With a perimeter of 35 and 5. sides of equal length, the length of one side is \( \frac{35}{5}\) = 7.

There were a total of 33 customers who bought caramel candy. Subtract from these from the 4 who bought both and you are left with the 29 who bought only caramel.

Only factors of 36 (numbers that can be divided evenly into 36) can be the number of different colors in the bag. Since 5 is not a factor of 36, choice (D) is the correct answer.

The whole number must be less than 14 and also between 12 and 18. The only whole number that meets these criteria is 13 (choice D).

Soap operas take up 90 degrees out of a total of 360 degrees, which is one-fourth of the pie chart. Therefore, Susan spent about one-fourth of 12 hours, which is 3 hours, watching soap operas.

To solve for \( R \), multiply both sides of the equation by 3, thus \( R = 36 \). Plugging 36 back into the expression \( \frac{1}{3} R \) gives us: \( \frac{1}{3} \times 36 = 12 \).

Calculating \( \frac{1}{4} \) of 49 gives us approximately 12.25. Among the given options, the one that is closest is choice (A) which represents 13.

To find the average, we sum the sales figures: $250,000 + $260,000 + $270,000 + $260,000 + $260,000 = $1,300,000. Dividing by 5 gives us an average of $260,000.

This problem calls for substitution based on the operation defined as \( u \oplus v = u – (1 – \frac{1}{v}) \). For \( u = 4 \) and \( v = 5 \):

\( 4 \oplus 5 = 4 – (1 – \frac{1}{5}) = 4 – (1 – 0.2) = 4 – 0.8 = 3.2. \) Therefore, the answer is choice (C) which can be represented as \( 3 \frac{1}{5} \).

Substituting the values, we define \( u = a \) and \( C = 3 \), where \( a \oplus 3 = 2 \frac{1}{3} \). This can be expressed as \( a – (1 – 3) = 2 \frac{1}{3} \). Thus, \( a – 3 = 2 \frac{1}{3} \) leads to \( a = 3 + 2 \frac{1}{3} = 3 + \frac{7}{3} = 3 + 2.333… = 5.333… = 3 \).

A point on the earth’s surface completes one full rotation (360°) each day. In one and a half days, the total angle rotated is \( 360° \times 1.5 = 540° \).

To compare the sizes of the fractions, convert them to decimals or find a common denominator. The correct order from smallest to largest is \( \frac{3}{7}, \frac{13}{32}, \frac{11}{23}, \frac{1}{2}, \frac{9}{16} \).

The length of the rectangle is \( 3x \). The perimeter \( P \) of a rectangle is given by the formula \( P = 2 \times (length + width) = 2 \times (3x + x) = 2 \times 4x = 8x \).

Using the Pythagorean theorem, the diagonal \( d \) of a square can be found using \( d = \sqrt{(side^2 + side^2)} = \sqrt{(1^2 + 1^2)} = \sqrt{2} \) inches.

Each section is 3 feet 2 inches long, which is equivalent to 38 inches. Therefore, 8 sections require \( 8 \times 38 = 304 \) inches. Converting to feet, \( 304 \) inches is \( \frac{304}{12} \approx 25.33 \) feet. Since each section is 10 feet, the plumber needs to buy 3 sections.

If the shaded area covers a width of \( \frac{X}{4} \) and the length of the square is \( X \), then the area of the shaded part is \( \frac{X}{4} \times X = \frac{X^2}{4} \). The unshaded part would be the remaining area of the square, which is \( X^2 – \frac{X^2}{4} = \frac{3X^2}{4} \). The ratio of shaded to unshaded is \( \frac{\frac{X^2}{4}}{\frac{3X^2}{4}} = \frac{1}{3} \).

Using the formula distance = rate × time, we can find the rate. The total distance traveled is \( 2,000 + 400 = 2,400 \) miles. The total time is 3 hours 40 minutes, which is \( 3 + \frac{40}{60} = \frac{11}{3} \) hours. Thus, rate \( = \frac{2,400}{\frac{11}{3}} \approx 654.5 \) mph, which rounds to approximately 655 mph.

This is a simple proportion problem. Let \( x \) be the unknown width. Setting up the proportion: \( \frac{7}{9} = \frac{x}{6} \). Cross-multiply: \( 9x = 42 \). Solving for \( x \) gives \( x = \frac{42}{9} = 4\frac{2}{3} \) inches.

Subtract the area of the circle from the area of the square. The diameter of the circle equals the side length of the square. The area of the square is \( s^2 = 4 \text{ in}^2 \). The area of the circle is \( \pi r^2 = \pi left(1\right)^2 = \pi \text{ in}^2 \). So, the shaded area is: \( 4 – \pi \approx 0.86 \text{ in}^2 \).

The population would reproduce 6 times in 18 mins – \( 2^6 = 64 \)

Given \( z = y + 4 \), substitute to find \( 4z + 3 \). \( 4z + 3 = 4(y + 4) + 3 = 4y + 16 + 3 = 4y + 19 \).

Choosing specific values for \( x \) and \( y \) can help solve this. Let \( x = \frac{1}{2} \) and \( y = 3 \). For these values, we have: (A) \( \frac{y}{x} = 6 \), (B) \( \frac{x}{y} = \frac{1}{6} \), (C) \( xy = \frac{3}{2} \), and (D) \( \frac{1}{x-y} = \frac{1}{\frac{1}{2} – 3} = \frac{1}{-2.5} = -\frac{2}{5} \). Since option D is negative, it is the smallest value.

If 4 people can sit at each of \( x \) tables and 8 people can sit at each of \( y \) tables, the maximum number of people that may be seated is \( 4x + 8y \).

Let the side length of the smallest piece be \( s \). Then the middle piece has a side of \( 3s \), and the largest piece has a side of \( 6s \). The area of the smallest piece is \( s^2 \), and the area of the largest piece is \( (6s)^2 = 36s^2 \). Therefore, the area of the largest piece is 36 times the area of the smallest piece.

Determine the total amount of gas needed for 30 trips: \( \frac{3}{2} \times 30 = 45 \) gallons. Since his gas tank holds 9 gallons, Mr. Dali needs \( \frac{45}{9} = 5 \) tanks of gas.