Answer: 7/26
Step-by-step explanation:
Number of purple marbles = 6
Number of white marbles = 7
Total number of marbles = 13
The probability of first drawing a white marble will be = 7/13
The probability of drawing a purple marble the second time will be = 6/12 = 1/2
The probability that the first marble is white and the second one is purple will now be:
= 7/13 × 1/2
= 7/26
Note that since there are 13 marbles, when the first purple marble is drawn, there'll be 12 marbles left.
Answer:
Step-by-step explanation:
The point at the terminal side of an acute angle is given by 
.
That is,
and 
.
Let r be the length of line segment drawn from the origin to the point and is given by the formula:
Substituting the values of x and y into r,
Thus, 
Also, 
is given by:
Substituting values of x and r,
Answer:
x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))
Step-by-step explanation:
Firstly let us split this up, we need to first work out what g(h(x)) is:
h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2
Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6
= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6
= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6
= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6
= x^2 - 4x * sqrt(x) + 12x - 16 * sqrt(x) + 10
= x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))
Answer:
7. (4x +10)/(x^3 +3x^2 -16x -48)
9. -320/93
Step-by-step explanation:
7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.
6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))
= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator
= (6x +18 -2x -8)/((x -4)(x +3)(x +4))
= (4x +10)/((x^2 -16)(x +3))
= (4x +10)/(x^3 +3x^2 -16x -48)
_____
9. First you simplify the denominator:
2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400
Then you perform the division. This can be done by multiplying by the inverse of the denominator.
(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93
It’s D I also trust the other guy
