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Sample Question of the Day
Question:
Simplify the expression (x^(1/3) * y^(1/6))^6 using the properties of exponents.
💡 Explanation:
Using the properties of exponents, when raising a power to a power, you multiply the exponents.
Therefore, (x^(1/3))^6 = x^(1/3 * 6) = x^2 and (y^(1/6))^6 = y^(1/6 * 6) = y^1 = y.
Hence, the expression simplifies to x^2 * y.
Standard: N.RN.A.2 | DOK: 2
Recent Questions
Question:
Which of the following are characteristics of the Roman Justinian Code that influenced the American legal system? Select all that apply.
Answer Choices:
- A) A comprehensive written code of laws
- B) Trial by a jury of peers
- C) Concept of legal precedents
- D) Emphasis on individual rights
- E) Separation of powers into three branches of government
💡 Explanation:
- The Roman Justinian Code was one of the earliest comprehensive written codes of laws, which influenced the American legal system by providing a structured legal framework.
- It also introduced the concept of legal precedents, where past decisions influence future legal rulings.
- However, the ideas of trial by a jury of peers, emphasis on individual rights, and separation of powers are more modern developments not directly rooted in the Justinian Code.
Standard: 6.2.8.CivicsDP.3.a | DOK: 1
Question:
A rectangular box has a length of 5 units, a width of 3 units, and a height of 4 units. Which of the following expressions can be used to correctly find the volume of the box? Select all that apply.
Answer Choices:
- A) 5 + 3 + 4
- B) 5 x 3 x 4
- C) (5 x 3) + (3 x 4)
- D) (5 x 4) + (3 x 4)
- E) 5 x (3 + 4)
💡 Explanation:
To find the volume of a rectangular box, you multiply the length, width, and height together.
Therefore, the expression 5 x 3 x 4 is correct.
The other expressions do not correctly calculate the volume.
Standard: 5.M.B.2 | DOK: 2
Question:
A gardener is planting flowers in rows. She has 1,872 flowers and wants to divide them equally into 26 rows. How many flowers will each row have?
Answer Choices:
- A) 64
- B) 72
- C) 68
- D) 70
💡 Explanation:
To find out how many flowers each row will have, divide the total number of flowers by the number of rows.
1,872 divided by 26 equals 72.
Standard: 6.NS.B.2 | DOK: 3
Question:
Which of the following statements correctly describe the concepts of unions, intersections, and complements in probability? Select all that apply.
Answer Choices:
- A) The union of two events includes all outcomes that are in either event.
- B) The intersection of two events includes only outcomes that are in both events.
- C) The complement of an event includes all outcomes that are not in the event.
- D) The intersection of two events includes all outcomes that are in either of the events.
- E) The union of two events includes only outcomes that are in both events.
💡 Explanation:
In probability, the union of two events A and B (written as A ∪ B) includes all outcomes that are in either A, B, or both.
The intersection of two events A and B (written as A ∩ B) includes only the outcomes that are in both A and B.
The complement of an event A includes all outcomes in the sample space that are not in A.
Standard: S.CP.A.1 | DOK: 1
Question:
How do specific animal behaviors and plant structures impact reproduction success?
Answer Choices:
- A) Animal behaviors such as nest building or elaborate mating dances increase reproduction success by [Select]
- B) Plant structures like brightly colored flowers enhance reproduction success by [Select]
💡 Explanation:
- Animal behaviors like nest building or mating dances attract mates or protect offspring, thereby increasing the chances of successful reproduction.
- Similarly, specialized plant structures like brightly colored flowers attract pollinators, which are essential for the transfer of pollen and successful plant reproduction.
Standard: MS-LS1-4 | DOK: 3
Question:
Consider the circle in the coordinate plane with the center at (h, k) and radius r. The equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2. If the equation of a circle is given as x^2 + y^2 - 6x + 4y - 12 = 0, use the method of completing the square to find the center and radius of the circle. Select the correct values from the dropdowns.
Answer Choices:
- A) Center: (3, -2); Radius: 5
- B) Center: (3, -2); Radius: 4
- C) Center: (2, -3); Radius: 5
- D) Center: (2, -3); Radius: 4
💡 Explanation:
To find the center and radius, we rewrite the given circle equation by completing the square.
Start with the equation x^2 + y^2 - 6x + 4y - 12 = 0.
\n\nFirst, complete the square for x: \n\n1.
Group the x terms: (x^2 - 6x)\n2.
Take half of -6, which is -3, and square it to get 9.
Add 9 and subtract 9 to the equation: (x^2 - 6x + 9 - 9)\n3.
Rewrite as: ((x - 3)^2 - 9)\n\nNext, complete the square for y:\n\n1.
Group the y terms: (y^2 + 4y)\n2.
Take half of 4, which is 2, and square it to get 4.
Add 4 and subtract 4 to the equation: (y^2 + 4y + 4 - 4)\n3.
Rewrite as: ((y + 2)^2 - 4)\n\nCombine these results:\n\n(x - 3)^2 - 9 + (y + 2)^2 - 4 = 12\n\nSimplify:\n\n(x - 3)^2 + (y + 2)^2 = 25\n\nThis equation is in the standard form (x - h)^2 + (y - k)^2 = r^2, where the center is (h, k) = (3, -2) and the radius r = √25 = 5.
Standard: G.GPE.A.1 | DOK: 4