More Algebra 2 problems.

__June 2017, Part II__

All Questions in Part II are worth up tp 2 credits. Partial credit is possible.

*31. Write (x) ^{(1/3)} * (x)^{(1/2)} as a single term with a rational exponent.
*

**Answer: **

First of all, please look at the image. This is how the question was asked. I typed it the best way that I could for this medium.

That said, you're first step is to rewrite the equation as:

^{(1/3)}* (x)

^{(1/2)}

Now use the rules of exponents:

(x)

^{(1/3)}* (x)

^{(1/2)}=

**(x)**

^{(5/6)}Leave your answer in this form with the rational (fractional) exponent. Do NOT rewrite it with a radical symbol.

*Note: (1/3) + (1/2) = (2/6) + (3/6) = (5/6)
*

*32. Data collected about jogging from students with two older siblings in the table below.
*

Neither Sibling Jogs | One Sibling Jogs | Both Sibling Jog | |

Student Does Not Jog | 1168 | 1823 | 1380 |

Student Jogs | 188 | 416 | 400 |

Using these data, determine whether a student with two older siblings is more likely to jog if one sibling jogs or if both siblings job. Justify your answer.

Using these data, determine whether a student with two older siblings is more likely to jog if one sibling jogs or if both siblings job. Justify your answer.

**Answer: **

Sum up the second and the third columns. The number of students with one sibling who jogs is 1823 + 416 = 2239. The number of students with two siblings who jog is 1380 + 400 = 1780.

The probability that a student jogs if one sibling jogs is

P(student | one sibling) = 416/2239 = .186

The probability that a student jogs if both siblings jog is

P(student | both sibling) = 400/1780 = .225

It is more likely that a student with two older siblings will jog if both of their older siblings jog.

Comments and questions welcome.

More Algebra 2 problems.

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