An unbiased six-sided die is to be rolled five times. Suppose all these trials are independent. Let $E_1$ be the number of times the die shows a 1, 2 or 3. Let $E_2$ be the number of times the die shows a 4 or a 5. Find $P(E_1 = 2, E_2 = 1)$.
I have tried to solve this question this way:
To...
@LeakyNun Oh ok. In this instance, a variable is defined as a 'symbol which can be given different values, and it represented by letters.' This is for grade 8 so they're just learning about variables and constants for the first time.
Hi! I came across an instance where the combination of a variable and a constant (e.g. 5+$x$) is also called a variable. I've never heard of the combination being called a variable before. While 5+$x$ will vary depending on the value of $x$, is it correct to call it a variable?
@TobiasKildetoft Perhaps. But, I'm making this assumption because the problem is assigned to young students who haven't studied the concept of a slope, much less anything beyond real numbers.
Yeah that's true. But regarding the idea of $x$ being a multiple of $2$, why can't we figure out the domain without it? Considering that the domain of $f$ where $f=x/2$ is the set of all real numbers, stating that $x$ is between $4$ and $12$ should mean that the domain is between $4$ and $12$ too, no? @TobiasKildetoft
@TedShifrin Yes. If we take it from the positive side though, it comes out to be $4\pi/3$ and then after taking the square root, $2\pi/3$. In theory, shouldn't this work too?
@TedShifrin I worked my way from inside and got $r=2$ and $\theta=-\pi/3$. But since it didn't fit in with the position of $-2-i 2\sqrt3$ so I took $\theta=4\pi/6$ and my final answer is incorrect due to this. I took half the angle but after assuming that $-2-i 2\sqrt3$ was in the third quadrant. So should I just stick with $\theta=-\pi/3$ even though it doesn't match up with the quadrant before i take the square root of the complex number?
@TedShifrin Does that mean that nth root has something to do with the quadrants? And why would the square root of a number be in the second or fourth quadrant?
@TedShifrin ok. I know that it's simple enough but I don't get why wolframalpha gives this position in the complex plane for z. Since x and y are both negative, shouldn't it be in the third quadrant?
Hi, I'm studying about the bisection method for the first time. If we approach a problem with this method, how do we select the tolerance? Any help would be appreciated, thanks.
Can anyone please clarify something in this question? Given vector $A= (2,-1,-1)$ and vector $C=(0,1,1)$, $C$ rotates about $A$ with an angular velocity of 2 rad/s . Find the velocity of the head of $C$. As velocity is the cross product of angular velocity $w$ and $r$ and $w$ is in the direction of $A$, so the velocity should be a cross product of $A$ and $C$? If so, where does the angular velocity 2 rad/s fit in?
@Sie your initial columns for p and q are correct, just not the implication one. If you have F,F,T,T for p and T,T,F,F for q, then you'll be repeating two rows and your truth table will be incomplete
Can anyone please clarify something in this question? Given vector $A= (2,-1,-1)$ and vector $C=(0,1,1)$, $C$ rotates about $A$ with an angular velocity of 2 rad/s . Find the velocity of the head of $C$. As velocity is the cross product of angular velocity $w$ and $r$ and $w$ is in the direction of $A$, so the velocity should be a cross product of $A$ and $C$? If so, where does the angular velocity 2 rad/s fit in?
An unbiased six-sided die is to be rolled five times. Suppose all these trials are independent. Let $E_1$ be the number of times the die shows a 1, 2 or 3. Let $E_2$ be the number of times the die shows a 4 or a 5. Find $P(E_1 = 2, E_2 = 1)$.
I have tried to solve this question this way:
To...
