E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
Y+2x=24
product is max
xy=max
we have
y+2x=24
minus 2x both sides
y=24-2x
sub that for y in xy=max
(24-2x)(x)=max
-2x^2+24x=max
we have a parabola opening down
the coordinates of the vertex is our answer
the x value of the vertex is -b/2a where
ax^2+bx+c=y
-24/2(-2)=-24/-4=6
xvalue=6
we can just sub
y=24-2x
y=24-2(6)
y=24-12
y=12
the numbers are 6 and 12
the product is 72
the numbers are 6 and 12
Answer:
-10%
Step-by-step explanation:
price elasticity of demand = % change in demand / % change in price
Here, the "price" changes from 15 to 45, so its percent change is ...
((new value)/(old value) -1) × 100%
= (45/15 -1) × 100%
= 200%
The % change in demand is given as -20%, so the price elasticity is ...
price elasticity of demand = (-20%)/(200%) = -0.10 = -10%
Answer:
i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
ii) 
And using the normal standard table or excel we got:
iv) 
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
Step-by-step explanation:
Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:
Where 
and 
Part i and iii
In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
Part ii
We are interested on this probability:
We can use the z score formula given by:
Using this formula we have:
And using the normal standard table or excel we got:
Part iv
We want this probability:
Using the z score formula we got:
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
