Mixed Deck — All MDTP Topics Flashcards

A car travels 240 miles in 4 hours. What is its average speed in miles per hour?

Answer: 60 mph

Average speed = total distance ÷ total time = 240 ÷ 4 = 60 mph.

What is cos(π/3)?

Answer: 1/2

π/3 radians = 60°, and cos(60°) = 1/2 from the standard 30-60-90 triangle.

What is the value of tan(45°)?

Answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.

Two events A and B are mutually exclusive. P(A) = 0.3 and P(B) = 0.4. What is P(A or B)?

Answer: 0.7

For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.3 + 0.4 = 0.7.

Which value cannot be a probability?

Answer: 1.5

Probabilities must be between 0 and 1 inclusive; 1.5 exceeds this range.

Simplify: (3/5) / (9/10)

Answer: 2/3

3/5 ÷ 9/10 = 3/5 × 10/9 = 30/45 = 2/3.

Solve for x: 3x - 7 = 14

Answer: x = 7

Adding 7 to both sides gives 3x = 21, then dividing by 3 gives x = 7.

Which of the following is the fundamental Pythagorean identity?

Answer: sin²(θ) + cos²(θ) = 1

sin²(θ) + cos²(θ) = 1 follows directly from the Pythagorean theorem applied to a point on the unit circle.

How many outcomes are possible when rolling two dice?

Answer: 36

Each die has 6 faces, so total outcomes = 6 × 6 = 36.

In a data set, the range is defined as:

Answer: The difference between the highest and lowest values

The range is a simple measure of data dispersion that indicates the spread of a data set. It is calculated by subtracting the lowest value from the highest value in the set. This provides a quick and easy way to understand the total span of the data.

Which of the following is equivalent to 2(x + 4) - 3x?

Answer: -x + 8

Distributing gives 2x + 8 - 3x, which simplifies to -x + 8.

If a bag contains 5 red, 3 blue, and 2 green marbles, what fraction of marbles are blue?

Answer: 3/10

Total marbles = 10; fraction blue = 3/10.

Which of the following is a property of similar triangles?

Answer: They have proportional corresponding side lengths and equal corresponding angles

Similar triangles are triangles that have the same shape but not necessarily the same size. This means their corresponding angles are equal, and the lengths of their corresponding sides are in proportion. This proportionality is key to understanding their relationship.

If a recipe calls for 2/3 cup of sugar and you want to make 1.5 times the recipe, how much sugar do you need?

Answer: 1 cup

2/3 × 3/2 = 6/6 = 1 cup.

What is the primary goal of inferential statistics?

Answer: To make inferences about a population based on a sample

The primary goal of inferential statistics is to make generalizations or inferences about a larger population based on data collected from a smaller sample. This involves using statistical methods to draw conclusions, make predictions, and test hypotheses about population parameters. It extends findings beyond the observed data.

How many solutions does 2sin(x) = 1 have on the interval [0, 2π)?

Answer: 2

sin(x) = 1/2 gives x = π/6 and x = 5π/6, two solutions in [0, 2π).

Which is the scientific notation for 0.00047?

Answer: 4.7 × 10⁻⁴

Moving the decimal 4 places right: 0.00047 = 4.7 × 10⁻⁴.

What is the value of sin(30°)?

Answer: 1/2

sin(30°) = 1/2, a standard value from the 30-60-90 triangle where the opposite side is half the hypotenuse.

What is 3/4 + 5/6?

Answer: 19/12

Finding a common denominator of 12: 9/12 + 10/12 = 19/12.

What is the vertex of the parabola y = (x - 3)² + 2?

Answer: (3, 2)

In vertex form y = (x - h)² + k, the vertex is (h, k) = (3, 2).