Answer:
d. The variance is 9.56 and the standard deviation is 3.09.
Step-by-step explanation:
From the above question, we are given the following data set.
3, 7, 8, 8, 8, 9, 10, 10, 13, 14
a) Mean = 3 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 13 + 14/ 10
= 90/10
= 9
b) Variance
The formula for sample Variance = (Mean - x)²/ n - 1
Mean = 9
n = 10
Sample Variance =
(3 - 9)² + (7 - 9)² + (8 - 9)² + (8 - 9)² + (8 - 9)² + (9 - 9)² + (10 - 9)² + (10 - 9)² + (13 - 9)² + (14 - 9)² / 10 - 1
= 36 + 4 + 1 + 1 + 1 + 0 + 1 + 1 + 16 + 25/9
= 86/9
= 9.555555556
≈ Approximately 9.56
Variance = 9.56
Sample Standard deviation = √Sample Variance
= √9.56
= 3.0919249667
≈ Approximately 3.09
Answer:
a: 3
b. 6973568802
Step-by-step explanation:
a₁ = 6 , r = 3 , a₂₀ =?
Result:
a₂₀ = 6973568802
Explanation:
To find a₂₀ we use the formula
aₙ = a₁ · r
^ⁿ⁻¹
In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above
formula, we obtain:
aₙ = a₁ · r
^ⁿ⁻¹
a₂₀ = 6 · 3
^²⁰⁻¹
a₂₀ = 6 · 1162261467
a₂₀ = 6973568802
Answer:
-> a + c = 1250 ____________ (1)
-> 8a + 5c = 7300 __________(2)
There were 900 children and 350 adults.
Step-by-step explanation:
Let the number of children at the carnival be c.
Let the number of adults at the carnival be a.
The admission fee at a carnival is $5 for children and $8 for adults on Friday.
1250 people attended the carnival and $7300 was collected. This means two things:
-> a + c = 1250 ____________ (1)
-> 8a + 5c = 7300 __________(2)
We now have a system of equations representing the problem.
To solve, make a subject of formula in (1):
a = 1250 - c _______(3)
Put (3) in (2):
8(1250 - c) + 5c = 7300
10000 - 8c + 5c = 7300
10000 - 7300 = 3c
3c = 2700
c = 2700 / 3 = 900
Put the value of c back in (3):
a = 1250 - 900 = 350
Therefore, there were 900 children and 350 adults at the carnival.
Answer:
14x^3+39x^2+18x+20
Step-by-step explanation:
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Define adult and student tickets
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Let the number of adult tickets be x
Adult tickets = x
Student tickets = x + 69
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Form equation and solve for x
------------------------------------------
x + x + 69 = 569
2x + 69 = 569 ← Combine like terms
2x = 569 - 69 ← Subtract 69 from both sides
2x = 500
x = 250 ← Divide by 2 to find x
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Find the number of adult tickets and student tickets
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Adult tickets = x = 250
Student tickets = x + 69 = 319
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Answer: Adult tickets = 250 ; Student tickets = 319
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