We need to find the distance between (7, 5) and (10, 11) and double it, since they run it twice. We can do this as follows: 2√(11-5)² + (10-7)² = 2√36 + 9 = 2√45 = 6√5.
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Hope this helps!
Answer:
The perimeter of the hexagon is 48.5 feet
Step-by-step explanation:
In this question, we are asked to calculate the perimeter of a regular hexagon, given the length of its apothem and its area value
Recall;
Mathematically the area of a regular hexagon A = 1/2 * P * a
where P is the perimeter of the hexagon which is unknown according to the question, a is the apothem of the hexagon which is 7 feet and A is the area which is 169.74 sq.feet according to the question
Plugging these values into the equation, we have;
169.74 = 0.5 * 7 * P
P = 169.74/3.5
P = 48.50 ft
First, let me do the Mathematical part of that, and then I shall explain the theory behind it.
Mathematical part:
We are going to multiply 513 with 46. So the two partial products that we are going to choose are 40 and 6.
Multiply 513 with 6 first.
513
x46
--------------------------
18 (as 6*3 = 18)
60 (as 6*10 = 60; In 513, the digit at tenths place is 1, so 1*10=10)
3000 (as 6*500 = 3000; In 513, 5 is at hundredth place, so 5*100=500)
120 (as 40*3 = 120; since 4 is at the tenth place, so 4*10=40)
400 (as 40*10 = 400)
20000 (as 40*500 = 20000)
--------------------------
23598 (Add all of them)
Theory:
As you can see above that we have chosen the two partial products individually which are 6 and 40. Since 4 in 46 is in tenth place, we have to consider it 40 (since 4*10 = 40). One by one, we first multiply 6 with 513. Then we move to the tenth place, and multiply 513 with 40. At the end, we have added all the results we found after multiplication.
Check: If we check the multiplication result by using the calculator, we would get the same result (23598).
Another Method (instant):
513 * (40+6) = (513*40) + (513*6) = 23598.
The volume of a spherical shaped object is given by
Given that the <span>solid ball has a radius of 20.0 millimeters, the volume of the solid ball is given by
Therefore, the </span><span>closest to the volume of the synthetic compound ball, in cubic millimeters is 33,500 cubic milimeters.</span>
Answer:
(a) 0.06154
(b) 0.2389
(c) 0.6052
(d) 2478
Step-by-step explanation:
probability density function of the time to failure of an electronic component in a copier (in hours) is
P(x) = 1/1076e^−x/1076
λ = 1/1076
A) A component lasts more than 3000 hours before failure:
P(x>3000) = 1 − e^−3000/1076
= 0.06154
B) A component fails in the interval from 1000 to 2000 hours:
P(1000>x>2000) =1 − e^−2000/1076 − 1 +e^−1000/1076 = e^−1000/1076 − e^−2000/1076 = 0.3948 − 0.1559
= 0.2389
C) A component fails before 1000 hours:
P(x<1000) = 0.6052
D) The number of hours at which 10% of all components have failed:
e^−x/1076 = 0.1
= −x/1076
= ln(0.1)
x =(2.3026)×(1076)
x = 2478
