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Q: Sarah has $ \frac{3}{4} $ of a pound of candy. She buys $ \frac{2}{3} $ of a pound more. How much candy does she have now in total?

$ \frac{17}{12} $ or 1$ \frac{5}{12} $ pounds

Sample Question of the Day

Short answer📘 6.1.8.HistoryUP.5.b🧠 DOK 1

Question:

What role did African Americans play in the Civil War?

✅ Answer:

African Americans served in various capacities during the Civil War, including as soldiers in the Union Army, laborers, and support staff. They played a crucial role in the Union's war effort, and the Emancipation Proclamation allowed many to enlist and fight for their freedom.

💡 Explanation:

African Americans were integral to the Union's efforts during the Civil War, with many serving as soldiers in segregated units such as the United States Colored Troops.
Their involvement was a significant step towards ending slavery and gaining equal rights.
This participation was recognized as a turning point in the fight for civil rights.

Standard: 6.1.8.HistoryUP.5.b | DOK: 1

Recent Questions

Multiple select📘 G.SRT.A.1🧠 DOK 4

Question:

A triangle ABC undergoes a dilation centered at point O with a scale factor of 2, resulting in triangle A'B'C'. Subsequently, triangle A'B'C' undergoes another dilation centered at point O with a scale factor of 0.5, resulting in triangle A"B"C". Select all statements that are true about the relationship between triangle ABC and triangle A"B"C".

Answer Choices:

A) Triangle ABC is similar to triangle A"B"C".
B) The scale factor from triangle ABC to triangle A"B"C" is 1.
C) Triangle A"B"C" is congruent to triangle ABC.
D) Triangle A"B"C" is not similar to triangle ABC.
E) The scale factor from triangle A"B"C" to triangle ABC is 1.

✅ Answer:

Triangle ABC is similar to triangle A"B"C".; The scale factor from triangle ABC to triangle A"B"C" is 1.; Triangle A"B"C" is congruent to triangle ABC.

💡 Explanation:

Since the total effect of the dilations is a scale factor of 1 (2 * 0.5 = 1), triangle A"B"C" is congruent to triangle ABC, meaning all corresponding angles are equal and all corresponding sides are proportional with a scale factor of 1.
Therefore, triangle ABC is similar to triangle A"B"C" with a scale factor of 1, and they are also congruent due to identical size and shape.

Standard: G.SRT.A.1 | DOK: 4

Multiple select📘 A.APR.C.1🧠 DOK 4

Question:

Which of the following polynomial identities can be used to derive numerical relationships similar to the way the difference of two squares or the sum and difference of two cubes can? Select all that apply.

Answer Choices:

A) (x^2 - y^2)^2 = (x-y)^2(x+y)^2
B) (x^3 + y^3) = (x + y)(x^2 - xy + y^2)
C) (x^2 + y^2)^2 - (x^2 - y^2)^2 = 4x^2y^2
D) (x^4 - y^4) = (x^2 - y^2)(x^2 + y^2)
E) (x^3 - y^3) = (x - y)(x^2 + xy + y^2)

✅ Answer:

(x^3 + y^3) = (x + y)(x^2 - xy + y^2); (x^2 + y^2)^2 - (x^2 - y^2)^2 = 4x^2y^2; (x^3 - y^3) = (x - y)(x^2 + xy + y^2)

💡 Explanation:

Polynomial identities such as the sum of cubes, difference of cubes, and certain quadratic identities can be used to derive numerical relationships and solve algebraic equations.
Specifically, the identity (x^3 + y^3) = (x + y)(x^2 - xy + y^2) and (x^3 - y^3) = (x - y)(x^2 + xy + y^2) are analogous to the sum and difference of cubes, while (x^2 + y^2)^2 - (x^2 - y^2)^2 = 4x^2y^2 can be used to generate Pythagorean triples, similar to the difference of squares.

