For this item, i go with letter D. Rational. The hat size cannot be integers as it includes negative numbers. For instance the person's hat size is 7 + 5/8 which leads to an answer of 7.625. That is a rational number.
First we have to assume that each quarter touched each other. Hence the area of the table not covered by the coins (A) is equal to the total area of the table (At) minus the total area of the coins (Ac). Coins are circle, so
![A = \pi r^{2}](https://tex.z-dn.net/?f=A%20%3D%20%20%5Cpi%20%20r%5E%7B2%7D%20)
and r =24.26mm. The area of one coin is then 1848.98mm^2. Hence the equation is A = At - xAc where x is the number of coins.
Since ∝ < β you can throw out answers C and D. Using the relationship of sine and cosine being complementary angles you can plug in the two smallest values. Out of those two for 13° you get sin18°=cos72° and 13°+72°=90°, meaning these two angles are complementary.
X-4y=0
Turn to slope intercept form y=mx+b
-4y=-x
y=x/4. Slope in this case is 1/4.. because it’s 1x/4 and 1/4 is in front of x. So the slope is 1/4