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:
a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work
Answer:
-162
Step-by-step explanation:
23=5-2/3d
2/3d=-18
d= -27
6d= 6* -27
6d= -162
6 because 1 in 1/6 represents how many he took and the denominator in the other fractions gets smaller because it's less and less each time
