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**Mathegocart**- Replies: 1

16. A sphere has radius 6 inches. What is the volume, in cubic inches, of the smallest cube that contains the ENTIRE sphere?

Is it 1728?

Zeeshan 01 wrote:

no i dont mean this

my eq.is solved by taking integral.???

You are quite ambiguous on this, do you mean you are trying to solve a differential equation?

Silly mistake fixed, thanks to zetafunc for suggesting modulo.

**Mathegocart**- Replies: 8

I was doing this triangle problem,

1) There are 3 angles in a triangle, a,b, and c. a < 40, b = c+1, and if c is an integer, what is the least possible value of c?

Is it 71?

2) 15. Let f(a,b) be defined as a^2+b^2-2,(where a and b are positive integers) which of the following CANNOT be the value of f(a,b)?

(a) 0

(b) 2

(c) 3

(d) 6

Is it 2?

3) In a store, 5 customers have bought 7 items, 11 people have bought 6 items, 14 people have bought 5 items, 60 people have bought 4 items, and 10 have bought fewer than 4 items(the number is not specifically known.), which information can be determined?

I. The average amount of items purchased per customer

II. Median number of items purchased per consumer

III. Mode of number of items purchased by consumer

Is it II and III?

4) Flipping y=3x-1 over the y axis obtains -3x-1. Right?

bobbym wrote:

Hi Mathegocart;

Any chance we can get some clarification on 2,3,8 and

http://latex.artofproblemsolving.com/9/6/9/969d1960185e877ca37aa5ae592fb3ab24c3614f.png

The equation described in 2 equals 0,

In 8, you got equation (1) and your neighbor got (2). For what values of a and b(a and b are distinct), for at least 1 of the solutions are the same?

[modified by admin]

For (9), what is the range of

ElainaVW wrote:

You know who he is in real life??

**Mathegocart**- Replies: 9

1. Find the sum of all the integers between 50 and 350 whose final digit is 1.

1a. How much greater is this than the sum of all the integers from 1 to 50?

2. Find the complete set of real solutions for the equation where y is real.

3. How many primes can be represented as ? Say NONE if no primes can be represented, say ALL if every prime can be represented.

4. Find all solutions (x,y) where x and y are integers, to the equation

5. For what values of a does

and have at least one root in common?

6. Find the last digit of (2^1232)*(2^5+3^7)?

7.Find the coefficient of p if the difference between the roots in this equation is 9.

8. Bobbym and his neighbor were solving equations late in the night and they were solving two quadratics,

(1) and

(2).

His neighbor switched up bobbym's equation and got (2). For what values of a and b are at least one of the roots the same?

**Mathegocart**- Replies: 2

1. How many 2-digit numbers are divisible by 4? Is it 22?

2.Joe began to increase the speed of his car at 2 pm. Since that time, the speed of Joe's car has been increasing by 1.5 miles per hour for each half minute that has passed. If his car is now travelling at 65.5 mph, for how many minutes has the car been exceeding the 55mph speed limit? He starts at 0mph.

3. Ang has x dollars and Julia has y dollars. Ang gives Julia 1/3 of his money. Julia spends 1/4 of the total money she now has. Express the money spent in x and y.

Is it y/4 + x/12

4. A cube has 1000 cubic feet of volume. The container is being filled with 7 cubic feet of water per minute. It is draining at 2 cubic feet per minute. If it is half full at 9 am, at what time is it full? Is it 10:40 am?

bobbym wrote:

Hi;

You mean at least one.

That is what I meant, silly overlook.

**Mathegocart**- Replies: 3

How many ways are there to make 75 cents with only nickels,dimes, and quarters if you must have 1 of every coin?

bobbym wrote:

Nice vid! Could have been improved without the 4 guys. Guy number 4, a Balakrishnan prime, of course is correct.

The biology guy was nice, don't you think?

I note you could definitely integrate a volume to find the area/volume of no 7.

**Mathegocart**- Replies: 3

A box contains 4 red cards, 6 g blue cards, and 10 green cards.

What is the smallest number of cards we must remove from the box to get 2 cards of THE SAME COLOR?

Is it 4?

2. Max is reading a book. He has read 1/4 of the book. If he stopped at page 67, how many pages are in there fully?

3. 4 lines can intersect at a maximum of... x points. Find x.

4. CD is 6 inches from AB and AB is parallel to CD. Point K is 4 inches from AB and not between the two lines. How many points on CD are exactly 10 inches from K?

5. If 5 different distinct integers sum to 55, what is the largest value any of these numbers can have?

bobbym wrote:

Oh! I thought that was 2x, I am sorry.

bobbym that is ok I have major oversights sometimes.

It is

I placed you link between the url tags so it would show. - bobbym

bobbym wrote:

You have 2x not x, so it is 2 x 43 = 86 which leaves a remainder of 1 when divided by 5.

bobbym that was my indicator for the 2nd question. 2.

thickhead wrote:

correct

thickhead wrote:

TH, aren't there more solutions for 6?

bobbym wrote:

Hi;

Bobbym 43 % 5 = 3 not 1

thickhead wrote:

Thickhead thanks for helping me gain a better understanding of similar combo. problems like these.

**Mathegocart**- Replies: 10

1. there are 4 coins with values 1,2,4, and 8. How many different amounts can be made with one or more of the 4 coins?

Each coin can ONLY BE USED ONCE.

Is it 14?

there are 4 1 coin combinations.

There are 3+2+1 2 coin combos

There are 4 3 coin combos(1,2,4),(1,4,8),(1,2,8),(2,4,8)

There is 1 4-coin combo (1,2,4,8)

thus there are 4 + 6 + 4 + 1(15 combos)

Am I right?

2.x mod 5 =1

x mod 7 =1

Find the least number x > 10 that satisfies these 2 equations. Is it 71?

I solved it.

**Mathegocart**- Replies: 2

Tennis balls come in cases of 3 balls each. L, M and C play tennis for a month. During that time L bought 6 cans and M bought 4 cans. C bought no cans. She figures(C) she owes 15 dollars. Of the 15 dollars, how much should go to L?

(A tennis ball is worth $1.5)