Answer:
114
Step-by-step explanation:
Given that
THe data that was collected over a 40 years is 112, 98, 139, 142, 120, 110, 114, 123, 137, 114, 92, 140, 109, 133
We need to find out the mode
As we know that
The mode is the value that is highly repeated
So according to the data, 114 would be repeated two times
So this represent the mode of the data
Find the mid point interval for all of the scores and multiply it by it’s respected frequency
10x9
13x29.5
21x49.5
34x69.5
17x89.5
Then add all of the equations together say the answer is x
Then you will go x/94
To get the mean
Answer:
Decrease amount: $1484 Year-end amount: $4116
Step-by-step explanation:
26.5% of 5600 is 1484. We then subtract 1484 from 5600 because that is how the percentage of decrease, which gives us 4116 dollars. This means her year-end account is 4116 dollars, and the decrease amount is 1484 dollars. Hope this helps!
First problem: draw a line segment through the vertex R and a point C on PQ such that the segment is perpendicular to PQ, thus forming an altitude of the triangle. This new segment CR, the new segment CP, and PR form a 30-60-90 right triangle, where the measure of angle PCR is 90 degrees. CR then occurs with PR in a ratio of
![\sqrt3](https://tex.z-dn.net/?f=%5Csqrt3)
to 2, so
![\dfrac{CR}{PR}=\dfrac{CR}5=\dfrac{\sqrt3}2\implies CR=\dfrac{5\sqrt3}2](https://tex.z-dn.net/?f=%5Cdfrac%7BCR%7D%7BPR%7D%3D%5Cdfrac%7BCR%7D5%3D%5Cdfrac%7B%5Csqrt3%7D2%5Cimplies%20CR%3D%5Cdfrac%7B5%5Csqrt3%7D2)
and this can be considered the height of a triangle whose base is PQ. The area is then
![\dfrac12\cdot6\cdot\dfrac{5\sqrt3}2=\dfrac{15\sqrt3}2\approx13](https://tex.z-dn.net/?f=%5Cdfrac12%5Ccdot6%5Ccdot%5Cdfrac%7B5%5Csqrt3%7D2%3D%5Cdfrac%7B15%5Csqrt3%7D2%5Capprox13)
Second problem: the sum of the interior angles of any triangle is 180, so the measure of the missing angle must be 180 - 20 - 35 = 125 degrees. By the law of sines, the length of the missing side (call it
![x](https://tex.z-dn.net/?f=x)
) satisfies
![\dfrac{\sin20^\circ}9=\dfrac{\sin125^\circ}x\implies x\approx21.56](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin20%5E%5Ccirc%7D9%3D%5Cdfrac%7B%5Csin125%5E%5Ccirc%7Dx%5Cimplies%20x%5Capprox21.56)
Use Heron's formula to find the area of the triangle:
![A=\sqrt{s(s-a)(s-b)(s-c)}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D)
where
![A](https://tex.z-dn.net/?f=A)
is the area,
![a,b,c](https://tex.z-dn.net/?f=a%2Cb%2Cc)
are the lengths of the sides, and
![s=\dfrac{a+b+c}2](https://tex.z-dn.net/?f=s%3D%5Cdfrac%7Ba%2Bb%2Bc%7D2)
is the half the perimeter of the triangle. Then the area is about
![A\approx54.62](https://tex.z-dn.net/?f=A%5Capprox54.62)
square feet. Convert to square yards:
![54.62\text{ ft}^2\cdot\left(\dfrac{1\text{ yd}}{3\text{ ft}}\right)^2\approx6.07\text{ yd}^2](https://tex.z-dn.net/?f=54.62%5Ctext%7B%20ft%7D%5E2%5Ccdot%5Cleft%28%5Cdfrac%7B1%5Ctext%7B%20yd%7D%7D%7B3%5Ctext%7B%20ft%7D%7D%5Cright%29%5E2%5Capprox6.07%5Ctext%7B%20yd%7D%5E2)
then round up to 7 square yards. At a price of $12.50 per square yard, the total price will be $87.50.