The average rate of change of a function  on the interval  is equal to 

.

Restated, it is the slope of the line that passes through  and .

To find the correct value of  that answers this question, it suffices to examine the line with slope  through  and find the point among those given that is closest to the line. This line falls 4 units for every 5 horizontal units, so the line looks like this:

The -coordinate of the point of intersection is closer to 2 than to any other of the values in the other four choices. This makes 2 the correct choice.

A counterexample is a single example that disproves a statement. In order to disprove "If an integer is odd and is between 10 and 20, then it must be prime," you must show that there is an integer that is odd and is between 10 and 20, but is not prime. 

While 9 is odd and is not prime, it is not between 10 and 20. 16 is also not prime, but it is not odd.

15 is the answer because it is odd and is between 10 and 20, but is not prime, because it is divisible by 5 and 3, in addition to being divisible by itself and 1. 

The value we are trying to find is an average rate of decrease. In other words, we are looking for how much, on average, the water level decreased in a minute. To find the average, take the total difference in water level and divide it by the total difference in time. 

The total change in water height is given by the ending height minus the starting height: 

The total change in time is the amount of minutes that pass between 8:56 AM and 9:10 PM:

Therefore, the average rate of decrease is , which is equivalent to:

A triangle that has interior angles of  and  is necessarily a 30-60-90 triangle—a special right triangle. We can tell that the third angle about which we're not told anything has to be  because a triangle's interior angles always sum to , allowing us to solve for the third angle like so:

Since we know this triangle is a 30-60-90 triangle, we can use the special ratios that always hold true for this triangle's sides and angles to figure out the lengths of its other sides. The following ratio holds true for all 30-60-90 triangles, where the side in a fraction with a given angle is the side opposite that angle.

We're told that the hypotenuse of our triangle has a length of . The hypotenuse is the triangle's longest side, so it will be located directly across from its largest angle. In this case, that angle is . So, we need to set  equivalent to  and solve for .

As you can see, for this particular triangle, . Using this information, we can now calculate the lengths of the other sides of the triangle. The side opposite the  angle will be equal to  inches; since , this side's length is . The side opposite the  angle will be equal to . Substituting in  into this expression, we find that this side has a length of .

Thus, the correct answer is .

Since  is a right angle - that is,  - and , it follows that

,

making  a 30-60-90 triangle. 

By the 30-60-90 Triangle Theorem, 

,

and

Refer to the diagram below:

The area of a right triangle is equal to half the product of the lengths of its legs, so

,

the correct response.

Since  is a right angle - that is,  - and , it follows that

,

making  a 30-60-90 triangle. 

By the 30-60-90 Triangle Theorem, 

,

and

Refer to the diagram below:

The perimeter - the sum of the sidelengths - is 

.

6% of 10.49 is equal to

,

which, to the nearest cent, rounds to . 

Add this tax to the price of the pizza; the amount paid is 

Mike pays $4, so Morris will pay half the remainder, or 

.

The question is asking for unit of length. Of the units given in the five choices, only centimeters is a unit of length, and ten centimeters—the metric equivalent of about four inches—is a reasonable length for a candy bar.

Of the other units:

The kilogram is a unit of mass which corresponds to a little over two ounces.

The hectare is a unit of area, usually land, and is equivalent to about two and a half acres.

The milliliter is a very small unit of volume.

The kilowatt is a unit of power.