Assignment:
Q1) Marlene rides her bicycle to her friend Jonâ's house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on level ground, 4 mph when going uphill, and 12 mph when going downhill. If her total time riding was 2 hours, how far is it to Jonâ's house?
Q2) A standard 6-sided die is weighted so that the probabilities of rolling 2,3,4,5, or 6 are equal and the probability of rolling is 1 is twice the probably of rolling a 2. If the die is thrown twice, what is the probability that the sum of the numbers thrown will be 4? (Must be written in fraction form).
Q3) A cone has an altitude of 15 cm and a radius of 3 cm. A right circular cylinder of radius r and height h is inscribed in the come as shown in the figure. Write h as a function of r.
H=h(r)=
Q4) If 2f(x)+f(1-x)=x^2, what is f(x).
Provide complete and step by step solution for the question and show calculations and use formulas.