Find the number of sides of a regular polygon if one interior angle is 120 degrees
2 answers:
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Step-by-step explanation:
1.) The equation for the line of least squares regression is given by
where Y = Output Variable = Average Cost (in thousands of dollars)
X = Input Variable = Number of years after 2000
Thus, the given data table transforms as follows:
No. of years after 3 4 5 6 7 8 9 10
after 2000 (X)
Average Cost (Y) 15.505 16.510 17.451 18.471 19.363 20.409 21.093 22.092
To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)
Let us take any two random values of X and Y from the above table, so that we have
X₁ = 3; Y₁ = 15.505 and X₂ = 8; Y₂ = 20.409
Plugging in these two sets of values, we get the following two equations:
15.505 = (3)m + c and
20.409 = (8)m + c
Let us subtract the upper one from the lower one so that we have
20.409 - 15.505 = 8m + c - 3m - c
4.904 = 5m
Hence, m = 0.9808
Using this value and plugging it in one of the above equations yields the value of c as
20.409 = 8(0.9808) + c
Therefore, c = 12.563
So, the required equation for the line of least squares regression is
Y = (0.9808)X + 12.563
2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.
We have Y = 0 + 12.563
Thus, the cost of tuition in 2000 was $12,563.
3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have
Y = (0.9808)(20) + 12.563 = 32.179
Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.
4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.
One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.
One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.
Answer:
Step-by-step explanation:
<u>Step 1: Find the true length of each side</u>
We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of , then we get the true length of each side, so we would get
for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation
. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:
AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm
<u>Step 2: Calculate the Height</u>
Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: . So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.
<u>Step 3: Calculate the Area</u>
Lastly, we can calculate the area. The formula is . In this case, the numbers would be
I know this is a lot, so let me know if you have any questions!