Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
- a² = b² +c² -2bc·cos(A)
- k² = 31² +53² -2·31·53·cos(37°)
<h3>Comparison</h3>
Comparing the two equations, we note these correspondences:
Comparing these values to the given information, we see that ...
- KN = c = 53 . . . . . . . . . . matching values 53
- NM = a = k . . . . . . . . . . . matching values k
- KM = b = n = 31 . . . . . . . matching values 31
- ∠K = ∠A = 37° . . . . . . . matching side/angle names
Abby apparently knew that ∠K = 37° and n = 31.
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<em>Additional comment</em>
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
This is the anwser to your equation
Answer: Third quartile =$21.58
Step-by-step explanation:
Let x be value of a stock .
For uniform distribution,
probability density function = 
Let a be the stock value such that P(x<a) =75% or 0.75
![\Rightarrow\ \int ^{a}_{10.82}f(x)\ dx=0.75\\\\\Rightarrow\ \int ^{a}_{10.82}\dfrac{100}{1435}\ dx=0.75\\\\\Rightarrow\dfrac{100}{1435}[x]^{a}_{10.82}=0.75\\\\\Rightarrow \dfrac{100}{1435}(a-10.82)=0.75\\\\\Rightarrow a-10.82=0.75\times\dfrac{1435}{100}\\\\\Rightarrow a-10.82=10.7625\\\\\Rightarrow a= 10.7625+10.82= $$21.5825\approx $$21.58](https://tex.z-dn.net/?f=%5CRightarrow%5C%20%5Cint%20%5E%7Ba%7D_%7B10.82%7Df%28x%29%5C%20dx%3D0.75%5C%5C%5C%5C%5CRightarrow%5C%20%5Cint%20%5E%7Ba%7D_%7B10.82%7D%5Cdfrac%7B100%7D%7B1435%7D%5C%20dx%3D0.75%5C%5C%5C%5C%5CRightarrow%5Cdfrac%7B100%7D%7B1435%7D%5Bx%5D%5E%7Ba%7D_%7B10.82%7D%3D0.75%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B100%7D%7B1435%7D%28a-10.82%29%3D0.75%5C%5C%5C%5C%5CRightarrow%20a-10.82%3D0.75%5Ctimes%5Cdfrac%7B1435%7D%7B100%7D%5C%5C%5C%5C%5CRightarrow%20a-10.82%3D10.7625%5C%5C%5C%5C%5CRightarrow%20a%3D%2010.7625%2B10.82%3D%09%24%2421.5825%5Capprox%09%24%2421.58)
Hence, 75% of all days the stock is below $21.58 or Third quartile =$21.58 .
Answer:
f⁻¹(x) = (x - 1)/8
Or
f⁻¹(x) = 1/8 x - 1/8
Step-by-step explanation:
To find the inverse of a function, switch the "x" and "y" variables, then isolate "y".
Remember <u>"f(x)" is the same thing as "y"</u>. Change from function notation to "y".
f(x) = 8x + 1
y = 8x + 1
<u>Switch the "x" and "y" variables</u>
x = 8y + 1
<u>Isolate "y"</u>. Move the "y" variable to the left for standard formatting
8y + 1 = x
8y + 1 - 1 = x - 1 Subtract 1 from both sides
8y = x - 1
Divide both sides by 8 and simplify
Inverse equation
Slope-intercept form
<u>Use function notation</u>, change "y"
Simplified
Slope-intercept form
Probability works by showing the outcome of a chance. For example , there are 2 yellow balls and 3 red balls . the outcome of drawing a yellow ball is 2/5 20% out of 50%
