We need 2 equations, because we have 2 unkown variables. Let  = the entrance fee, and  = the fee per ride. One ride costs  dollars. We know that Lisa spent 120 dollars in total. Since Lisa went on 6 rides, she spent  dollars on rides. Her only other expense was the entrance fee, : 

Apply similar logic to Tom:

Subtracting the second equation from the first equation results in:

Divide both sides by 2:

So every ride costs 12.5 dollars. Plugging 12.5 back into one of the original equations allows us to solve for the entrance fee:

Subtract 50 from both sides:

The purpose of this question is to calculate tax rates using dollar amounts.

First, the amount of tax payed must be determined. This is done by finding the difference between the amount paid and the listed price

,

which equals $3.15.

Then, that must be translated into a percentage of $45.

Therefore,

, yielding .07 of 1. This is a 7% tax rate.

The probability that the spinner will stop in a particular sector depends on the angle of the sector, not on the size of the sector. The radii of the sectors is therefore irrelevant.

The two larger green sectors are each one third of a quarter circle, and each is a sector of measure

.

The two smaller ones are each a half of a quarter circle, and each is a sector of measure 

.

Therefore, the total angle measure of the green sectors is

.

The probability that the spinner will stop in a green sector is found by taking this out of a total of :

The given table reports the average high and low temperatures over four years. The question asks to calculate the average rate of change for the high temperature over the four years depicted.

To calculate average rate of change use the following formula.

Substitute these values into the formula looks as follows.

Therefore, the average rate of change for the high temperature from 2002 to 2005 is 2 degrees Fahrenheit.

The table reports the average high and low temperatures over four years. To calculate the fraction of average low temperatures in 2002 to 2005 first identify the average low temperature in 2002 and in 2005.

Examining the table,

Average low temperature in 2002: 34 degrees Fahrenheit.

Average low temperature in 2005: 45 degrees Fahrenheit.

From here, to find the fraction of average low temperatures during this time period, use the following formula.

The general equation for a circle with center (h, k) and radius r is given by

.

In our case, our h-value is 1 and our k-value is 1. Our r-value is 10.

Substituting each of these values into the equation for a circle gives us

Tommy throws a rock off a 10 meter ledge at a speed of 3 meters/second. To calculate when the rock hits the ground first identify what is known.

Using the equation 

where

it is known that,

Substituting the given values into the position  equation looks as follows.

Now to calculate when the rock hits the ground, find the  value that results in .

Use graphing technology to graph .

It appears that the rock hits the ground approximately 1.75 seconds after Tommy throws it.

First, we will determine the total number of ballots:

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

Let's look at the table.

We can see the first column lists all the students.  The next column shows all of the classes.  And the last column shows the grade they received in those classes.

Now, to find which class Craig received the highest grade, we must first locate Craig.  We can see all of Craig's classes are at the very bottom of the table.

Now, we will look at the grade he got in each class by following along the rows with Craig's name.

We can see Craig's first class is Math.  He received a B.

Craig's second class is Science.  He received an A.

Craig's third class is Art.  He received a B.

Knowing this, we can see the highest grade Craig received was an A.  The class where he received an A was Science.

Therefore, the class that Craig received the highest grade was Science.

The eqiatopm of  is given in the vertex form

,

so the vertex of its parabola is . The graphs of  and  are parabolas with the same vertex, so they must have the same values for  and . 

For the function ,  and .

Of the five choices, the only equation of   that has these same values, and that therefore has a parabola with the same vertex, is .

To verify, graph both functions on the same grid.