We will begin by grouping the x terms together and the y terms together so we can complete the square and see what we're looking at. 
. Now we need to move that 36 over by adding to isolate the x and y terms. 
. Now we need to complete the square on the x terms and the y terms. Can't do that, though, til the leading coefficients on the squared terms are 1's. Right now they are 9 and 4. Factor them out: 
. Now let's complete the square on the x's. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so add it into the parenthesis. BUT don't forget about the 9 hanging around out front there that refuses to be forgotten. It is a multiplier. So we are really adding in is 9*4 which is 36. Half the linear term on the y's is 3. 3 squared is 9, but again, what we are really adding in is -4*9 which is -36. Putting that altogether looks like this thus far: 
. The right side simplifies of course to just 36. Since we have a minus sign between those x and y terms, this is a hyperbola. The hyperbola has to be set to equal 1. So we divide by 36. At the same time we will form the perfect square binomials we created for this very purpose on the left: 
. Since the 9 is the bigger of the 2 values there, and it is under the y terms, our hyperbola has a horizontal transverse axis. a^2=4 so a=2; b^2=9 so b=3. Our asymptotes have the formula for the slope of 
which for us is a slope of negative and positive 3/2. Using the slope and the fact that we now know the center of the hyperbola to be (2, 3), we can solve for b and rewrite the equations of the asymptotes. 
give us a b of 0 so that equation is y = 3/2x. For the negative slope, we have 
which gives us a b value of 6. That equation then is y = -3/2x + 6. And there you go!
Lesson Check (6.NS.C.7a) 1. Andrea has 37 yards of purple ribbon, 3.7 yards of pink ribbon, and 3$ yards of blue ribbon. List th
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Using the z-distribution, it is found that the lower limit of the 95% confidence interval is of $99,002.
<h3>What is a z-distribution confidence interval?</h3>The confidence interval is:
In which:
is the sample mean.
- z is the critical value.
- n is the sample size.
is the standard deviation for the population.
In this problem, we have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
The other parameters are given as follows:
Hence, the lower bound of the interval is:
The lower limit of the 95% confidence interval is of $99,002.
More can be learned about the z-distribution at brainly.com/question/25890103
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Answer:
The value of a is "3", to complete the coordinate point (3,7) on the line.
Step-by-step explanation:
We are given the slope of the line, and also one point through which the line passes. Therefore, we can find the actual equation of the line by using the slope-point form of the line:
Now, we need to find which value of "x" renders a y-value of "7", to complete the coordinate pair (a, 7) as requested. Therefore, we ask for the y-value in the previous equation to be "7", and solve for its associated x-value:
Therefore, x = 3
Answer:
And using the normal standard distribution or excel we got:
Step-by-step explanation:
Previous concepts
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".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where and
Since the dsitribution for x is normal then we know that the distribution for the sample mean is given by:
We want to find this probability:
And we can use the z score formula given by;
And if we find the z score for the limits given we got:
So we can calculate this probability like this:
And using the normal standard distribution or excel we got: