Answer:
Degree of freedom = 2
Expected frequency = 80%
Critical value, = 5.991
χ² statistic = 3.5
Step-by-step explanation:
Given the data :
Hong Kong New York Paris
Yes 86% 76% 78%
No 14% 24% 22%
The degree of freedom for the Chisquare statistic is given as :
(no of rows - 1) * (number of columns - 1)
Number of rows = 2
Number of columns = 3
. Degree of freedom = (2-1) * (3-1) = 1*2 = 2
Expected frequency = (Row total * column total) / grand total
The expected frequency of Hong Kong / Yes cell :
Row total = (86+76+78) = 240
Column total = (86+14) = 100
Grand total, N = (14+24+22)+240 = 300
Expected frequency = (240*100)/300 = 80%
The critical value :
At α - level = 0.05 ; df = 2
Critical value = 5.991
χ² = Σ(observed - Expected)² / Expected
The expected values :
80 80 80
20 20 20
Hence,
χ² = Σ(86-80)²/80 + (76-80)²/80 + (78-80)²/80 + (14-20)²/20 + (24-20)²/20 + (22-20)²/20
χ² statistic = 3.5
Answer:
8, 10
Step-by-step explanation:
Multiplying the equation by the product of the denominators, we have ...
40(x+2) +40x = 9x(x+2)
80x +80 = 9x^2 +18x . . . . eliminate parentheses
9x^2 -62x -80 = 0 . . . . . . put in standard form
9x^2 -72x +10x -80 = 0 . . . prepare to factor by grouping
9x(x -8) +10(x -8) = 0 . . . . . factor pairs of terms
(9x +10)(x -8) = 0
Solutions are ...
x = -10/9 and x = 8
The integers are 8 and 10.
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<em>Comment on the attachment</em>
I find a graphing calculator to be a nice tool for solving these. It finds zeros easily, so writing the equation so it equals zero is a useful first step.
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Define x and y:
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Let the length be x.
Let the width be y.
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Formula:
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Perimeter = 2(Length + Width)
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Construct equations and solve for x and y:
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2x + 2y = 56 ---------------------- (1)
2(x+8) + 4y = 82 -----------------------(2)
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From equation 1:
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2x + 2y = 56
x + y = 28
x = 28 - y
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From equation 2:
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2(x+8) + 4y = 82
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33
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Substitute x = 28 - y into equation 2:
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x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5
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Substitute y = 5 into equation 1:
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x = 28 - y
x = 28 - 5
x = 23
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Find Length and Width
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Length = x = 23 m
Width = y = 5m
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Answer: Length = 23m and Width = 5m
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