Answer:
[ 0.4964, 0.5836 ]
Step-by-step explanation:
Data provided in the question:
Total sample size = 500
person voting for smith = 270
thus,
P( person voting for smith ), p = = 0.54
Confidence level = 95%
now,
standard error, SE =
or
SE =
or
SE = 0.0223
now,
Confidence interval = p ± ( z × SE )
here,
z value for 95% confidence interval is 1.96
Confidence interval = [ 0.54 - ( 1.96 × 0.0223 ), 0.54 + ( 1.96 × 0.0223 ) ]
= [ 0.54 - 0.0436 , 0.54 + 0.0436 ]
= [ 0.4964, 0.5836 ]
Answer:
Step-by-step explanation:
1. The Pythagorean theorem applies, so the sum of the squares of the legs is equal to the square of the hypotenuse.
x² + (x+3)² = (√29)²
2x² +6x +9 = 29 . . . . . . eliminate parentheses, collect terms
2x² +6x -20 = 0 . . . . . . subtract 29
x² +3x -10 = 0 . . . . . . . . divide by 2
(x +5)(x -2) = 0 . . . . . . . . factor
x = -5 or +2 . . . . . . . . . . . . values that make the factors zero (-5 is extraneous)
The value of x is 2.
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2. Even though the figure is drawn incorrectly the Pythagorean theorem still applies. (The second attachment shows the circle in the right place. The figure is not to scale.)
14² + r² = (r+2)²
196 + r² = r² +4r +4 . . . . eliminate parentheses
192 = 4r . . . . . . . . . . . . . .subtract r²+4 from both sides
48 = r . . . . . . . . . . . . . . . . divide by 4
The value of r is 48.
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3. You will recognize that the triangle involving the distance above the ground, the distance along the ground, and the straight-line bullet path is an isosceles right triangle. So, the hypotenuse is √2 times the length of either leg. The path length of the bullet is ...
(2500 ft)√2 ≈ 3536 ft
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4. see below for the diagram
The length to the terminal point is found using the Pythagorean theorem:
d = √(3² +(-1)²) = √10
The distance from the origin to the terminal point is √10 ≈ 3.16.
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5. Angles "a" and "8a" total 90°, so we have ...
a + 8a = 90°
9a = 90° . . . . . . . . collect terms
a = 10° . . . . . . . . . . divide by 9
The value of a is 10°.
Answer:
Step-by-step explanation:
Let us first generate the frequency table from the information given:
Hurricane number(X) Frequency(f) f(X)
6 9 54
8 13 104
12 16 192
14 12 168
Total ∑(f) = 50 ∑f(x) =518
In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:
Let the last frequency be f
9 + 3 + 16 + f = 50
38 + f = 50
f = 50 - 38 = 12
Now, calculating mean:
Therefore mean number of hurricanes = 10.4 (to one decimal place)