find the coordinate of U' after a 90° counterclockwise rotation of the triangle about the origin and then a translation of 2 uni
ts down and 5 units left.
1 answer:
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Answer:
See below.
Step-by-step explanation:
4)
So we have the expression:
We can use the power of a product property, where:
So:
For the left, -6 squared is the same as -6 times -6. This equals positive 36.
For the right, we can use the power of a power property. The property says that:
So:
So, all together, we have:
6)
We have the expression:
First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:
And that's the simplest we can do :)
Notes for 6)
We <em>can</em> put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:
And vice versa:
So, we can write the above as:
However, traditionally, we want only positive exponents, so this wouldn't be correct.
Answer:
Step-by-step explanation:
Assuming this problem: "Ann has 30 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. Bob has 30 jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with mean 52 minutes and standard deviation 15 minutes. Ann's and Bob's times are independent. Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs".
Previous concepts
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
For this case we can create some notation.
Let A the values for Ann we know that n1 = 30 jobs solved in sequence and we can assume that the random variable the time in order to do the ith job for
. We will have the following parameters for A.
W can assume that B represent Bob we know that n2 = 30 jobs solved in sequence and we can assume that the random variable [tex[X_i[/tex] the time in order to do the ith job for . We will have the following parameters for A
And we can find the distribution for the total, if we remember the definition of mean we have:
And
And the
So then we have:
Since we want this probability "Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs" we can express like this:
Since we have independence (condition given by the problem) we can find the parameters for the random variable
And now we can find the probability like this: