Step-by-step explanation:
1/6 (3 - 2x) < 1/3 x
let's multiply everything by 6
3 - 2x < 6/3 x
3 - 2x < 2x
3 < 4x
3/4 < x
so, x > 3/4
since 3/4 is never equal to x but is purely smaller than x, the interval of valid x values starts right after 3/4 and goes to infinity.
x = 3/4 is not valid, because 3/4 is not smaller than 3/4 (it is equal to) ...
Answer:
the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Step-by-step explanation:
since the random variable X= time taken to make a grilled cheese sandwich is uniformly distributed, then the probability is governed by
P(a<X<b)= proportion of the time considered / total time range = (a-b)/(c-d) , where c is the maximum time and d is the minimum one
then
P(4<X<5) = (5-4)/(11-3) = 1/8 = 0.125
since we already know that takes less than 6 minutes , then
P(X<6)= P(3<X<6) = (6-3)/(11-3) = 3/8 = 0.375
then using the theorem of Bayes
P( 4<X<5 | X<6 ) = P ( 4<X<5 ∩ X<6 ) / P(X<6) = P(4<X<5)/P(3<X<6) = 0.125 /0.375 = 1/3 (33.33%)
therefore given that we already know that will take Michelle less than 6 minutes , the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Sec^2 x = 1 + tan^2 x
tan^2 x = sec^2 x - 1
tan x = sqrt ( sec^2 x - 1) answer
Answer:
AC: -1.5,-3 BD: 2, -1
Step-by-step explanation:
Midpt Formula x coord: (x1+x2)/2 y-coord:(y1+y2_/2