Answer:
1) (2x + 2)(x + 2)
2) 2(x + 1)(x - 1)
3) (x^2 + 3)(x^2 - 3)
4) 2x(x + 5)(x - 2)
5) (5x + 2y)(5x - 2y)
Step-by-step explanation:
1)
2x^2 + 6x + 4
= 2x^2 + 4x + 2x + 4
= 2x(x + 2) + 2(x + 2)
= (2x + 2)(x + 2)
2)
2x^2 - 2
= 2(x^ 2 - 1) (The difference of two squares)
= 2(x + 1)(x - 1)
3)
x^4 - 9 (The difference of two squares)
=(x^2 + 3)(x^2 - 3)
4)
2x^3 + 6x^2 - 20x
= 2x(x^2 + 3x - 10)
= 2x(x + 5)(x - 2)
5)
25x^2 - 4y^2 (The difference of two squares)
= (5x + 2y)(5x - 2y)
Answer: If the initial term of an arithmetic sequence is a 1 and the common difference of successive members is d, then the nth term of the sequence is given by: a n = a 1 + (n - 1)d The sum of the first n terms S n of an arithmetic sequence is calculated by the following formula: S n = n (a 1 + a n)/2 = n [2a 1 + (n - 1)d]/2
Answer:
Step-by-step explanation:
Given that a researcher is trying to decide how many people to survey.
We have confidence intervals are intervals with middle value as the mean and on either side margin of error.
Confidence interval = Mean ± Margin of error
Thus confidence interval width depends on margin of error.
Margin of error = 
Thus for the same confidence level and std deviation we find margin of error is inversely proportional to square root of sample size.
Hence for small n we get wide intervals.
So if sample size = 300, the researcher will get wider confidence interval
Answer:
$7
Step-by-step explanation:
overtime = 1/2 x daily hourly rate
daily hourly rate = amount earned in a week / total hours worked
560 /40 = 14
overtime = 14/2 = 7
