Answer:
Step-by-step explanation:
We can model this situation with an arithmetic series.
we have to find the number of all the seats, so we need to sum up the number of seats in all of the 22 rows.
1st row: 23
2nd row: 27
3rd row: 31
Notice how we are adding 4 each time.
So we have an arithmetic series with a first term of 23 and a common difference of 4.
We need to find the total number of seats. To do this, we use the formula for the sum of an arithmetic series (first n terms):
Sₙ = (n/2)(t₁ + tₙ)
where n is the term numbers, t₁ is the first term, tₙ is the nth term
We want to sum up to 22 terms, so we need to find the 22nd term
Formula for general term of an arithmetic sequence:
tₙ = t₁ + (n-1)d,
where t1 is the first term, n is the term number, d is the common difference. Since first term is 23 and common difference is 4, the general term for this situation is
tₙ = 23 + (n-1)(4)
The 22nd term, which is the 22nd row, is
t₂₂ = 23 + (22-1)(4) = 107
There are 107 seats in the 22nd row.
So we use the sum formula to find the total number of seats:
S₂₂ = (22/2)(23 + 107) = 1430 seats
Total of 1430 seats.
If all the seats are taken, then the total sale profit is
1430 * $29.99 = $42885.70
Answer:
From inspection of the diagram, we can see that the spinner is divided into <u>4 equal parts</u>, where 3 parts are red and 1 part is yellow.
Therefore,
<u>Multiplication Rule for Independent Events</u>
For independent events A and B:
Therefore,
<h3><u>Conclusion</u></h3>
Ari is incorrect. The spinner is divided into 4 parts, where only one part is yellow. Therefore, the probability of spinning a yellow is 1/4. As the events are independent, the Multiplication Rule should be used to calculate the probability of spinning 2 yellows. So the probability of spinning 2 yellows is 1/4 x 1/4 = 1/16.
Answer: Pick an x value like x = 2
Note that f(2) = 1 and g(2) = 2. This shows we've doubled the f(x) value to get g(x). Therefore k = 2.
Or you could pick on x = 4 to see f(4) = 2 and g(4) = 4. The output of f(x) has been doubled as well.
It doesn't matter what x is since we'll have this doubling effect go on. I recommend picking x values where the points on the blue graph land perfectly on a grid location. Something like x = 5 seems a bit tricky.
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