Answer:
The coordinates are
A(-4,-3) →A'(-1, -1)
B(-1, 1) → B'(2, 3)
C(3, 5) → C'(6, 7)
D(2,-5) → D'(5,-3)
Step-by-step explanation:
Given the graph of figure whose coordinates are
A(-4, -3), B(-1, 1), C(3, 5), D(2, -5)
We have to find the coordinates of the image after a translation using T(x, y) → (x + 3, y + 2).
Coordinates after translation are
A(-4,-3) → A'(-4+3, -3+2)=A'(-1, -1)
B(-1, 1) → B'(-1+3, 1+2)=B'(2, 3)
C(3, 5) → C'(3+3, 5+2)=C'(6, 7)
D(2,-5) → D'(2+3, -5+2)=D'(5,-3)
which are required coordinates of the image after a translation of the figure below using (x, y) → (x + 3, y + 2).
Answer:
20 gallons of water is leaked after an hour.
Step-by-step explanation:
Water is leaking at a constant rate of 1/3 gallon per minute.
a) We have to write a linear equation in two variables that show the amount of water, w, in gallons, that is leaked from the faucet after t minutes.
So, the equation is ......... (1) (Answer)
b) Now, if t = 1 hour i.e. 60 minutes, then from equation (1) we can write
gallons.
Therefore, 20 gallons of water is leaked after an hour. (Answer)
Answer:
a)
b)
c)
Step-by-step explanation:
Data given: 126,111,141,96,123,115,116,113,127,114,122,116,104,126,126,132,139,111,143,121,119,107,154,125,120,135,142,132,94,103,143,115,132,107,118,105,101,135,94,153
Part a
For this case we can calculate the sample mean with the following formula:
And after replace we got:
Part b
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
For this case we assume that the population deviation is , we can calculate the standard error with this formula:
Part c
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that
Now we have everything in order to replace into formula (1):
Ok, so I worked out the problem.
So for part a) you just multiply 8 by 25% then add the product to get the new perimeter.
Part B you Add all sides for the original square and the new square to get the perimeters of each then you divide the old square perimeter by the new square perimeter to get the percentage.
Part C you get the areas pf bother squares then divide the old square area by the new square area to get the percentage change.
If you have any questions, let me know.
