Answer:
{1, 2, 3}, {3, 4, 5}
Step-by-step explanation:
Write expressions for three consecutive integers: n, n + 1, n + 2.
Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).
(n + 1)(n + 2) = 7n - 1
Multiply (FOIL) the left side.
n^2 + 3n + 2 = 7n - 1
Subtract 7n and subtract 1 to make the right side 0.
n^2 - 4n + 3 = 0
Factor.
(n - 1)(n - 3) = 0
Set the two factors equal to 0
n - 1 = 0, n - 3 = 0
Solve for n.
n = 1, n = 3
One set of integers begins with 1, so it's {1, 2, 3}.
The other set begins with 3, so it's {3, 4, 5}
Answer: 9 and 10
Step-by-step explanation:
To understand this question we need to first understand how to solve square root equations! The easiest way to learn how to solve square root problems is by finding the reverse of the problem.
For example, if you tried to find the square root of 25, you would reverse the problem to do 5^2 = 5 x 5 = 25.
So if we were to implement this problem, we would look at these two whole numbers.
9^2 = 9 x 9 = 81
10^2 = 10 x 10 = 100
Thus meaning that the only two numbers that the square root of 97 lies between can be 9 and 10!
It's important to rely on your knowledge of multiplication to develop a strong base for square roots.
For large sample confidence intervals about the mean you have:
xBar ± z * sx / sqrt(n)
where xBar is the sample mean z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α sx is the sample standard deviation n is the sample size
We need only to concern ourselves with the error term of the CI, In order to find the sample size needed for a confidence interval of a given size.
z * sx / sqrt(n) = width.
so the z-score for the confidence interval of .98 is the value of z such that 0.01 is in each tail of the distribution. z = 2.326348
The equation we need to solve is:
z * sx / sqrt(n) = width
n = (z * sx / width) ^ 2.
n = ( 2.326348 * 6 / 3 ) ^ 2
n = 21.64758
Since n must be integer valued we need to take the ceiling of this solution.
n = 22
A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is amultiple of both.
you dont use the distributive property
(8x-1)(7x-1)
then you foil it and combine like terms
