Question 1: A triangle with sides measuring 8 inches, 12 inches, and 15 inches has a perimeter of

• 15 inches
• 27 inches
• 35 inches (Correct answer)
• 225 inches
• 433 inches

Correct answer: 35 inches

The perimeter of any polygon, including a triangle, is the total length of all its sides. To find the perimeter, you simply add the lengths of the three given sides together. In this case, adding 8 inches, 12 inches, and 15 inches results in a total perimeter of 35 inches.

Question 2: A decomposition reaction in a solid material usually brought on by the introduction of heat that is a precursor to combustion is known as

• light
• pyrolysis (Correct answer)
• oxygen
• fuel

Correct answer: pyrolysis

Pyrolysis is the chemical decomposition of solid materials by heat in the absence of oxygen. This process breaks down complex organic compounds into simpler volatile gases, liquids, and char, which are then available to ignite and sustain combustion. It is a critical precursor to combustion for solid fuels, as the solid material itself doesn't burn directly but rather the gases produced by pyrolysis do.

Question 3: A square having a side measuring 6 inches has a perimeter of

• 16 inches
• 20 inches
• 24 inches (Correct answer)
• 28 inches

Correct answer: 24 inches

A square is a quadrilateral with four equal sides. The perimeter of any polygon is found by summing the lengths of all its sides. For a square with a side length of 6 inches, the perimeter is calculated by multiplying the side length by 4 (6 inches * 4), resulting in 24 inches.

Question 4: Choose the correct answer

• 2 inches
• 3 in (Correct answer)
• 4 in
• 6 in
• 16 in

Correct answer: 3 in

This question is presented without context or an accompanying problem statement. Assuming '3 in' is the designated correct answer for an unprovided question, it represents a specific measurement. Without the original problem, a detailed explanation of its derivation is not possible.

Question 5: The water tank of a fire department apparatus is 8 feet length, 4 feet wide, and 3 feet high. The number of cubic feet of water the tank can hold is?

• 32
• 64
• 96 (Correct answer)
• 128

Correct answer: 96

To calculate the volume of a rectangular tank, you multiply its length, width, and height. For a tank measuring 8 feet long, 4 feet wide, and 3 feet high, the volume is 8 ft * 4 ft * 3 ft. This calculation yields a total volume of 96 cubic feet, which is the amount of water the tank can hold.

Question 6: Choose the correct answer

• straight, 180 degrees
• acute, less than 90 degrees
• obtuse, more than 90 degrees
• right, 90 degrees (Correct answer)

Correct answer: right, 90 degrees

This question lacks specific context or a diagram to evaluate. However, a 'right' angle is precisely defined in geometry as an angle that measures exactly 90 degrees. It forms a perfect corner, often indicated by a small square symbol at the vertex.

Question 7: The math symbol : means

• Sum
• Absolute value
• Ratio (Correct answer)
• Not equal to

Correct answer: Ratio

In mathematics, the colon symbol (:) is primarily used to denote a ratio, expressing the relationship between two numbers or quantities. For example, a ratio of 2:3 means 2 to 3. While it can also represent division in some contexts, its most common and fundamental meaning as a mathematical symbol is a ratio.

Question 8: l -11 l is equal to

• 11 (Correct answer)
• -11
• -121
• 121

Correct answer: 11

The vertical bars around -11 (l -11 l) indicate the absolute value of the number. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the absolute value of -11 is 11, as distance is always a non-negative quantity.

Question 9: 48\/-6

• 8
• -8 (Correct answer)
• 16
• -16

Correct answer: -8

This problem involves dividing a positive number by a negative number. When performing division with numbers of opposite signs, the result is always negative. Dividing 48 by 6 yields 8, so 48 divided by -6 results in -8.

Question 10: (-12)(-5)

• 17
• -17
• 60 (Correct answer)
• -60

Correct answer: 60

This problem involves multiplying two negative numbers. A fundamental rule of multiplication states that when two negative numbers are multiplied together, the product is always positive. Therefore, multiplying -12 by -5 results in a positive 60.

