Mixed Deck — All Math Topics Flashcards

Which equation models 'the sum of two consecutive integers equals 47'?

Answer: n + (n + 1) = 47

Consecutive integers differ by 1, so the two numbers are n and n+1, and their sum is 47.

The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

Answer: 170 centimeters

To find the predicted height for a metacarpal bone length of 4.45 centimeters, locate 4.45 on the x-axis (metacarpal bone length). Then, move vertically up from 4.45 until you intersect the line of best fit. From that intersection point, move horizontally to the left to read the corresponding value on the y-axis (height), which will be approximately 170 centimeters.

What is the surface area of a rectangular box that is 3 cm × 4 cm × 5 cm?

Answer: 94 cm²

Surface area = 2(lw + lh + wh) = 2(12 + 15 + 20) = 2 × 47 = 94 cm².

Which inequality represents 'a number y is more than 5 units away from zero'?

Answer: |y| > 5

Distance from zero is absolute value, and 'more than 5' means |y| > 5.

The writer is considering deleting the underlined sentence. Should the sentence be kept or deleted?

Answer: Deleted, because it blurs the paragraph’s focus on the community stakeholders with whom transportation planners work.

The sentence should be deleted because it shifts the focus away from the paragraph's main topic, which is the community stakeholders transportation planners work with. Discussing the general benefits of walking, while potentially related to urban planning, does not directly contribute to the specific theme of stakeholder engagement. Deleting it improves the paragraph's coherence and focus.

A recipe requires r cups of flour for 12 cookies. Which expression gives the cups needed for 60 cookies?

Answer: 5r

60 cookies is 5 times 12 cookies, so you need 5r cups of flour.

What is the area of a circle with diameter 10 cm? (Use π ≈ 3.14)

Answer: 78.5 cm²

Radius = 5 cm; Area = πr² = 3.14 × 25 = 78.5 cm².

A vendor sells apples for $0.50 each and oranges for $0.75 each. Which expression gives the total cost for a apples and g oranges?

Answer: 0.50a + 0.75g

Multiply each item's price by its quantity and add: 0.50a + 0.75g.

When a parenthesis is preceded by a minus sign, each phrase changes to a different sign when the parentheses are removed.

Answer: True

When a parenthesis is preceded by a minus sign, it indicates that every term inside the parentheses must be multiplied by -1. This operation effectively reverses the sign of each term: positive terms become negative, and negative terms become positive. For example, -(a - b + c) correctly expands to -a + b - c, demonstrating that each term's sign changes.

The height ratio between two structures is 7 to 5. The tallest structure is 210 feet. How high is the second structure?

Answer: 150

The height ratio between the two structures is 7 to 5, with the tallest structure corresponding to the '7' part of the ratio. Given that the tallest structure is 210 feet, we can set up a proportion: 7/5 = 210/x, where x is the height of the second structure. Cross-multiplying gives 7x = 5 * 210, which simplifies to 7x = 1050. Dividing both sides by 7, we find x = 150 feet for the second structure.

A frequency table shows scores: 70 (×3), 80 (×4), 90 (×3). What is the mean score?

Answer: 80

Mean = (70×3 + 80×4 + 90×3) ÷ 10 = (210 + 320 + 270) ÷ 10 = 800 ÷ 10 = 80.

A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?

Answer: 1/2

P(blue) = 5 ÷ (3 + 5 + 2) = 5/10 = 1/2.

Based on the passage, which choice best describes the relationship between Putman’s and Lohmann’s research?

Answer: Putman’s research builds on Lohmann’s.

The phrase 'builds on' indicates that Putman's research uses Lohmann's work as a foundation or starting point, expanding upon it or developing new insights based on Lohmann's findings. This suggests a collaborative or sequential relationship where Lohmann's earlier discoveries provided the necessary groundwork for Putman's subsequent investigations. It implies progress and development in the field of study.

A population of 500 bacteria doubles every hour. Which expression gives the population P after h hours?

Answer: P = 500 · 2^h

Doubling each hour is exponential growth: P = 500 · 2^h.

As used in line 2, “tracked” most nearly means

Answer: followed.

In the context of a journey, 'tracked' refers to monitoring or observing the path taken by someone or something. Therefore, 'followed' is the closest synonym, implying that Adelita's movements were observed and recorded throughout her 9,000-mile journey. The other options, such as 'searched for' or 'hunted,' suggest an active pursuit rather than passive observation of a known path.

Two fair six-sided dice are rolled. What is the probability that both show a number greater than 4?

Answer: 1/9

Numbers greater than 4 on one die: {5, 6} → probability = 2/6 = 1/3. For two independent dice: (1/3) × (1/3) = 1/9.

If the number 5, 876, 984 is increased by 1, 035, what will the result be?

Answer: 5,878,019

The problem requires a straightforward addition of the two given numbers. Aligning the numbers by place value and adding from right to left (ones, tens, hundreds, etc.) yields the sum. Specifically, 5,876,984 increased by 1,035 results in 5,878,019.

What is the domain of f(x) = √(x − 4)?

Answer: x ≥ 4

The expression under the square root must be ≥ 0: x − 4 ≥ 0, so x ≥ 4.

IF 10 is divided into two parts, the second of which is represented by y.

Answer: 10 - y

If a total amount (10) is divided into two parts, and one part is represented by 'y', then the other part must be the total minus the known part. This is a fundamental concept in algebra for representing parts of a whole. Therefore, 10 - y correctly represents the remaining part.

A road runs 3 miles north and then 4 miles east. How far is the endpoint from the start?

Answer: 5 miles

Using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 miles.