Answer:
Decimal 0.333 to a fraction in simplest form is: 
Step-by-step explanation:
Given the decimal

Multiply and divide by 10 for every number after the decimal point.
There are three digits to the right of the decimal point, therefore multiply and divide by 1000.
Thus,

∵ 0.333×1000 = 333
Let us check if we can reduce the fraction 
For this, we need to find a common factor of 333 and 1000 in order to cancel it out.
But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000
<u>Greatest Common Divisor (GCD) : </u>
The GCD of a, b is the largest positive number that divides both a and b without a remainder.
Prime Factorization of 333: 3 · 3 · 37
Prime Factorization of 1000: 2 · 2 · 2 · 5 · 5 · 5
As there is no common factor for 333 and 1000, therefore, the GCD is 1.
Important Tip:
- As GCD is 1, therefore the fraction can not be simplified.
Therefore, decimal 0.333 to a fraction in simplest form is: 
Answer:
117
Step-by-step explanation:
The angles line up~ P is the same as angel I.
9514 1404 393
Answer:
48°
Step-by-step explanation:
ΔACB is isosceles, so angles A and B have the same measure. The measure of angle C in that triangle is ...
∠C = 180° -2(69°) = 42°
Angle C in ΔCDE has the same measure. Angle D is the complement of that:
∠D = 90° -42° = 48°
_____
The relations we used are ...
- the sum of angles in a triangle is 180°
- base angles of an isosceles triangle are congruent
- vertical angles are congruent
- acute angles in a right triangle are complementary
Cos(2 arctan(4/3)) = cos(2 arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arcsin(4/5)) = (3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25.