Graphs are used to represent real life situations
- Point (1, 0.75) represents 1 cookie costs $0.75
- Point (0,0) represents 0 cookie costs $0
The x and the y coordinates of the graph are used to represent the following variables
- x : The number of cookies
- y : The cost of the number of cookies
This means that:
Point (1, 0.75) represents 1 cookie costs $0.75 and point (0,0) represents 0 cookie costs $0
Read more about graphs and points at:
brainly.com/question/14323743
![\frac{cot^2x -cosec\ x}{cosec^2x} = cos^2x - sin\ x](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%5E2x%20-cosec%5C%20x%7D%7Bcosec%5E2x%7D%20%3D%20cos%5E2x%20-%20sin%5C%20x)
<em><u>Solution:</u></em>
<em><u>Given that we have to prove:</u></em>
![\frac{cot^2x -cosec\ x}{cosec^2x} = cos^2x - sin\ x](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%5E2x%20-cosec%5C%20x%7D%7Bcosec%5E2x%7D%20%3D%20cos%5E2x%20-%20sin%5C%20x)
Take the L.H.S of above
![\frac{cot^2x -cosec\ x}{cosec^2x}](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%5E2x%20-cosec%5C%20x%7D%7Bcosec%5E2x%7D)
Simplify
![\frac{cot^2x}{cosec^2x} -\frac{cosec\ x}{cosec^2x}\\\\Simplify\\\\\frac{cot^2x}{cosec^2x} -\frac{1}{cosec\ x}](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%5E2x%7D%7Bcosec%5E2x%7D%20-%5Cfrac%7Bcosec%5C%20x%7D%7Bcosec%5E2x%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5C%5Cfrac%7Bcot%5E2x%7D%7Bcosec%5E2x%7D%20-%5Cfrac%7B1%7D%7Bcosec%5C%20x%7D)
We know that,
![sin\ x = \frac{1}{cosec\ x}](https://tex.z-dn.net/?f=sin%5C%20x%20%3D%20%5Cfrac%7B1%7D%7Bcosec%5C%20x%7D)
Therefore,
![\frac{cot^2x}{cosec^2x} -sin\ x](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%5E2x%7D%7Bcosec%5E2x%7D%20-sin%5C%20x)
Also we know that,
![cot^2x = \frac{cos^2\ x}{sin^2\ x}](https://tex.z-dn.net/?f=cot%5E2x%20%3D%20%5Cfrac%7Bcos%5E2%5C%20x%7D%7Bsin%5E2%5C%20x%7D)
![cosec^2\ x = \frac{1}{sin^2\ x}](https://tex.z-dn.net/?f=cosec%5E2%5C%20x%20%3D%20%5Cfrac%7B1%7D%7Bsin%5E2%5C%20x%7D)
Thus we get,
![\frac{\frac{cos^2\ x}{sin^2 x}}{\frac{1}{sin^2\ x}} - sin\ x\\\\Simplify\\\\\frac{cos^2\ x}{sin^2 x} \times sin^2\ x - sin x\\\\Simplify\\\\cos^2\ x - sin\ x](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bcos%5E2%5C%20x%7D%7Bsin%5E2%20x%7D%7D%7B%5Cfrac%7B1%7D%7Bsin%5E2%5C%20x%7D%7D%20-%20sin%5C%20x%5C%5C%5C%5CSimplify%5C%5C%5C%5C%5Cfrac%7Bcos%5E2%5C%20x%7D%7Bsin%5E2%20x%7D%20%5Ctimes%20sin%5E2%5C%20x%20-%20sin%20x%5C%5C%5C%5CSimplify%5C%5C%5C%5Ccos%5E2%5C%20x%20-%20sin%5C%20x)
Thus,
L.H.S = R.H.S
Thus proved
Answer:
(0.4958, 0.7422)
Step-by-step explanation:
Let p be the true proportion of water specimens that contain detectable levels of lead. The point estimate for p is
. The estimated standard deviation is given by
. Because we have a large sample, the 90% confidence interval for p is given by
where
is the value that satisfies that above this and under the standard normal density there is an area of 0.05. So, the confidence interval is
, i.e., (0.4958, 0.7422).
Answer:
178 m
Step-by-step explanation:
The area of a square is the square of one of its sides, so the square root of the area is the length of one of its sides.
√31684 = 178
4/12 of the fans are kids because 1/4 can be multaplied by 3 to get 3/12