Answer:
a.
lower Quartile= 57.5
Upper Quartile=81
b.
23.5
c.
box-plot is attached in excel file
Step-by-step explanation:
The data is arranged in ascending order so, the lower quartile denoted as Q1 can be calculated as under
Q1=((n+1)/4)th score=(41/4)th score=(10.25)th score
Q1=10th score+0.25(11th-10th)score
Q1=57+0.25(59-57)=57+0.5=57.5
Q1=57.5
The data is arranged in ascending order so, the third quartile denoted as Q3 can be calculated as under
Q3=(3(n+1)/4)th score=(3*41/4)th score=(30.75)th score
Q3=30th score+0.75(31th-30th)score
Q3=81+0.75(81-81)=81+0=81
Q3=81
b)
Interquartile range=IQR=Q3-Q1=81-57.5=23.5
IQR=23.5
c)
The box-plot is made in excel and it shows no outlier. The box-plot shows the 5-number summary(minimum-Q1-median-Q3-maximum) as 25-57.5-72-81-98.
Answer: The maximum revenue is $7482 . To get a maximum yield , The number of trees per acre needed is 43.
Step-by-step explanation:
Solution:
Let x represent the extra tree
So for an additional tree the yield of each tree will decrease by 4 bushels.
(80 +x)(26-4x) by expanding
2080 - 320x +26x -4x^2
Using x= -b/2a
X= 294/ -8
X= - 36.75
So apparently he currently has far too many trees per acre. To get the maximum yield , she needs to reduce the number of trees per acre by 36.75
So the number of trees per acre for maximum yield is
80-36.75
=43.25
Approximately x=43
So by reducing he get extra bushel in the tune of 174.
Total revenue= 174 ×43× 1$
=$7482
If you draw out the polygon with the vertices given, you'll see a trapezoid with one base of 6 units long, one base of 4 units long and a height of 4 units.
Using the formula for area of a trapezoid : h(b1 + b2)/2
h is the height, b is the base
After inputting your numbers into the formula you get, 4(4+6)/2
Which comes out to be 4(10)/2 or 40/2
Which will get you the answer, 20.
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6 units
the answer needs more characters
Step-by-step explanation:
x² + y² + 2x + 6y = 39
( x + 1)² - 1 + ( y + 3)² - 9 = 39
( x + 1)² + ( y + 3)² - 10 = 39
(x + 1)² + (y + 3)² = 49
radius= √49 = 7
center = ( -1 , -3)
x² + y² - 4x - 2y + 1 = 0
(x - 2)² - 4 + (y - 1)² -1 + 1 = 0
(x - 2)² + (y - 1)² = 4
radius = √4 = 2
center = (2 , 1)