Circumference = 360 degrees
<span>Circumference = 2π radians (comes from 2*pi*radius) </span>
<span>Therefore </span>
<span>360 deg. = 2*π radians </span>
<span>180 deg. = π radians </span>
<span>1 deg. = (π/180) radians </span>
<span>75 deg. = 75(π/180) radians </span>
<span>75 deg. = 75π / 180 radians </span>
<span>don't bother to try and simplify π (it is an irrational number) </span>
<span>however you can simplify 75/180 </span>
<span>both are divisible by 5 </span>
<span>75π/180 = 15π/36 </span>
<span>both are divisible by 3 </span>
<span>75 deg. = 5π/12 radians </span>
<span>We normally don't bother to go further, unless you actually need it as a decimal fraction (in which case, you will have an approximation) </span>
<span>75 deg. ≈ 1.308997 radians</span>
There are 6! = 720 ways of arranging the lamps.
If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.
Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.
Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.
Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So
P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4
Answer:
2 different perimeters, 32 cm and 40 cm
Step-by-step explanation:
Given the area of a rectangle is 64 cm squared.
We know, Area of the rectangle is = length x breath
∴ 64 = 8 x 8
Hence the sides can be 8 cm by 8 cm.
So the perimeter of the rectangle is = 8 cm + 8 cm + 8 cm +8 cm
= 32 cm
Also, Area of the rectangle is = length x breath
∴ 64 = 16 x 4
So the perimeter of the rectangle is = 16 cm + 4 cm + 16 cm +4 cm
= 40 cm
5 to the power of 2 is 25
40(60/100) 4(6/10) =24/10 = 2.4
