Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For city 1,
x = 22
n1 = 155
p1 = 22/155 = 0.14
For city 2,
x = 12
n2 = 135
p2 = 12/135 = 0.09
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.14(1 - 0.14)/155 + 0.09(1 - 0.09)/135]
= 1.96 × √0.00138344086
= 0.073
Confidence interval = 0.12 - 0.09 ± 0.073
= 0.03 ± 0.073
C. Since the confidence interval does not include zero, there is evidence that the vacancy rates are different between the two cities.
The altitude of the kite:
h = 5 + 250 · sin 45°
h = 5 + 250 · √2 / 2
h = 5 + 250 · 0.7071 = 5 + 176.77 = 181.77 ≈ 182 ft
Answer: The altitude is 183 ft.
Answer: the cost of one daylilies is $4
the cost of one ivy is $9
Step-by-step explanation:
Let x represent the cost of one daylilies.
Let y represent the cost of one ivy.
Nicole and Kim bought their supplies from the same store. Nicole spent $99 on 9 daylilies and 7 pots of ivy. This means that
9x + 7y = 99 - - - - - - - -1
Kim spent $144 on 9 daylilies and 12 pots of ivy. This means that
9x + 12y = 144 - - - - - - - - -2
We will eliminate x by subtracting equation 2 from equation 1, it becomes
- 5y = - 45
y = - 45/-5 = 9
Substituting y = 9 into equation 2, it becomes
9x + 12 × 9 = 144
9x + 108 = 144
9x = 144 - 108 = 36
x = 36/9 = 4
Answer:
x = 96.23 if x is the area of the base
x =21 if x is the side length of the base
Step-by-step explanation:
The volume of a square pyramid is given by
V=1/3 a^ 2 h
We know the volume is 441 and the area of the base is a^2 which is x
and the height is 1/7x
Substituting these values in
441 = 1/3 (x) 1/7x
441 =1/21 x^2
Multiply each side by 21
441*21 = 21*1/21 x^2
9261 = x^2
Take the square root of each side
sqrt(9261) = sqrt(x^2)
x = 96.23
I am thinking you mean x is the side length on the base
We know the volume is 441 and the area of the base is a^2 which is x^2
and the height is 1/7x
Substituting these values in
441 = 1/3 (x^2) 1/7x
441 =1/21 x^3
Multiply each side by 21
441*21 = 21*1/21 x^3
9261 = x^3
Take the cube root of each side
(9261) ^ (1/3) = (x^3)^(1/3)
21 =x
Answer and Step-by-step explanation:
To find the area of a rectangle, you must multiple the length times the width.
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<em><u>#teamtrees #PAW (Plant And Water)</u></em>