Events A and B are termed independent when
if not, events A and B are classified as dependent.
The events A, B and A∩B are:
- A - Jane plans to attend a ballgame on Monday;
- B - Kate intends to go to a ballgame on Monday;
- A∩B - Both Kate and Jane will be at the ballgame on Monday.
Answer: events A and B are dependent
The maximum area that can be enclosed is 64 ft². To achieve the largest area while minimizing the perimeter, the dimensions should be as equal as possible. Allocating 32 feet of fencing for four sides gives us 8 feet per side, resulting in a square with a side length of 8; thus, the area equals 8*8 = 64.
The solution is 85, based on the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
To find the combined function (f+g)(x), we proceed as follows:
(f+g)(x) = f(x) + g(x) = x^2 + 3x + 5 + x^2 + 2x = 2x^2 + 5x + 5
Therefore, the graph of (f+g)(x) depicts a parabola with the vertex located at (-5/4, 15/8).
I hope this is helpful.
A step-by-step analysis reveals the occurrences over the years: 1 in 1949, 2 in 1956 (difference of 7 years), 3 in 1963 (another 7 years), and 4 in 1970 (yet again 7 years). The consistent gap of 7 years establishes a linear function to define future sightings of the comet. For instance, examining years following 1970, 2017 is not a multiple of 7, 2018 is also not, but 2019 is a multiple, identifying the comet’s next appearance. If one is born in 2005, the difference from 1949 to 2005 is 56 years, indicating the comet would have been observed 8 times throughout their lifetime.
