Answer:
The minimum sample size required is 207.
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population mean <em>μ</em> is:
The margin of error of this confidence interval is:
Given:
*Use a <em>z</em>-table for the critical value.
Compute the value of <em>n</em> as follows:
![MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207](https://tex.z-dn.net/?f=MOE%3Dz_%7B%5Calpha%20%2F2%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C3%3D2.576%5Ctimes%20%5Cfrac%7B29%7D%7B%5Csqrt%7Bn%7D%7D%20%5C%5Cn%3D%5B%5Cfrac%7B2.576%5Ctimes29%7D%7B3%7D%20%5D%5E%7B2%7D%5C%5C%3D206.69%5C%5C%5Capprox207)
Thus, the minimum sample size required is 207.
5/54 or approximately 0.092592593
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
r = 4, y = 2, b = 1, so n = 3 + 1 = 4
r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
r = 5, y = 2, b = 1, so n = 9 + 1 = 10
And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
r = 6, y = 2, b = 1, so n = 19 + 1 = 20
And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
9514 1404 393
Answer:
Step-by-step explanation:
The cost of each plan (y) is the sum of the initial fee and the product of the mileage charge and the number of miles (x).
First Plan: y = 40 +0.13x
Second Plan: y = 53 +0.08x
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We can find when the costs are the same by solving this system of equations. A way to do that is to subtract the second equation from the first:
(y) -(y) = (40 +0.13x) -(53 +0.08x)
0 = -13 +0.05x
Multiplying by 20 gives ...
0 = -260 +x
Adding 260, we have ...
x = 260
The plans cost the same for 260 miles of driving.
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The cost of the plans for that distance is ...
y = 40 +0.13x = 40 +0.13(260) = 40 +33.80
y = 73.80
The cost when the two plans cost the same is $73.80.
Answer:
42.3
Step-by-step explanation:
add both angles then subtract by 180 and the negative number is your answer
Answer:
5 months will be the same cost at each gym.
Step-by-step explanation:
As
- Exercise Plus charges a yearly fee of $75 plus $10 a month.
- Gym and Swim charges a yearly fee of $50 plus $15 a month.
Let 
by the number of months
Therefore, 5 months will be the same cost at each gym.
