3 x^2 - 42 = 1 / 3x
Note that the term on the right side can be written as 3-x
So we have
3 x^2 - 42 = 3 -x
Since the bases are the same, we can solve for the exponents
x^2 - 42 = - x add x to both sides
x^2 + x - 42 = 0 factor
( x + 7) ( x - 6) = 0
Setting each factor to 0 and solving for x produces the integer solutions
x = -7 or x = 6
P(A l B ) = P (A and B) / P(B) = 0.2 / 0.4 = 0.5
Independent because P(A l B) = P(A)
99.7% of the data fall within 3 standard deviations from the mean
So....
Low end of the range is 60 - 3(4.5) = 46.5 in
High end of the range s 60 + 3(4.5) = 73.5 in
We have this sum
4^1 + 4^2 + 4^3 + 4^4 + 4^5 =
4 + 16 + 64 + 256 + 1024 =
1364
Correct !!!!
P(A l B) = P (A and B) / P(B) = .05 / .2 = 0.25
Since
P(A l B) = P(A).....these events are independent
First box ⇒ independent
Second box ⇒ P (A l B ) = P(A)
We have 5 numbers divisible by 2 = 2, 4, 6, 8, 10
We have 2 numbers divisible by 5 = 5,10
So....the number of outcomes =
5 * 2 =
10
A.
The majority of the data is to the left of the mean.
A little tricky
The probabilty is
[ area of red square - area of blue square ] / area of red square =
[ 196 - 64 ] / [ 196 ] =
132 / 196 =
0.6732 =
0.67
We have replacement here....so....
P(purple on 1st draw) = 3/10
P(orange ball on 2nd draw) = 2/10
So...
(3/10) (2/10) = 6/100 = 3 / 100
P(drawing a black card 1st) = 6/12 = 1/2
P(drawing a red card second) = 6/11
So....the probability is
(1/2) (6/11) = 6 / 22 = 3 / 11
