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3d ago

What I just read sequitur ...
1. Sometimes a simple random sample may not be representative (?)
So different techniques are required
2. Stratified random sample. Say a school has juniors and seniors and we want both these groups represented in our study. So we take random samples from both groups.
2. Cluster sampling. Say in the same school there are some clubs that have juniors and seniors in numbers that reflect those in the population. We randomly select some of these...
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4d ago

Do you know if [math]\mathbf{k}\cdot\nabla\times(\mathbf{a}\cdot\nabla\mathbf{a})[/math] can be rewritten?
If so, which rules are applied?
EDIT: The term seems to equal [math](\mathbf{a}\cdot\nabla\mathbf{k}\cdot\nabla\times\mathbf{a}) + (\mathbf{k}\cdot\nabla\times\mathbf{a}\nabla\cdot\mathbf{a})[/math] Can that be true ..read more

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5d ago

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5d ago

here is the question
How to find the voltage across the capacitor?
my attemp
\(\displaystyle v = iR\) this voltage across resistor
\(\displaystyle v = L\frac{di}{dt}\) this voltage across conductor
\(\displaystyle i = C\frac{dv}{dt}\) the problem for capacitor it give derivative of voltage
i need a way to get the current in term of time to be able to solve the differential equation
\(\displaystyle \int i \ dt = C\int dv\)
\(\displaystyle v = \frac{1}{C}\int i \ dt\)
i'm stuck here ..read more

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5d ago

Suppose a, b, c, and d are integers with the property that 2a + 4b + 3c + d is a multiple of 5. Prove that a + 2b + 4c + 3d is a multiple of 5. [Note: Your proof must work for all integers a, b, c, and d, not just one or several specific choices of these values.]
I'm not sure how I can get started on this problem.
If 2a + 4b + 3c + d is a multiple of 5, we can have 2a + 4b + 3c + d = 5k where k is an integer
For a + 2b + 4c + 3d can I assume it is a multiple of 5 and then try to prove...
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1w ago

Hi. I have the following scenario.
I have 10 machines which we maintain for a customer. Each machine lasts 10 years, and each one requires 2 overhauls, roughly every 4 years, the timing of which depends on level of use, operation, condition etc. Each overhaul takes around 100 days. Assume an infinite capacity i.e. there's no limit to the amount of machines that can be overhauled at once.
When a machine is sent for overhaul, the customer needs a spare machine to cover for when the original...
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1w ago

I'm probably missing the definition of this, but I can't seem to find it anywhere in the book. Can someone please explain the notation [imath]P(C|A, B)[/imath]? I'm familiar with [imath]P(B|A)[/imath] notation (Probability of A given that B has occurred), but I don't understand the first notation. Is it Probability of C given (A and B), Probability of C given A and the B means something else? Thanks in advance ..read more

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1w ago

We have the set of naturals [imath]\mathbb{N}[/imath]
We have the set of rationals [imath]\mathbb{Q}[/imath]
We have the set of irrationals [imath]\mathbb{Q'}[/imath]
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We have the set of rational approximations of irrationals [imath]_\text{a} \mathbb{Q'}[/imath]
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The set [imath]\mathbb{Q'}[/imath] is in bijection with the set [imath]_\text{a} \mathbb{Q'}[/imath] (every irrational has its own rational approximation)
That is to say [imath]|\mathbb{Q'}| = |_\text{a} \mathbb{Q'}|[/imath] ... (A)
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[imath]_\text{a} \mathbb{Q'} \subseteq...[/imath]
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1w ago

Hello, is there anyone who can help me solve this question? All little tips are welcome. thank you!
At a party, there isn't a single boy who has danced with every girl, but every girl has
danced with at least 1 boy. Show that there are at least 2 couples Boy-Girl and Boy2-Girl2 who have danced, so that Boy does not dance with Girl2
and Boy2 did not dance with Girl ..read more

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1w ago

Well... Although my program prerequisite didn't have a single differential question, it turns out my studies uses some and doesn't teach about it (it teaches what I assume is what a student knowing about differential would need to learn).
is how I passed my program prerequisite, so I intend to study that way. Which would be the most efficient path to learn differential? If there's a path that would take **a little** longer, how longer do you think it would be and how longer on...
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