Think of factor pairs. She could buy 1 pair for $54, 54 pairs for $1, 2 pairs for $27, 27 pairs for $2, 3 pairs for $18, 18 for $3, 6 pairs for $9, or 9 pairs for $6
A-10B-1
C-4
D-7
E-3
F-6
G-2
H-5
I-9
J-8
Answer:
(-5 -1i)
Step-by-step explanation:
You first add (3 - 8)...(it will be negative 8 because you'll use the sign of the bigger number) you'll get (-5)
Then you'll add 5i + (-6i)...remember you'll use sign of the bigger number so you'll get (-1i)
And all together it will be (-5 -1i)
Hope you understand :)
Answer:
120,000
Step-by-step explanation:
Let's say Rio gets 5x, Kim gets 7x, and Leo gets 3x. In the ratio 5:7:3:1, x = 1
5x + 7x + 3x = total = 15x
3x = 24000
divide both sides by 3 to get x
x = 8000
15x = 8000*15 = 120000
Answer:
a
![f(x)= 100 [x - 0.2050]](https://tex.z-dn.net/?f=f%28x%29%3D%20100%20%5Bx%20-%200.2050%5D)
b
![P(X > 0.2125) = 0.25](https://tex.z-dn.net/?f=P%28X%20%3E%200.2125%29%20%3D%20%200.25%20)
c
![a = 0.2140](https://tex.z-dn.net/?f=a%20%3D%200.2140)
d
Mean ![\mu = 0.21](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%200.21)
Variance
Step-by-step explanation:
From the question we are told that
The thickness of photoresist follows a uniform distribution
So
![X\ \~{}\ U \{ 0.2050 , 0.2150 \}](https://tex.z-dn.net/?f=X%5C%20%20%20%5C~%7B%7D%5C%20U%20%5C%7B%20%200.2050%20%2C%200.2150%20%5C%7D)
Generally the probability density function is mathematically represented as
![F(x) = \left \{ \frac{1}{ 0.2150 - 02050} , 0.2150< x < 0.2150](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%20%5Cleft%20%5C%7B%20%20%5Cfrac%7B1%7D%7B%200.2150%20-%2002050%7D%20%2C%200.2150%3C%20x%20%3C%200.2150)
=> ![F(x) = \left \{ 100 , 0.2150< x < 0.2150](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%20%5Cleft%20%5C%7B%20%20%20100%20%2C%200.2150%3C%20x%20%3C%200.2150)
Generally the cumulative distribution function is
![f(x) = \int\limits^{x}_{- \infty} {F(x)} \, dx](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Cint%5Climits%5E%7Bx%7D_%7B-%20%5Cinfty%7D%20%7BF%28x%29%7D%20%5C%2C%20dx)
Here
means the lower limit which in this case is 02050
So
![f(x) = \int\limits^{x}_{0.2050} {100} \, dx](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Cint%5Climits%5E%7Bx%7D_%7B0.2050%7D%20%7B100%7D%20%5C%2C%20dx)
![f(x) = 100 \int\limits^{x}_{0.2050} {1} \, dx](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20100%20%5Cint%5Climits%5E%7Bx%7D_%7B0.2050%7D%20%7B1%7D%20%5C%2C%20dx)
=> ![f(x)=100 [ x ] | \left \ x} \atop {0.2050}} \right.](https://tex.z-dn.net/?f=%20f%28x%29%3D100%20%5B%20x%20%5D%20%7C%20%5Cleft%20%5C%20x%7D%20%5Catop%20%7B0.2050%7D%7D%20%5Cright.)
=> ![f(x)= 100 [x - 0.2050]](https://tex.z-dn.net/?f=f%28x%29%3D%20100%20%5Bx%20-%200.2050%5D)
Generally the proportion of wafers that exceeds 0.2125 is mathematically represented as
![P(X > 0.2125) = 1 - F(0.2125)](https://tex.z-dn.net/?f=P%28X%20%3E%200.2125%29%20%3D%20%201%20-%20F%280.2125%29)
=> ![P(X > 0.2125) = 1- 100[0.2125 - 0.2050]](https://tex.z-dn.net/?f=P%28X%20%3E%200.2125%29%20%3D%20%201-%20100%5B0.2125%20-%200.2050%5D)
=> ![P(X > 0.2125) = 0.25](https://tex.z-dn.net/?f=P%28X%20%3E%200.2125%29%20%3D%20%200.25%20)
Generally the thickness which is exceeded by 10% of the wafers is mathematically represented as
![P(X > a ) = 0.10](https://tex.z-dn.net/?f=P%28X%20%20%3E%20a%20%29%20%3D%20%200.10)
=> ![1 - F(a) = 0.10](https://tex.z-dn.net/?f=1%20-%20F%28a%29%20%3D%200.10)
=> ![1 -100 (a - 0.2050) = 0.10](https://tex.z-dn.net/?f=1%20-100%20%28a%20-%200.2050%29%20%3D%200.10)
=> ![100(a -0.2050) = 0.90](https://tex.z-dn.net/?f=100%28a%20-0.2050%29%20%3D%20%200.90)
=> ![a - 0.2050 = 0.009](https://tex.z-dn.net/?f=a%20-%200.2050%20%3D%20%200.009)
=> ![a = 0.2140](https://tex.z-dn.net/?f=a%20%3D%200.2140)
Generally the mean is mathematically represented as
![\mu = \frac{ 0.2050 -0.2150 }{2}](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20%5Cfrac%7B%200.2050%20-0.2150%20%7D%7B2%7D)
=> ![\mu = 0.21](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%200.21)
Generally the variance is mathematically represented as
![\sigma ^2 = \frac{1}{12} [0.2150 - 0.2050]^2](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D%20%20%5Cfrac%7B1%7D%7B12%7D%20%5B0.2150%20-%200.2050%5D%5E2)
=>