Answer:
You end up getting the same equation!
Step-by-step explanation:
Answer:
![- 3x - 4y ^{2}](https://tex.z-dn.net/?f=%20-%203x%20-%204y%20%5E%7B2%7D%20)
Step-by-step explanation:
![- 3 - 2 ^{2} y ^{2}](https://tex.z-dn.net/?f=%20-%203%20-%202%20%5E%7B2%7D%20y%20%5E%7B2%7D%20)
![- 3x - 4y ^{2}](https://tex.z-dn.net/?f=%20-%203x%20-%204y%20%5E%7B2%7D%20)
These are just a few of the things you will learn in 6th grade. You will learn how to write a two- variable equation, how to identify the graph of an equation, graphing two-variable equations. how to interpret a graph and a word problem, and how to write an equation from a graph using a table, two-dimensional figures,Identify and classify polygons, Measure and classify angles,Estimate angle measurements, Classify triangles, Identify trapezoids, Classify quadrilaterals, Graph triangles and quadrilaterals, Find missing angles in triangles, and a lot more subjects. <span><span><span>Find missing angles in quadrilaterals
</span><span>Sums of angles in polygons
</span><span>Lines, line segments, and rays
</span><span>Name angles
</span><span>Complementary and supplementary angles
</span><span>Transversal of parallel lines
</span><span>Find lengths and measures of bisected line segments and angles
</span><span>Parts of a circle
</span><span>Central angles of circles</span></span>Symmetry and transformations
<span><span>Symmetry
</span><span>Reflection, rotation, and translation
</span><span>Translations: graph the image
</span><span>Reflections: graph the image
</span><span>Rotations: graph the image
</span><span>Similar and congruent figures
</span><span>Find side lengths of similar figures</span></span>Three-dimensional figures
<span><span>Identify polyhedra
</span><span>Which figure is being described
</span><span>Nets of three-dimensional figures
</span><span>Front, side, and top view</span></span>Geometric measurement
<span><span>Perimeter
</span><span>Area of rectangles and squares
</span><span>Area of triangles
</span><span>Area of parallelograms and trapezoids
</span><span>Area of quadrilaterals
</span><span>Area of compound figures
</span><span>Area between two rectangles
</span><span>Area between two triangles
</span><span>Rectangles: relationship between perimeter and area
</span><span>compare area and perimeter of two figures
</span><span>Circles: calculate area, circumference, radius, and diameter
</span><span>Circles: word problems
</span><span>Area between two circles
</span><span>Volume of cubes and rectangular prisms
</span><span>Surface area of cubes and rectangular prisms
</span><span>Volume and surface area of triangular prisms
</span><span>Volume and surface area of cylinders
</span><span>Relate volume and surface area
</span><span>Semicircles: calculate area, perimeter, radius, and diameter
</span><span>Quarter circles: calculate area, perimeter, and radius
</span><span>Area of compound figures with triangles, semicircles, and quarter circles</span></span>Data and graphs
<span><span>Interpret pictographs
</span><span>Create pictographs
</span><span>Interpret line plots
</span><span>Create line plots
</span><span>Create and interpret line plots with fractions
</span><span>Create frequency tables
</span><span>Interpret bar graphs
</span><span>Create bar graphs
</span><span>Interpret double bar graphs</span><span>
</span></span><span>
</span></span>
Answer:
0.14% probability that the sample proportion exceeds 0.2
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
![E(X) = np](https://tex.z-dn.net/?f=E%28X%29%20%3D%20np)
The standard deviation of the binomial distribution is:
![\sqrt{V(X)} = \sqrt{np(1-p)}](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D)
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that
,
.
In this problem, we have that:
![n = 108, p = 0.11](https://tex.z-dn.net/?f=n%20%3D%20108%2C%20p%20%3D%200.11)
So
![\mu = E(X) = np = 108*0.11 = 11.88](https://tex.z-dn.net/?f=%5Cmu%20%3D%20E%28X%29%20%3D%20np%20%3D%20108%2A0.11%20%3D%2011.88)
![\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{108*0.11*0.89} = 3.2516](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D%20%3D%20%5Csqrt%7B108%2A0.11%2A0.89%7D%20%3D%203.2516)
What is the probability that the sample proportion exceeds 0.2
This is 1 subtracted by the pvalue of Z when X = 0.2*108 = 21.6. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{21.6 - 11.8}{3.2516}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B21.6%20-%2011.8%7D%7B3.2516%7D)
![Z = 2.99](https://tex.z-dn.net/?f=Z%20%3D%202.99)
has a pvalue of 0.9986
1 - 0.9986 = 0.0014
0.14% probability that the sample proportion exceeds 0.2
The sum exterior angles of a square are:
4*90=360°