T2 #3. if cards selected from a deck, what is prob of 3 cards are black??
If 3 cards are selected, what is the prob they are all black... is that the question?
26/52 * 25/51 * 24/50 = 2/17.
20. (x+3)^5. find 3rd term expansion..
is there any easier way to figure this out??? what if the question asked for 4th or 5th term??????
3rd term uses (5 C 2).
(First term = (5 C 0), second term = (5 C 1), ..., sixth (final) term = (5 C 5). Got it? Remember there are 6 terms if the highest power is 5: exponent power of 5, 4, 3, 2, 1, and 0 the constant term.)
The x value uses the third highest power, which is 3 here (5, 4, 3). The other value uses the power equal to the exponent minus the 'x' exponent. Here the exponent is 5. The 'x' exponent we found was 3. So the other value uses the exponent of 2. Now we plug in and solve.
(5 C 2) = 10.
x^3 = x^3.
(+3)^2 = 9.
So our 3rd term is 10*x^3*9 = 90x^3.
Our 4th term, FYI:
(5 C 3) = 10.
Use x^2 (remember 5, 4, 3, 2 so 2 is the 4th highest) = x^2.
(+3)^3 (remember 5-2 = 3) = 27.
So 10*x^2*27 = 270x^2 is the 4th term.
In general with (x+y)^n and you are looking for the 'r' term in order:
(n C (r-1)) * x^(n-r+1) * y^(r-1)
T1.
problem 3. I don't know why X is 60'...
17. 4 csc ^2 symbol -1 = 0. 0<symbol<360
solve:
can you explain this?????
4csc^2(theta) - 1 = 0
4csc^2(theta) = 1
csc^2(theta) = 1/4
Remember csc = 1/sin
sin^2(theta) = 4
sin(theta) = 2
The sine function is bounded by -1 and 1. It can never give you a value of 2. This is therefore undefined.
problem 24.... no idea on this too...
thank you!
