I'm having trouble writing equations for word problems. I would like help in figuring out how to set up the right equations in order to find solutions to the following problems:

1) Marlene rides her bicycle to her friend JonÃ¢??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 JonÃ¢??s house?

2) 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.)

3) 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)=

4) If 2f(x)+f(1-x)=x^2, what is f(x)

Solution Summary

In order to solve one question, this solution uses similar triangles.

... in all other cases, the player keeps rolling. ... gives an intuitive approach to probability problems involving ... is illustrated by calculating probabilities for the ...

... Frequencies of Dice Roll Combinations and Probabilities of Dice Rolls... 36 pairs can occur at the same probability 1/36 ... we denote the sum of a particular roll by X ...

Statistics: Probability of Die Rolls. A 6-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in ...

1. If two balanced die are rolled, the possible outcomes can be represented as follows: ... Determine the probability of rolling the sum of 9 with two balanced ...

... There are 6 outcomes of a die roll. Probability that 1 is rolled = 1/6 Probability that 3 is rolled = 1/6 Probability of rolling 1 or 3 = (1/6) + (1/6) = 1/3. ...

... In an Empirical approach to estimating or calculating probabilities the exact ... this empirical evidence our estimate of the probability that rolling this six ...

... A success is seen as rolling a 6, this has probability equal to 1 ... The roll can be a success (a 6) or a failure (not a 6). We have n=4 (4 rolls), p=1/6 (chance ...