Answer:
The least number of tennis balls needed for the sample is 1849.
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population proportion is:
The margin of error for this interval is:
Assume that the proportion of all defective tennis balls is <em>p</em> = 0.50.
The information provided is:
MOE = 0.03
Confidence level = 99%
<em>α</em> = 1%
Compute the critical value of <em>z</em> for <em>α</em> = 1% as follows:
*Use a <em>z</em>-table.
Compute the sample size required as follows:
![n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}](https://tex.z-dn.net/?f=n%3D%5B%5Cfrac%7Bz_%7B%5Calpha%2F2%7D%5Ctimes%20%5Csqrt%7B%5Chat%20p%281-%5Chat%20p%29%7D%20%7D%7BMOE%7D%5D%5E%7B2%7D)
![=[\frac{2.58\times \sqrt{0.50(1-0.50)} }{0.03}]^{2}\\\\=1849](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B2.58%5Ctimes%20%5Csqrt%7B0.50%281-0.50%29%7D%20%7D%7B0.03%7D%5D%5E%7B2%7D%5C%5C%5C%5C%3D1849)
Thus, the least number of tennis balls needed for the sample is 1849.
<span>Data:
infinite geometric series
A1
= 880
r = 1 / 4
The sum of a geometric series in sigma
notation is:
n 1 - r^n
∑ Ai = A ----------- ; where A = A1
i = 1 1-r
When | r | < 1 the infinite sum exists and is equal to</span><span><span>:
∞ A
∑ Ai = ---------- ; where A = A1
i = 1 1 - r</span>
So, in this case</span><span><span>:
∞ 880
∑ Ai = -------------- = 4 * 880 / 3 = 3520 /3 = 1173 + 1/3
i = 1 1 - (1/4)</span> </span>
Answer: 1173 and 1/3
1.4 because if you do your math it gives you a sum of 1.4
The average rate of change over an interval can be found with the following formula:
The parabola goes through (2, -3) and (3, -1). We want to find the average rate of change over the interval [2,3]. Plug these values into the formula:
The average rate of change will be
2.
Well we know that it grows 8 in a year. so after 1 year has grown 1 * 8 and after 2 years 2 * 8 and after 3 years 3 * 8 and so on. since x is the year we can say 8x. but it starts with 5 ft so we add in the 5 to get h.
h = 8x + 5
