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Sample Question of the Day
Question:
Calculate the quotient of 726 ÷ 3 using the standard algorithm. Show your work step by step.
💡 Explanation:
To divide 726 by 3 using the standard algorithm, follow these steps: 1.
Divide the first digit of the dividend (7) by 3.
The quotient is 2, with a remainder of 1.
2.
Bring down the next digit of the dividend (2), making the number 12.
3.
Divide 12 by 3.
The quotient is 4, with no remainder.
4.
Bring down the next digit of the dividend (6), making the number 6.
5.
Divide 6 by 3.
The quotient is 2, with no remainder.
Thus, 726 ÷ 3 = 242.
Standard: 6.NS.B.2 | DOK: 2
Recent Questions
Question:
A small business owner is deciding whether to invest in a new project. The project could result in a profit of $10,000, a break-even scenario with no profit or loss, or a loss of $5,000. The probabilities of these outcomes are 0.3 for the profit, 0.4 for the break-even, and 0.3 for the loss. Which of the following statements are true regarding the expected value of the project and the decision-making process based on this expected value?
Answer Choices:
- A) The expected value of the project is $1,500.
- B) The expected value of the project is $0.
- C) The expected value of the project is negative, indicating it is a loss-making decision.
- D) Investing in the project is a risk-neutral decision based on the expected value.
- E) The project should be rejected since the expected value is negative.
- The expected value of the project is $1,500.
- Investing in the project is a risk-neutral decision based on the expected value.
💡 Explanation:
To calculate the expected value, multiply each outcome by its probability and sum the results: (0.3 * $10,000) + (0.4 * $0) + (0.3 * -$5,000) = $3,000 + $0 - $1,500 = $1,500.
The positive expected value suggests that, on average, the project yields a profit, making it a risk-neutral decision for the business owner.
Standard: S.MD.B.5 | DOK: 3
In a small town surrounded by mountains, a young girl named Lily loved exploring the outdoors. She often hiked up the trails, collecting unique rocks and observing wildlife. Her curiosity led her to learn more about the local ecosystem and how each plant and animal played a role in it. Inspired by her discoveries, Lily started a nature club at her school to share her knowledge with her classmates.
Question:
How did Lily's curiosity about the outdoors influence her actions?
Answer Choices:
- A) She decided to become a scientist.
- B) She started a nature club at her school.
- C) She moved to a bigger city.
- D) She stopped exploring the outdoors.
💡 Explanation:
- Lily's curiosity about the local ecosystem inspired her to start a nature club to share her knowledge with her classmates.
Standard: RI.IT.8.3 | DOK: 1
Sarah eagerly opened her new book, "The Adventures of Tom Sawyer." As she turned the pages, she noticed the author's unique style of writing. Some words were spelled differently than she was used to seeing. Despite this, she found the story captivating and couldn't put it down.
Question:
What is the main reason some words in Sarah's new book are spelled differently than she is used to?
Answer Choices:
- A) The author made spelling errors.
- B) The book uses old-fashioned spelling conventions.
- C) The printer made a mistake in the book.
- D) Sarah is not familiar with English spelling.
💡 Explanation:
- The passage mentions the author's unique style of writing, which includes using different spelling conventions that might appear old-fashioned compared to modern spelling.
Standard: L.SS.8.1.g | DOK: 1
Question:
Consider two functions: a linear function f(x) = 3x + 2 and an exponential function g(x) = 2^x. As x increases, which function eventually grows faster?
Answer Choices:
- A) f(x) = 3x + 2
- B) g(x) = 2^x
💡 Explanation:
Exponential functions grow faster than linear functions as x increases.
While the linear function increases by a constant amount, the exponential function grows by a factor, which eventually surpasses the linear growth.
Standard: F.LE.A.6 | DOK: 1
Question:
A car travels at a constant speed of 60 miles per hour. How long will it take for the car to travel 180 miles? Use appropriate units to express your answer.
Answer Choices:
- A) 1 hour
- B) 2 hours
- C) 3 hours
- D) 4 hours
💡 Explanation:
To find the time it takes to travel a certain distance at a constant speed, use the formula: time = distance / speed.
Here, distance = 180 miles, and speed = 60 miles per hour, so time = 180 miles / 60 miles per hour = 3 hours.
The units of miles cancel out, leaving the units of hours, indicating the time taken.
Standard: N.Q.A.1 | DOK: 3
Question:
Which of the following statements explains the Pythagorean Theorem?
Answer Choices:
- A) In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
- B) In all triangles, the sum of the interior angles is 180 degrees.
- C) In an isosceles triangle, the angles opposite the equal sides are equal.
- D) In a triangle, the exterior angle is equal to the sum of the two interior opposite angles.
💡 Explanation:
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
This fundamental relation in Euclidean geometry applies only to right triangles.
Standard: 8.G.B.6 | DOK: 1