A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the
following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
2 answers:
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Answer:
The area of the figure is 28 units².
Step-by-step explanation:
Find the area of the full rectangle, ignoring the triangle.
Then, find the area of the triangle:
Finally, subtract:
We have been given a function . We are asked to find the interval on which function is increasing and decreasing.
(a). First of all, we will find the critical points of function by equating derivative with 0.
So are critical points and these will divide our function in 3 intervals
.
Now we will find derivative over each interval as:
Since , therefore, function is increasing on interval
.
Since , therefore, function is decreasing on interval
.
Let us check for the derivative at .
Since , therefore, function is increasing on interval
.
(b) Since are critical points, so these will be either a maximum or minimum.
Let us find values of f(x) on these two points.
Therefore, is a local maximum and
is a local minimum.
(c) To find inflection points, we need to check where 2nd derivative is equal to 0.
Let us find 2nd derivative.
Therefore, is an inflection point of given function.