the product of two consecutive integers is 420. an equation is written in standard form to solve for the smaller integer by fact
2 answers:
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Answer:
Step-by-step explanation:
Hello, please consider the following.
The polynomial function is
The rational root theorem states that each rational solution
, written in irreducible fraction, satisfies the two following:
p is a factor of the constant term
q is a factor of the leading coefficient
In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.
Let's proceed with the prime factorisation of 14:
14 = 2 * 7
Finally, the possible rational roots of this expression are :
1
2
7
14
and we need to test for negative ones too
-1
-2
-7
-14
From your list, the correct answer is 7.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
So the answer for this case would be n=159 rounded up to the nearest integer
Step-by-step explanation:
Assuming this complete question: A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.35 of ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.15 .
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
Since the Confidence is 0.95 or 95%, the value of The margin of error is given by this formula:
(a)
And on this case we have that ME =0.35 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (b) we got:
So the answer for this case would be n=159 rounded up to the nearest integer