Step-by-step explanation:
e^(x+h) is always larger than e^x.
so the minimum function value in that interval is e⁴.
and the maximum function value in that interval is e⁶.
e⁴ = 54.59815003... ≈ 54.60
e⁶ = 403.4287935... ≈ 403.43
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%)
Answer:
x = 42
Step-by-step explanation:
The marked angles are supplementary, so their sum is 180°.
(2x +8) +(2x +4) = 180
4x +12 = 180 . . . . . . . . . simplify
x +3 = 45 . . . . . . . divide by 4 (because we can)
x = 42 . . . . . . subtract 3
_____
<em>Additional comment</em>
A "two-step" linear equation like this one is usually solved by subtracting the unwanted constant, then dividing by the coefficient of the variable. Here, we have done those steps in reverse order. This makes the numbers smaller and eliminates the coefficient of the variable. Sometimes I find it easier to solve the equation this way.