So maybe it’s 5, it’s equivalent to the side with 6, just shorter
Answer:
Step-by-step explanation:
In this question, the sample space contains 8 elements and has been given as;
HHT HHH THH HTH HTT TTT TTH THT
1. For event A:
Outcomes of alternating tail and head = THH HTH HTT THT
= 4 outcomes
Pr(alternating tail and head (with either coming first)) = 
= 
2. For event B:
Outcomes of no tails on the first two tosses = HHT HHH
= 2 outcomes
Pr (No tails on the first two tosses) = 
= 
For event C:
Outcomes of a tail on both the first and the last tosses = THT TTT
= 2 outcomes
Pr(A tail on both the first and last tosses) = 
= 
(3/4)(4/4)=(3*4)/(4*4)=12/16
7/16
(5/8)(2/2)=(5*2)/(8*2)=10/16
/Answer: Option C. 12/16, 7/16, 10/16
9514 1404 393
Answer:
23) x = ±3i, ±√2
26) x = 4/3, (-2/3)(1 ± i√3)
Step-by-step explanation:
23) Put in standard form to make factoring easier.
x^4 +7x^2 -18 = 0
(x^2 +9)(x^2 -2) = 0 . . . . factors in integers
Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:
(x -3i)(x +3i)(x -√2)(x +√2) = 0
x = ±3i, ±√2
___
26) This will be the difference of cubes after you remove the common factor.
81x^3 -192 = 0
3(27x^3 -64) = 0
(3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes
The complex roots of the quadratic can be found using the quadratic formula.
x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)
Then the three solutions to the equation are ...
x = 4/3, (-2/3)(1 ± i√3)