# unit 8 project inferences and conclusions from data project, algebra homework help

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Unit 8 Project 1. 2. 3. 4. 5. 6. 7. 8. Find the next five terms of the arithmetic sequence 42, 37, 32, β¦ . Find the 24th term of an arithmetic sequence for which a1 = 2 and d = 6. Find the three arithmetic means between Β­4 and 16. Find the sum of the arithmetic series for which a1 = 7, n = 31, and an = 127. Find the next three terms of the geometric sequence 81, 27, 9, β¦ . Find the eight term of the geometric sequence for which a1 = 5 and r = Β­2. Find two geometric means between 7 and 189 Find the sum of the geometric series for which a1 = 125, r = β, and n = 4. Find the sum of each series, if it exists. 9. 15 β (14 β 2k) k=3 10. 91 + 85 + 79 + β¦ + (Β­29) Find the first five terms of each sequence. 11. 12. a1 = 2, an + 1 = an + 3 a1 = Β­4, an + 1 = an + n2 Find the variance, mean, median, mode, and standard deviation for the given values. 13. 13, 15, 12, 10, 4, 16, 17, 22, 9 14. Use the data that shows the ages of the U.S. population to create a histogram. Tell whether the data is positively skewed, negatively skewed, or if it has a normal distribution. 15. The number of home runs scored by teams in the Brooksfield baseball league are normally distributed and have a mean of 94 and a standard deviation of 8. What percentage of the teams have scored more than 102 home runs? Find the margin of error with the given conditions. Round to four decimal places. 16. 17. p = 33% and n = 600. 200 high school students were surveyed about whether they driving or taking the bus to school. 145 preferred driving.
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Unit 8 Project
1. Find the next five terms of the arithmetic sequence 42, 37, 32β¦
Solution: the next five terms are: 27, 22, 17, 12, and 7
2. Find the 24th term of an arithmetic sequence for which a1 = 2 and d = 6
Solution: ππ = π1 + (π β 1)π = 2 + (24 β 1) Γ 6 = πππ
3. Find the three arithmetic means between -4 and 16
Solution:
Assume the arithmetic means to be: a, b, c, so the arithmetic sequence will
be: -4, a, b, c, 16
π1 = β4, π5 = 16
ππ = π1 + (π β 1)π
β΄ π5 = π1 + (5 β 1)π
20
β΄ 16 = β4 + 4π
β΄ 4π = 16 + 4 = 20 β΄ π =
=5
4
β΄ π = β4 + π = β4 + 5 = 1
β΄π = π+π = 1+5=6
β΄ π = 6 + 5 = 11
Then the three arithmetic means are: 1, 6, and 11
4. Find the sum of the arithmetic series for which a1 = 7, n = 31, and an= 127.
Solution:
π
31
The sum of the arithmetic series= (π1 + ππ ) = Γ (7 + 127) = ππππ
2

2

5. Find the next three terms of the geometric sequence 81, 27, 9β¦
Solution: the next three terms are: π, π,

π
π

6. Find the eighth term of the geometric sequence for which a1 = 5 and r = -2.
Solution: ππ = π1 Γ π (πβ1) = 5 Γ (β2)(8β1) = 5 Γ (β2)7 = βπππ

7. Find two geometric means between 7 and 189
Solution: Assume the two geometric means are x and y
Then the geometric sequence will be: 7, x, y, 189
π1 = 7, π4 = 189
ππ = π1 Γ π (πβ1)
β΄ π4 = π1 Γ π (4β1)
189
3
β΄ 189 = 7 Γ π 3
β΄ π3 =
= 27 β΄ π = β27 = 3
7
β΄ π₯ = π1 Γ π = 7 Γ 3 = 21
β΄ π¦ = π₯ Γ π = 21 Γ 3 = 63
Then the two geometric means are: 21 and 63
8. Find the sum of the geometric series for which a1= 125, r = β, and n = 4
Solution:
The sum of the geometric series=

π1 (1βπ π )
1βπ

2 4

=

125Γ(1β(5) )
2

1β5

=...

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