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I have actually explained the solution to this problem in my videos on introduction to counting and probability.

The solutions are 8 and 1/4.

This is (at least)  the second time that this question has been posed.

The correct answer is 2/5 and two correct solutions can be found in the most recent thread, apart from this one.

That wasn't right, sorry. Can someone else pls help?

Where are " The cards in Ms. Q's deck are shown below." ?!

First expression:  (6*10^3 + 9*10^2 + 4*10 + 7 - 17*10^2 - 8*10 + 8) / (2*10 + 3 - 7*10 - 11)== - 5175 / 58

2nd expression:  (4*10^2 - 7 + 1) / (2*10 + 3 - 7*10 - 11)== - 197 / 29

Do they look EQUAL to you ?! What have written or copied wrong? Perhaps, your brackets?

The probability is 21/200

The correct order is B, D, C, A, E.

There are 23 ways.

There are 23 ways.

I wrote a computer program:

count = 0

for (a = 1..10)

for (b = 1..36)

  if isinteger(sqrt(a + sqrt(b)) then count = count + 1

The result was 14.

See the answer here:  https://web2.0calc.com/questions/angles_86

Cool!

6 / 3 = 2 - each person gets 2 cards

B = Blue,  R = Red

{BBBRRR} P 2 =4 permutations, BB,  BR,  RB,  RR - maximum number of combination that any of the 3 persons can have. I'm assuming that the 3 Blues and the 3 Reds are indistinguishable within each group of 3 cards. That is the 3 blue cards are identical and the 3 red cards are identical.

Since each person can have as many as 3 red [BR, RB, RR] combinations out of maximum number of 4 [BB, BR, RB, RR], therefore the probability of having at least 1 red is: 3/4.

Therefore, each of the other 2 persons will have the exact same probability of 3 / 4.

And the overall probability that each person has one red card is: [3 / 4]^3 = 27 / 64 =42.1875%

The derivative of cos(2x)*sec(x) is sec(x) (cos(2x) tan(x) - 2*sin(2x)).  This is 0 when x is a multiple of pi.

Checking the multiples of pi, we see that minimum of the function occurs at x = pi, the minimum value is -1.

So the asymptote is y = -1.

You can use complimentary counting, first let S = total number of possible subsets.

Let N = the number of subsets with no prime number, then the answer we are looking for is S - N.

S = 2^18 since there are 18 items.

N is any set with 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

There are a total of 10 items.

So S - N = 2^18 - 2^10

261120 subsets