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.
Answer:
Number of heavy equipment operators hired were 22
Number of general laborers hired were 11
Explanation:
Assume that number of heavy equipment operators hired is x and that number of general laborers is y.
We are given that:
1- Total number of hired people is 33. This means that:
x + y = 33
This can be rewritten as:
x = 33 - y ...........> equation I
2- heavy equipment operators are paid $135, general laborers are paid $89 and that the total payment was $3949. This means that:
135x + 89y = 3949 ............> equation II
Substitute with equation I in equation II and solve for y as follows:
135x + 89y = 3949
135(33-y) + 89y = 3949
4455 - 135y + 89y = 3949
506 = 46y
y = 506 / 46
y = 11
Substitute with y in equation I to get the value of x as follows:
x = 33 - y
x = 33 - 11
x = 22
Hope this helps :)
Answer: he collected 22 quarters and 8 fifty-cent pieces
Step-by-step explanation:
Given;
The total amount of money he is to collect is;
A = 20 - 10.50 = $9.50
Let x represent the number of quarter he collected.
Then the number of fifty-cent pieces he collected will be; 30-x
Therefore we can represent it with the equation below;
0.25x + 0.50(30-x) = 9.50
0.25x + 15 - 0.50x = 9.50
0.25x = 15-9.50
x = (15-9.50)/0.25
x = 5.50/0.25
x = 22
The number of fifty-cent is equal to;
30-x = 30-22 = 8
Therefore, he collected 22 quarters and 8 fifty-cent pieces
