Answer:
(a) 1/4
(b) answer in explanation
Step-by-step explanation:
In this question, we are told that we have a spinner and the spinner has 12 equal sized sections with three of the sections purple in color. We are now asked to calculate the probability of the spinner landing on the color purple.
Checking, we can see that this is a probability question. The spinner has the options of stopping at 12 different positions but amongst these 12 positions, 3 of the positions are painted purple. We now need to know the probability of the spinner landing on purple.
To get the probability of this, what we simply do is to divide the number of purple options by the total number of outcomes we have. The number of purple options is 3 while the total outcome we have is 12. The probability is thus P(of purple is) = 3/12 = 1/4
(b) we are asked to use words to describe the probability
From the probability in the question, what we can see is that if the spinner is spinner 4 different times, there is a chance that 1 out of all the chances will produce a result where we have the spinner landing on one of the purple color section.
What this actually means is that there is a 25% chance within every spin for the spin to land in the purple color section of the spinner
Answer:
Waves superimpose upon each other when they collide, while objects do not
Step-by-step explanation:
The main difference between the collision of waves and the collision of objects is simply the superposition principle.
When waves collide, they do not do so in the same way objects do. The superposition principle explains that waves can either collide in a constructive or destructive manner.
Case A: Waves colliding in a constructive manner
When waves collide in a constructive manner, this means that they are in phase, in simpler terms, it means that they have the same shape as they move through space-time. Constructive collision leads to a formation of a bigger wave with a higher amplitude. This is how stereo speakers operate. They produce louder sounds by releasing the same audio waves, causing them to superimpose upon each other.
Case B: Waves colliding in a destructive manner:
When waves are out of phase(i.e do not have the same shape as they move through space-time) and they collide, they try to cancel each other out, leading to a new wave with a weaker amplitude. This is how noise-cancelling headphones work. They emit an equal and opposite wave sound to the noise around your ears, thus cancelling it out.
Answer:
Cardiac output:
Step-by-step explanation:
Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.
To Find : Find the cardiac output.
Solution:
Formula of cardiac output:
---1
A = 3 mg
Do, integration by parts
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B20t%5Cint%7Be%5E%7B-0.6t%7D%20%5C%2Cdt%7D-%5Cint%5B%5Cfrac%7Bd%5B20t%5D%7D%7Bdt%7D%5Cint%20%7Be%5E%7B-0.6t%7D%20%5C%2C%20dt%5Ddt%5D%5E%7B10%7D_0)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-20te%5E%7B-0.6t%7D%7D%7B0.6%7D%2B%5Cfrac%7B20%7D%7B0.6%7D%5Cint%20%7Be%5E%7B-0.6t%7D%20%5C%2Cdt%5D%5E%7B10%7D_0)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-20te%5E%7B-0.6t%7D%7D%7B0.6%7D%2B%5Cfrac%7B20e%5E%7B-0.6t%7D%7D%7B%280.6%29%5E2%7D%5D%5E%7B10%7D_%7B0%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-200e%5E%7B-6%7D%7D%7B0.6%7D%2B%5Cfrac%7B20e%5E%7B-6%7D%7D%7B%280.6%29%5E2%7D%5D%2B%5Cfrac%7B20%7D%7B%280.60%5E2%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5Cfrac%7B20%281-e%5E%7B-6%7D%7D%7B%280.6%29%5E2%7D-%5Cfrac%7B200e%5E%7B-6%7D%7D%7B0.6%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%5Csim%20%7B54.49%7D)
Substitute the value in 1
Cardiac output:
Cardiac output:
Hence Cardiac output:
Answer: 
Step-by-step explanation:
