Hard Calculus! So intense that I lost my breath!?

Question

1. The probability of you receiving a 7 by rolling two dices is
greater than, or less than, or equal to 16%?
Explain your reasoning.
2. There are four apples on the table. You take away 3. How many do you have?
3. You can use the toilet in 2.5 minutes while your friend can do his job in 3.25 minutes. If you both used the toilet, how long would it take?
4. The rate at which you relase poop within the 4 seconds of release is modeled by the function f(x) = squareroot(x), where x represents the force used and f(x) represents amount dumped in toilet.
a. Evaluate f'(x)
b. Please explain the meaning of f'(x)? f''(x)?
c. Is there a meaning for the integral of f(x)? If no, explain.
5. You go and play roulette at casino. You realize your chances are 50/50 to win per roll. You have lost for 5 consecutive tries. What are your chances of really winning on the 6th roll.

AS A SIDE NOTE: THESE ARE SERIOUS QUESTIONS (YOU CAN IGNORE NUMBER FOUR IF YOU LIKE). For number 5, pretend that it IS 50/50 and tell me your real chances of winning on the 6th roll. Thank you.

50/50 does not mean 1 in this case. Read logically. 50% winning on the roll...

Answer 1

1. There is no way to tell unless you roll the two dice at the same time.
2. Three
3.Depends.
4.a.1/2radical x dx
b. f'(x) is the velocity at which the poop was excreted, and f''(x) is the acceleration at which it underwent.
c. There is no meaning to the integral, as it is the area under the curve, which really translates realistically to nothing.
5. 50/50

Answer 2

Incidentally, only question #4 is calculus. The rest are either probability or addition (and #2 is a famous trick question). But any way ...

1) There are SIX ways to roll a 7 with two dice: (1,6); (2,5); (3,4); (4,3); (5,2); (6,1). The probability of a seven is 6/36, or 16.67%. So, it is GREATER THAN 16% (by two-thirds of a per cent)
2) You took away 3, so that is what you have - the three you took. The other one you left on the table, so you don't have it.
3) 3.25 minutes if you go at the same time. 5.75 minutes if you have to go one after the other.
4) You're on your own with this one.
5) Your chances are still 50/50. Probability of truly random events is not affected by what has already occurred.

Answer 3

I don't have time to do all of these. But I'll do nos.1, 2 and 5.
1. The probability is greater than 16% because
it is 1/6 which is 16 2/3%
2. You have 3 apples, because YOU took away 3.
5. Your chances of winning on the 6th roll are still
50/50. The spins are independent events. Each
spin has no effect on the next one.
Something like this happened at Monte Carlo
once. Half the numbers were red and half black.
It turned out that red came up 26 times in a row.
By the 20th spin people were betting (and losing)
huge sums of money that black would turn up next.

Answer 4

1. I can get 7 as (6+1),(1+6),(4+3),(3+4) hence the probability is 4/36 ~= 11.1%

2. I have 1, because 4-3=1
3. 5.75 minutes, if there is only one toilet, 3.25 if there is more than one
4. this is a perversion!
5. 50/50 as before, BTW in mathematics 50/50 = 1 = 100% means that I always win, BTW2 the chance of winning at the roulette are lower than 50%

Answer 5

Do you realize most of them has got nothing to do with calculus?

1. More than 16%, it's 16.67%
You can only get 16, 26, 34, 43, 52, and 61 out of 36 possibilities, so the probability is 6/36, which is 16.67%
2. 3
3. 5.75 minutes since you both will have to take turns.
4. At this point, I realized I fell for it.

Answer 6

i do no longer think of this could be a calc problem consistent with se. it particularly is sparkling up by diverse algebra approaches. first set up your equations like this: x + y = 8 x - y =0 then upload the two equations and get 2x = 8 x is comparable to 4 and for this reason y is likewise equivalent to 4 those are the only values of x and y that fulfill the two equations concurrently

Answer 7

1. You can get a 7 with any of the following: (1,6), (2,5), (3,4), (4,3), (5,2), or (6,1). The probability is 6/36 = 1/6. You figure out how this compares with 16%.

Answer 8

3 apples;
5.75 minutes;