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Sarah is building a fence for her dog's square play area. To reduce the cost, she is using her house as 1 side of the play area, meaning she only has to purchase fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per meter of fencing, what will be the cost of fencing in this square play area?

$\small \small \$ 112.50$

$\small \$ 562.50$

$\small \$ 140.63$

$\small \$ 45$

$\small \$75$

Explanation

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula:

$\small (area) = (base)^2$

Find the square root of both sides to calculate the length of the base of the square

$\small \small \small \small \sqrt225 = (base) = 15$

All the sides are of equivilent length, so the total amount of fence required is:

$\small \small (15)*3 = 45$

One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer:

$\small 45 * $2.50 = $112.50$

Michelle plays softball for her high school. She is the only pitcher on the team. She is the only player that is guaranteed to touch the ball on every play. The problem is, her hands are not big enough to get a grip on the ball because the ball is too big. What is the volume of the softball that has a diameter of 6 inches?

$36 \pi inches^3$

$288\pi inches^3$

$36\pi inches^2$

$288\pi inches^2$

$48\pi inches^3$

Explanation

The formula to find the volume of a sphere is $\frac{4}{3} * \pi * r^3$

Find the radius of the softball and substitute that in place of r.

Answer will be left in pi format.

$36\pi inches^3$

Solve for in the following equation:

$\frac{x}{2.5} = 10$

Explanation

When solving for x, we multiply both sides by 2.5.

So,

$\frac{x}{2.5} = 10$

$\frac{x}{2.5} \cdot 2.5 = 10 \cdot 2.5$

Note that even though there are decimals in the equation, you still solve it using the same methods.

Solve for .

Explanation

Divide both sides by . The denominator has less decimal places than the numerator so we just shift one decimal place for top and bottom: $\frac{4.12}{0.2}=\frac{41.2}{2}$ .

Solve:

$\frac{-2(2+2)}{-2(-2-2)}$

$\frac{1}{3}$

$-\frac{1}{3}$

Explanation

When solving this problem remember our orders of operation, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Evaluate the quantities inside the parentheses first.

$\frac{-2(2+2)}{-2(-2-2)}$

$\frac{-2(4)}{-2(-4)}$

$\frac{-8}{8}=-1$

Multiply: $39 \times 7$

Explanation

Multiply the ones digits together.

$9\times 7 =63$

The ones digit of the final answer is .

Carry over the to the next calculuation.

Multiply the with the tens digit of the first number, and add the carryover .

$7\times 3 +6 = 21+6 = 27$

The answer is:

Evaluate:

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Solve by dividing on both sides of the equation. Move the decimal two places to the right.

$\frac{0.09x}{0.09} = \frac{27}{0.09} =\frac{2700}{9}$

Now factor the numerator to find values that can cancel out.

$\frac{2700}{9}=\frac{9\cdot 300}{9}$

The nine in the numerator and denominator reduce to one and we are left with our final answer,

Solve for .

$\frac{x}{-0.9}=-3.1$

Explanation

$\frac{x}{-0.9}=-3.1$ Multiply both sides by . When multiplying decimals, first multiply normally and then count the number of decimal places in the problem. We have . So starting from the right, we shift two places to the left to get a decimal of . Since we are multiplying with negative numbers, we need to determine if the answer is negative. There are two negative numbers and that means the answer is positive.