobbym, can you explain why it is 9/9 for the first question?

bobbym wrote:

Hi;

Hey bobbym, how did you find the 3 exponents that add up to 400? Guess and check?

**MatheMelgocart**- Replies: 8

1. A bag contains 3 red marbles, 3 blue marbles, and 3 yellow marbles. 2 marbles are chosen randomly WITHOUT replacement. Find the probablity that both marbles chosen ARE the SAME color.

Reasoning: 3/9 * 2/8 = 6/72 = 1/12.

2. What is the area of a isosceles right triangle with a hypotenuse of 20 inches?

Reasoning: 1:1:√2

so

20/√2 * 20/√2 = 400/2 = 200/2 = 100/2 = 50

^ 1/2BH

3. If 400 were to be expressed as a sum of AT LEAST 2 distinct powers of two, what would be the least possible sum of the powers? i.e, 2^2 + 2^3 = 12, 2+3 =5.

Reasoning: Have no idea on how to approach effectively. tried for 20 mins and found nothing.

4. How many positive 5 digit numbers have 123 AS A BLOCK. 2 such numbers are 12399 and 91239

I said 300

5. If (4^5)(5^13) is written as a integer, how many digits are in it?

Reasoning: 12?

bobbym wrote:

Hi;

We are almost ready to solve this:

5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?

40% + 20%+ 20% = 80%

What happens the remaining 20% ?

Perhaps you would like to change the percentages to 40%, 30% and 30%.

Change it to what you say.

In a scale drawing, 1 inch represents 100 feet. How many square inches on the diagram represent 1 square foot?

thickhead wrote:

It is 2 even in 3D. If the line M has direction only one.

cool. I am also interested in 4 dimensions

bobbym wrote:

Howdy;

He has 10 hp.

**MatheMelgocart**- Replies: 6

1) P is a point that is not on line m. How many lines can be drawn through P that makes a 30 degree angle with m?

I said 2 because you can draw two ..

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**MatheMelgocart**- Replies: 3

1) Just a little nagging problem in the back of my head.

To turn the equation y=2x+1 into y=-2x+1, what would you do?

I said flip it over the y axis? true?

sorry for misunderstandings bobbym

bobbym wrote:

however h h h h h would be 2 pairs.

2 pairs? How do you get that?

because there are only two COMPLETE pairs of h.

Well bobbym there are fish that rest using 3 fins. Not legs but interesting.