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probability for rolling

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 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?

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 Preview

Please find solution/explanation attached herewith.

1) Marlene rides her bicycle to her friend Jon'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 Jon's house?
Solution:

Let the distance travelled on level ground be a and b be the distance while going uphill and c be the distance while going downhill.

Time taken while going = a/6 + b/4 + c/12

Time taken while returning = c/4 + b/12 + ...

Solution Summary

In order to solve one question, this solution uses similar triangles to solve the given problem regarding probability.

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