Answer:
Are the events A and B disjoint? Yes
Step-by-step explanation:
Disjoint events are those events that cannot occur at the same time, i.e. for events <em>X</em> and <em>Y</em> to be disjoint, 
.
The event <em>A</em> is defined as the number of students whose age is at most 32.
And event <em>B</em> is defined as the number of students whose age is at least 37.
The events <em>A</em> and <em>B</em> are disjoint events.
- The sample space for event <em>A</em> consists of all the students of age group (under 21), (21 - 24), (25 - 28) and (29 - 32).
- Whereas the sample space for event <em>B</em> consists of all the students of age group (33 - 36), (37 - 40) and (Over 40).
The sample space for the intersection of these two events is:
Sample space of (<em>A</em> ∩ <em>B</em>) = 0
As there are no common terms in both the sample.
Hence proved, events <em>A </em> and <em>B</em> are disjoint.
Answer:
71.6056
Step-by-step explanation:
c² = a² + b² - 2abcosC°
29² = 30² + 15² - 2(30)(15)cosC°
841 = 900 + 225 - 900cosC°
-59 = 225 - 900cosC°
-284 = -900cosC°
71/225 = cosC°
cos⁻¹(71/225) = C°
C° = 71.6056
First, determine the area of the whole circle by the equation, A = πr². Substituting,
A = π(6²) = 36π
Then, multiply this value with the ratio of the given angle to the whole revolution,
A(sector) = 36π x (120° / 360°)
The area of the sector is therefore 12π units².
Lucy packs plates faster she packs 5 plates every minute. Mike packs 4 plates every minute because 3/4 of an hour is 45 minutes, then you divide 180 by 45 and the answer is 4 per minute.
Franco would have to pack 90 plates every 20 minutes (1/3 of an hour) for his rate to be between Lucy's and Mike's. Lucy's rate is at 100 plates per 20 minutes because she can pack 5 plates every minute. Mike's it's at 80 plates per 20 minutes because he can pack 4 plates per minute. So that means that For Franco to be in the middle he has to pack 90 Plates every 20 minutes.
Hope this helps!!!
