Answer:
a. 0.38%
b. 266.75 days
Step-by-step explanation:
We have the following data, mean (m) 269 and standard deviation (sd) 15, therefore:
a. The first thing is to calculate the number z:
z (x) = (x - m) / sd
z (309) = (309-269) / 15 = 2.67
When looking in the normal distribution table (attached), we have that at this value of z, the probability is:
P (z> 2.67), that is to say we must look in the table -2.67 and this value corresponds to 0.0038, that is to say 0.38%
b. Find the z-value with a left tail of 44%, i.e. 0.44. We look in the table for this value and what value of z corresponds.
invNorm (0.44) = -0.15
Find the corresponding number of days:
x = z * sd + m
we replace
d = -0.15 * 15 + 269 = 266.75 days
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
Answer:
(0,1)
Step-by-step explanation:
The mid point of A(-2,2) and B(2,-4) is the coordinates of point P, which is (x,y)
Hence, the line AB = AP + PB.
At point AP: x = (-2+2)/2 = 0
also, point PB: y = (2 - 4)/2 = -1
Therefore, coordinates of point P = (0,-1)
Answer:
D. 116
Step-by-step explanation:
Let the grasshoppers with a white marking be 2x.
Let the grasshoppers without a white marking be 3x.
2x + 3x = 290
5x = 290
x = 290 / 5
x = 58
The grasshoppers with a white marking
= 2x
= 2 ( 58 )
= 116