Question 11: 9\/12 shown as a decimal is

• .05
• .5
• .075
• .75

To convert a fraction to a decimal, you divide the numerator by the denominator. For the fraction 9/12, dividing 9 by 12 yields 0.75. This can also be simplified first to 3/4, which is a common decimal equivalent.

Question 12: 48\/.6 =

• 8
• 80 (Correct answer)
• 800
• -8

Correct answer: 80

To divide by a decimal, it is often easiest to convert the divisor into a whole number by multiplying both the divisor and the dividend by a power of 10. Multiplying both 48 and 0.6 by 10 gives the equivalent problem 480 divided by 6. Performing this division (480 / 6) yields 80.

Question 13: The sum of 3\/4 and 2\/3 is

• 5\/7
• 5\/12
• 17\/12 (Correct answer)
• 12\/17

Correct answer: 17\/12

To add fractions, they must first have a common denominator. The least common multiple of 4 and 3 is 12. Convert 3/4 to 9/12 (by multiplying numerator and denominator by 3) and 2/3 to 8/12 (by multiplying numerator and denominator by 4). Adding the new numerators (9 + 8) gives 17, while keeping the common denominator of 12, resulting in 17/12.

Question 14: What is 25% of 200?

• 10
• 25
• 50 (Correct answer)
• 100

Correct answer: 50

To calculate a percentage of a number, convert the percentage to its decimal form and then multiply it by the number. 25% is equivalent to 0.25. Multiplying 0.25 by 200 yields 50. Alternatively, 25% is one-quarter, and one-quarter of 200 is 50.

Question 15: What percent of 61 is 28?

• 459.01%
• .45%
• 45.9% (Correct answer)
• 47%

Correct answer: 45.9%

To find what percentage 28 is of 61, you divide the part (28) by the whole (61) and then multiply the result by 100. The calculation (28 / 61) is approximately 0.459016. Multiplying this by 100 gives approximately 45.9016%, which rounds to 45.9%.

Question 16: 15 is 20% of what number?

• 30
• 50
• 60
• 75 (Correct answer)

Correct answer: 75

This problem can be set up as an algebraic equation: 15 = 20% * x, where x is the unknown number. Convert the percentage to a decimal (20% = 0.20), so the equation becomes 15 = 0.20 * x. To solve for x, divide 15 by 0.20, which equals 75.

Question 17: 9.06 x 14.1 =

• 12.774
• 127.746 (Correct answer)
• 1,277.46
• 1.21746

Correct answer: 127.746

To multiply decimals, first multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in the original numbers (9.06 has two, 14.1 has one, for a total of three). Place the decimal point in the product so that it has the same total number of decimal places, resulting in 127.746.

Question 18: .82 shown as a fraction is

• 82\/1
• 82\/10
• 82\/100 (Correct answer)
• 82\/1000

Correct answer: 82\/100

The decimal 0.82 is read as 'eighty-two hundredths.' The position of the last digit after the decimal point determines the denominator of the fraction. Since the '2' is in the hundredths place, the fraction is 82 over 100. This fraction can be simplified, but 82/100 is its direct fractional representation.

Question 19: (9+5 ) [ 7 + (6-3) ² ] =

• 18
• 89
• 224 (Correct answer)
• 1232

Correct answer: 224

Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). First, solve inside the parentheses: (9+5) = 14 and (6-3) = 3. Next, calculate the exponent: 3² = 9. Then, solve inside the brackets: [7 + 9] = 16. Finally, multiply the results: 14 * 16 = 224.

Question 20: 9\/10 - 3\/5 =

• 3\/5
• 3\/10 (Correct answer)
• 6\/10
• 12\/15

Correct answer: 3\/10

To subtract fractions, they must have a common denominator. The least common multiple of 10 and 5 is 10. Convert 3/5 to an equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2, which gives 6/10. Now, subtract the numerators: 9/10 - 6/10 = 3/10.