Melody

9+36=45

45+16=61

the asnwer is 61 units^2

What is the domain of the real-valued function (2x - 7) sqrt(x^2 - 5x + 6)?

\(\qquad (2x - 7) \sqrt{x^2 - 5x + 6}\\ \qquad x^2-5x+6\ge0\\ \qquad (x-2)(x-3)\ge0\\ \qquad x\le2\qquad or \qquad x\ge 3\)

(-3) x [(-2) + (+ 4)]

=(-3) x [-2 + 4]

=(-3) x -2

= -3 * -2

= 6

Mike draws six cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits? Express your answer as a simplified fraction.

52C6 = 20358520  ways to choose 6 cards from a deck

lets see what doesn't work

all 6 the same                                                            4*13C6 = 6864

5 the same the other different                              4*13C5*39 = 200772

4 the same and same and 2 the same    4C2*2*13C4*13C2 = 669240

3 the same, 3 the same                            4C2*13C3*13C3   =  490776

6864+200772+669240+490776 = 1367652

20358520-1367652 = 18990868

18990868/20358520 = 0.9328216392940155

factor(18990868) = (2^2*13^3)*2161

factor(20358520) = ((((2^3*5)*7^2)*13)*17)*47

\(\frac{18990868\div 4}{20358520\div 4}=\frac{4747717}{5089630}\)

And I do not think that can be further simplified.

If you are given an answer that is different (with some working or explanation) then please share it with us.

You answer this type of question with a contour probability map.

I have done the map here:

Two numbers, x and y are selected at random from the interval (0, 3). What is the probability that a triangle with sides of length 2, x, and y exists?

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Thanks for your integer solution helperid

I decided to take a look, using a modification of my contour map and see if I agreed with your answer.

There are 25 integer pairs in total,  and  17 of them are favourable.   So that is  17/25 or      68%

It is a bit different from yours becasue you have said that x and/or y can be 3,   but they can't, the brackets are open.

Here is the pic that you need to use.

Thanks Alan,

That will give me something to chew on.   

Here is a much better graph.   Unfortunately, the answer still alludes me. 

Ja, ich verstehe