Answer:
1. X^2+1/2x = 
2. X^2+2x-3 = 
3. (2x-3)^2 = (2x-3)(2x-3)
4. X^3+2x^2-19x-20 = 
Step-by-step explanation:
Each expression can be written as a product of linear factors as follows
1. X^2+1/2x ⇒ 
=
Hence, X^2+1/2x =
2. X^2+2x-3 ⇒ 
Hence, X^2+2x-3 =
3. (2x-3)^2 ⇒
Hence, (2x-3)^2 = (2x-3)(2x-3)
4. X^3+2x^2-19x-20 ⇒ 
First,
∴ 
Hence, X^3+2x^2-19x-20 =
We are given the following variables:
μ = the sample mean = 152 pounds
σ = the standard deviation = 26 pounds
x = the sample value we want to test = 180 pounds
n = the sample size = unknown
MOE = margin of error = 4% = 0.04
Confidence level = 96%
The first thing we can do is to find for the value of z
using the formula:
z = (x – μ) / σ
z = (180 – 152) / 26
z = 1.0769 = 1.08
Since we are looking for the people who weigh more than
180 pounds, therefore this is a right tailed z test. The p value is:
p = 0.1401
Then we can use the formula below to solve for n:
n = z^2 * p * (1 – p) / (MOE)^2
n = 1.08^2 * 0.1401 * (1 – 0.1401) / (0.04)^2
n = 87.82 = 88
Therefore around 88 people must be surveyed.
1. Find the "opposite side," if the angle is 60 degrees and the hyp is 6:
opp opp sqrt(3)
sin 60 deg = ------- = -------- = ----------
hyp 6 2
Cross-multiplying, 2(opp) = 6sqrt(3), so that opp = 3 sqrt(3) (answer)
2. Use the Pyth. Thm. to find the "adjacent side:"
[3sqrt(3)]^2 + x^2 = 6^2, or 9(3) + x^2 = 36, or x^2 = 9, or x = 3.
The lengths of the legs of this 30-60-90 triangle are 3 and 3 sqrt(3).
check: Does 3^2 + [3sqrt(3)]^2 = 6^2?
Does 9 + 9(3) = 6^2? YES
You can add these fractions to get 9/12 - 2/12 ( 7/12 )
3/12 + 4/12
1/12 + 6/12
2/12 + 5/12
