Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B25%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Width for n = 64:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B64%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Thus, the sample consisting of 64 data values would give a greater precision
Answer:
Step-by-step explanation:
v = {[(20sin36°)i + (20cos36°)j] + 10i} mi/h
vE = 20sin36º + 10 = 21.76 mi/h
vN = 20cos36° = 16.18 mi/h
v = √(vE2 + vN2) = √(21.762 + 16.182) mi/h = 27.12 mi/h
θ = tan-1(vN/vE) = tan-1(16.18/21.76) = 36.6º north of east
Answer:
is there an image or something idk the vid
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Given Information
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Total number of people = 165
Adult = $6
Child = $2
Total collected = $618
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Assumptions
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Let x be the number of adults and y be the number of children
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Form equations
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Total number of people
x + y = 165
Total amount collected
6x + 2y = 618
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Ans: The two equations are x + y = 165 and 6x + 2y = 618
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The question is not asking for it but if you need to solve the equation to find the answer to x and y
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Present the two equations and solve for x and y
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x + y = 165 ------------------------- (eqn 1)
6x + 2y = 618 ------------------------- (eqn 2)
(eqn 1) :
x + y = 165
x = 165 - y ------------------------- substitute into (eqn 2)
6(165 - y) + 2y = 618
990 - 6y + 2y = 618
4y = 990 - 618
4y = 372
y = 93 ------------------------- substitute into (eqn 1)
x + y = 165
x + 93 = 165
x = 165 - 93
x = 72
x = 72 and y = 93
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Ans: 72 adults and 93 children
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Answer:
2.30 years
Step-by-step explanation:
The number of fish tripled in the first year, making a total of 240 * 3 = 720 fishes.
(a) The formula for logistic equation is as the following
where P0 = 240 is the number of fishes initially, we can plug in P = 720 and t = 1 to calculate the constant k
b) Using the following formula
with P = 3000, P0 = 240, k = 1.1, we can calculate the number of years it takes to get to 3000 fishes
