\(15\) has factors that divide it evenly. These are: \(1, 3, 5,\) and \(15\), which gives a total of 4 factors.

To find how many CDs John owns, multiply the total number of CDs by \(\frac{1}{3}\): \(\frac{1}{3} \times 180 = 60\). So, John owns 60 CDs.

An equilateral triangle has three equal sides. The perimeter is the sum of all the sides: \(6 + 6 + 6 = 18\) inches.

Let James’s contribution be \(J\). Sharice pays twice as much as James: \(S = 2J\). Tyler pays six times as much as Sharice: \(T = 6S = 12J\). The total is \(J + S + T = 360\). Substituting: \(J + 2J + 12J = 360\), so \(15J = 360\), which gives \(J = 24\). Thus, Sharice pays \(2 \times 24 = 48\) dollars.

Let the original price be \(x\). After a 50% reduction, the price becomes \(0.5x\). After a further 10% reduction, the price becomes \(0.5x – 0.1(0.5x) = 0.45x\), which is 45% of the original price.

Let the number of green gumdrops be \(9x\) and the number of red gumdrops be \(5x\). The total is \(9x + 5x = 56\), so \(14x = 56\), which gives \(x = 4\). Therefore, the number of green gumdrops is \(9 \times 4 = 36\).

The perimeter is the sum of all the sides. Since all sides are equal, divide the perimeter by the number of sides: \(96 div 8 = 12\) inches per side.

Volume = length × width × height. The volume of the first box is \(6 \times 6 \times 10 = 360\). The volume of the second box is \(3 \times 10 \times \text{height} = 360\). Solving for height gives \(\text{height} = 12\).

Since each of the 500 attendees donated the same dollar amount, the total amount donated is the product of 500 and y, \(500 \times y\).

Substitute the values \(p = 500\), \(r = 0.08\), and \(t = 2.5\) into the formula: \(A = 500 + 500 \times 0.08 \times 2.5 = 600\).

Corresponding parts of similar triangles are in proportion. Using the ratios: \(\frac{4}{6} = \frac{x}{6}\), solving gives \(x = 9\).

\((3K^3)^2 = (3^2)(K^3)^2 = 9K^6\).

Cross-multiply: \(30y = 48 \times 5\). Solving for y gives \(y = 8\).

\(\frac{3}{x} – \frac{5}{x} = \frac{-2}{x}\).

If 50% of the original price is $22.97, then the original price is \(\frac{22.97}{0.5} = 45.94\).

The total percentage for food, rent, utilities, entertainment, and clothing is 87.3%. Miscellaneous expenses make up the remaining 12.7%. Therefore, the amount spent on miscellaneous is \(0.127 \times 480 = 60.96\).

The x-intercept occurs when \(y = 0\). Setting the equation equal to 0: \(0 = 4x + 5\). Solving for x gives \(x = -\frac{5}{4}\).

To break a number into its prime factors, break it into factors, and break those factors into factors, until you cannot go any further. It doesn’t matter what factors you begin with. You will reach the same prime factors. \(60 = 5 \times 2 \times 3 \times 2\).

There are two cases to solve:
Case 1: \(6a – 2 = 3\) leads to \(6a = 5\), so \(a = \frac{5}{6}\).
Case 2: \(6a – 2 = -3\) leads to \(6a = -1\), so \(a = -\frac{1}{6}\). The correct solution is \(\frac{5}{6}\).

The total of $145.60 represents 130% of the base amount (100% base + 30% tax and tip). Therefore, divide $145.60 by 1.3 to get the base amount: \(\frac{145.60}{1.3} = 112.00\).

If the diagonal of a square is 8, by the Pythagorean Theorem, the side length of the square is \(\frac{8}{\sqrt{2}} = 4\sqrt{2}\). The area of the square is then \((4\sqrt{2})^2 = 32\).

Converting the fractions to decimals: \(\frac{2}{3} \approx 0.666\) and \(\frac{4}{5} = 0.8\). The fraction \(\frac{7}{10}\) equals 0.7, which lies between 0.666 and 0.8.

Use the formula for the circumference of a circle: \(C = \pi d\), where \(d = 9\). So, \(C \approx 3.14 \times 9 = 28.26\) inches.

First, calculate the cost of buying the shares: \(10 \times 180 = 1,800\). Then calculate the amount she received from selling them: \(10 \times 240 = 2,400\). Finally, subtract the two: \(2,400 – 1,800 = 600\). Josie’s profit was $600.