Given:
The expressions are


To find:
The simplified form of each expression.
Solution:
We have,

![[\because x^{-n}=\dfrac{1}{x^n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20x%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Bx%5En%7D%5D)

Therefore, the simplified form of
is
.
We have,

![[\because x^{-n}=\dfrac{1}{x^n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20x%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Bx%5En%7D%5D)


Therefore, the simplified form of
is
.
The Confidence interval for 95% who believes that the local businesses overcharge = (0.7026, 0.7574)
<h3>
What is meant by confidence interval?</h3>
The range of values we see in our sample and hope to identify the value that most closely represents the population are referred to as a confidence interval.
<h3>According to the given information:</h3>
Sample size n = 1000
73% of town residents believed that local businesses overcharged for their products over 1000 resident.
= (1000/100) x 73
= 730
Sample proportion p = 730/1000
= .73
q = 1-p = 0.23
Std error of proportion = √(pq/n)
= √((.73*0.27)/1000)
= 0.0140
95% Z critical value = 1.96
Margin of error = 1.96*0.0140
= 0.0274
Confidence interval = sample proportion ±margin of error
(0.7026, 0.7574)
To know more About Confidence interval visit:
brainly.com/question/14018374
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Answer:
∠B ≈ 30.0°
Step-by-step explanation:
The law of sines can be used to solve a triangle when two sides and an angle opposite one of them are given.
__
sin(B)/b = sin(C)/c
sin(B) = (b/c)sin(C) . . . . solve for sin(B)
sin(B) = (14/28)sin(91°) ≈ 0.49992385
The angle is found using the inverse sine function:
B = arcsin(0.49992384) ≈ 29.99496°
Rounded to tenths, the angle is ...
m∠B ≈ 30.0°
_____
<em>Additional comments</em>
Many triangle solver apps and web sites are available if all you want is an answer.
When using your calculator, be sure the angle mode is set to "degrees."
The Law of Sines can also be used to solve a triangle when two angles and one side are known.
Answer:
16x -2
Step-by-step explanation:
You know how to compute the perimeter of a rectangle of length L and width W:
P = 2(L+W)
Here, you're asked to use the given algebraic expressions for length and width and simplify the result of putting those in the perimeter formula.
P = 2((5x-2) +(3x+1))
P = 2(8x -1)
P = 16x -2 . . . the perimeter of the rectangle
The answer should be 1 and three