John Glenn High School has approximately 1000 students. A survey randomly asked 20 students if they regularly buy lunch. Of thos
e asked, 8 said yes. The table shows their answers when asked what their favorite food is and about how many times each month they buy it.
What portion of students purchased their favorite food more than four times a month. Write your answer as a simplified fraction.
b. What is the mean number of times a student bought their favorite food? Round your answer to the nearest tenth.
c. Predict how many students from John Glenn regularly buy lunch and purchase their favorite food more than four times a month. Round your answer to the nearest whole number.
d. What is the mean number of times that a student regularly buys a salad? Round to the nearest tenth.
What portion of students purchased their favorite food more than four times a month. Write your answer as a simplified fraction.
b. What is the mean number of times a student bought their favorite food? Round your answer to the nearest tenth.
c. Predict how many students from John Glenn regularly buy lunch and purchase their favorite food more than four times a month. Round your answer to the nearest whole number.
d. What is the mean number of times that a student regularly buys a salad? Round to the nearest tenth.
1 answer:
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In an arithmetic sequence, consecutive terms have a fixed distance d between them. If a₁ is the first term, then
2nd term = a₂ = a₁ + d
3rd term = a₃ = a₂ + d = a₁ + 2d
4th term = a₄ = a₃ + d = a₁ + 3d
and so on, up to
nth term =
so that every term in the sequence can be expressed in terms of a₁ and d.
6. It's kind of hard to tell, but it looks like you're given a₁₃ = -53 and a₃₅ = -163.
We have
a₁₃ = a₁ + 12d = -53
a₃₅ = a₁ + 34d = -163
Solve for a₁ and d. Eliminating a₁ and solving for d gives
(a₁ + 12d) - (a₁ + 34d) = -53 - (-163)
-22d = 110
d = -5
and solving for a₁, we get
a₁ + 12•(-5) = -53
a₁ - 60 = -53
a₁ = 7
Then the nth term is recursively given by
and explicitly by
7. We do the same thing here. Use the known terms to find a₁ and d :
a₁₉ = a₁ + 18d = 15
a₃₈ = a₁ + 37d = 72
⇒ (a₁ + 18d) - (a₁ + 37d) = 15 - 72
⇒ -19d = -57
⇒ d = 3
⇒ a₁ + 18•3 = 15
⇒ a₁ = -39
Then the nth term is recursively obtained by
and explicitly by
8. I won't both reproducing the info I included in my answer to your other question about geometric sequences.
We're given that the 1st term is 3 and the 2nd term is 12, so the ratio is r = 12/3 = 4.
Then the next three terms in the sequence are
192 • 4 = 768
768 • 4 = 3072
3072 • 4 = 12,288
The recursive rule with a₁ = 3 and r = 4 is
and the explicit rule would be