Standard: A.APR.C.1 | DOK: 4

Dropdown📘 L.VL.5.2.b🧠 DOK 2

In the ancient world, philosophers often debated the concept of 'telepathy,' derived from the Greek roots 'tele,' meaning distant, and 'pathy,' meaning feeling. They pondered whether it was possible to communicate thoughts and feelings over great distances without any physical interaction. This idea fascinated many, leading to various experiments and fictional stories. Today, telepathy remains a popular theme in science fiction.

Question:

In the passage, the word 'telepathy' is used. Based on the Greek roots provided, what does 'telepathy' mean?

Answer Choices:

A) Communication through technology
B) Distant feeling
C) Instant messaging
D) Emotional bonding

✅ Answer:

Distant feeling

💡 Explanation:

The word 'telepathy' is derived from the Greek roots 'tele,' meaning distant, and 'pathy,' meaning feeling.
Thus, 'telepathy' refers to the concept of feeling or communication over a distance.

Standard: L.VL.5.2.b | DOK: 2

Multiple select📘 RI.CI.7.2🧠 DOK 2

The Amazon rainforest, often referred to as the "lungs of the planet," produces over 20% of the world's oxygen. It is home to a vast array of wildlife, including thousands of species of birds, mammals, and insects, many of which are not found anywhere else on Earth. Deforestation is a significant threat to this vital ecosystem, leading to loss of habitat and biodiversity. Conservation efforts are crucial to preserving the Amazon's unique environment and the global benefits it provides.

Question:

Which of the following statements convey the central idea of the passage? Select all that apply.

Answer Choices:

A) The Amazon rainforest is critical for global oxygen production.
B) Deforestation poses a threat to the Amazon's biodiversity.
C) Conservation is important for preserving the Amazon.
D) The Amazon is home to a variety of unique species.

✅ Answer:

The Amazon rainforest is critical for global oxygen production.; Deforestation poses a threat to the Amazon's biodiversity.; Conservation is important for preserving the Amazon.

💡 Explanation:

The central idea of the passage is that the Amazon rainforest is vital to the planet's health, providing oxygen and supporting biodiversity, and it is under threat from deforestation.
Conservation efforts are necessary to protect it.
The details about oxygen production, biodiversity, and conservation all convey this idea, while the mention of unique species is a specific detail rather than part of the central idea.

Standard: RI.CI.7.2 | DOK: 2

Short answer📘 5.NF.A.2🧠 DOK 1

Question:

Sarah has $\frac{3}{4}$ of a pound of candy. She buys $\frac{2}{3}$ of a pound more. How much candy does she have now in total?

✅ Answer:

$\frac{17}{12}$ or 1 $\frac{5}{12}$ pounds

💡 Explanation:

To find the total amount of candy Sarah has, add the two fractions: $\frac{3}{4} + \frac{2}{3}$ .
To add these fractions, find a common denominator, which in this case is 12.
Convert $\frac{3}{4}$ to $\frac{9}{12}$ and $\frac{2}{3}$ to $\frac{8}{12}$ .
Add the fractions: $\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$ .
This can also be expressed as the mixed number 1 $\frac{5}{12}$ pounds.

Standard: 5.NF.A.2 | DOK: 1

Multiple choice📘 N.CN.B.4🧠 DOK 4

Question:

Given the complex number z = 3 - 4i, convert this number into its polar form and determine which of the following options correctly represents z in polar form.

Answer Choices:

A) A) 5(cos(53.13°) + i sin(53.13°))
B) B) 5(cos(306.87°) + i sin(306.87°))
C) C) 5(cos(36.87°) + i sin(36.87°))
D) D) 5(cos(233.13°) + i sin(233.13°))

✅ Answer:

B) 5(cos(306.87°) + i sin(306.87°))

💡 Explanation:

To convert the complex number z = 3 - 4i into polar form, we first find the magnitude: |z| = sqrt(3^2 + (-4)^2) = 5.
The argument θ is found using tan(θ) = -4/3.
The correct angle in the fourth quadrant is θ = 306.87°.
Thus, the polar form is 5(cos(306.87°) + i sin(306.87°)).

Standard: N.CN.B.4 | DOK: 4

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