Answer:
The length of AP will be 14 units.
Step-by-step explanation:
As P is the centroid of ΔABC as shown in question figure.
As the side AB of the triangle has the midpoint D, the side AC of the triangle has the midpoint F and the side BC of the triangle has the
midpoint E.
Hence, CD, BF and AE being medians of ΔABC.
The point of intersection of these medians will be the centroid of the triangle. Hence, P is the centroid of ΔABC
According to rule, the centroid point of the triangle ΔABC divides each median into two segments in the ratio 2 : 1.
So,

As the value of AE = 21
So,

AP = 14
So, the length of AP will be 14 units.
Keywords: centroid, triangle
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Answer:
Option A) Inside the circle
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The radius is equal to the distance from the center to any point on the circle
the formula to calculate the distance between two points is equal to

we have
A(-5,-8),M(-1,-3)
substitute the values



step 2
Find the distance from the center to point V
we know that
If the distance from the center to point V is equal to the radius, then the point V lie on the circle
If the distance from the center to point V is less than the radius, then the point V lie inside the circle
If the distance from the center to point V is greater than the radius, then the point V lie outside the circle
we have
A(-5,-8),V(-11,-6)
substitute in the formula



so

The distance from the center to point V is less than the radius
therefore
The point V lie inside the circle
Hope that helped :)
Answer:
Step-by-step explanation:
given that certain tubes manufactured by a company have a mean lifetime of 800 hours and a standard deviation of 60 hours.
Sample size n =16
Std error of sample mean = 
x bar follows N(800, 15)
the probability that a random sample of 16 tubes taken from the group will have a mean lifetime
(a) between 790 and 810 hours,
=
(b) less than 785 hours

, (c) more than 820 hours,

(d) between 770 and 830 hours
=
Answer:
180
Step-by-step explanation:

192-12=180
Answer:
$4.85
Step-by-step explanation:
Add the numbers:
2.95
1.05
<u>0.85</u>
4.85