let's firstly convert the mixed fraction to improper fraction, and then divide it by 4 to see what our quotient is.
![\bf \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div 4\implies \cfrac{9}{4}\div \cfrac{4}{1}\implies \cfrac{9}{4}\cdot \cfrac{1}{4}\implies \cfrac{9}{16}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B9%7D%7B4%7D%5Cdiv%204%5Cimplies%20%5Ccfrac%7B9%7D%7B4%7D%5Cdiv%20%5Ccfrac%7B4%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B9%7D%7B4%7D%5Ccdot%20%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B9%7D%7B16%7D)
Answer:
the probability the rock has raritanium is 0.9670
Step-by-step explanation:
These events have been defined as
Z: sample has raritanium
Y: the reading from detector is positive
Z': sample has no raritanium
Y': Reading from detector is negative
P(z) = 0.13
P(y'/z) = 0.02
P(y/z')= 0.005
We need to find p(z/y)
= p(z/y) = p(z ∩ y)/p(y)
= P(z) - p(z∩y)/0.13 = 0.02
Remember the value of p(z) = 0.13
So when we cross multiply we get
0.13 - p(z ∩ y) = 0.02 x 0.13
0.13 - p(z ∩ y) = 0.0026
-p(z ∩ y) = 0.0026 - 0.13
Such that
p(z ∩ y) = 0.1274
P(y/z')= 0.005
P(z∩y') = 0.005
Since p(z) = 0.13
P(z') = 1-0.13
P(y) - p(z∩y)/0.87 = 0.005
We cross multiply
P(y) - 0.1274 = 0.005x0.87
P(y) = 0.1274+0.00435
P(y) = 0.13175
We have 0.1274/0.13175
= 0.9670
So we conclude that probability rock has raritanium is 0.9670
Answer:
v=37 degrees; u=53 degrees
The formula to finding a discriminant would be b^2-4ac, the b value of this trinomial being -5, the a value being 2, the c value being 3. Then, you plug the values in the equation and solve: (-5)^2-4(2)(3)
This would simplify to 1, meaning there are two solutions since the discriminant value is positive. If it is 0, there is one solution, if it is negative, then there are no real solutions.
67+74=141
180-141=39
Your answer is 39
