Explanation

Step 1: Calculate the expression

-3 + 12 = 9

Step 2: Compare the result to the options

Since √81 = 9 (because 9² = 81), the correct answer is √81.

Explanation

The distributive law for sets states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

Explanation

0.8 ÷ 0.1 = 8

Explanation

Exponential notation (scientific notation) is used to express very small (e.g., 0.0000001) or very large (e.g., 1000000000) quantities compactly by representing numbers as powers of 10.

Key Information:

Format: a × 10^n, where 1 ≤ a < 10 and n is an integer.

Used for very large or very small numbers.

Examples:

• Large number: 6.022 × 10^23 (Avogadro's number)
• Small number: 1.6 × 10^-19 (Charge of an electron)

Explanation

The pattern appears to be that the number on the right side of the equation is the last digit of the number on the left side.

The last digit of 57 is 7.

Explanation

Peacock, Pigeon, and Parrot:

Names are gender-neutral (can refer to males or females of the species).

• Peacock = Male/Female (though commonly used for males, the species is "peafowl").
• Pigeon = No distinct gender in the name.
• Parrot = No distinct gender in the name.

Peahen:

• Specifically refers to the female of the peafowl species.
• The male is called a peacock, making "peahen" gender-specific.

Explanation

Step 1: Recall the definition of a^0

Any non-zero number raised to the power of 0 is 1.

Step 2: Evaluate the options

𝑎/𝑎 = 1 (since any number divided by itself is 1, assuming 𝑎 ≠ 0)

𝑎^1−1 = 𝑎^0 = 1

Step 3: Determine the best answer

All the given options (𝑎/𝑎, 1, 𝑎^1−1) represent the value of 𝑎^0 correctly, assuming 𝑎 ≠ 0.

Explanation

The union of two sets A and B, denoted as A ∪ B, is the set of all elements that are in A, in B, or in both.

A = {𝑐, 𝑑, 𝑏, ℎ} and B = {𝑚, 𝑝, 𝑓, ℎ}

A ∪ B = {𝑐, 𝑑, 𝑏, ℎ, 𝑚, 𝑝, 𝑓}

Explanation

Cholesterol is a vital precursor in the biosynthesis of:

Vitamin D:

• Cholesterol converts to 7-dehydrocholesterol in the skin, which forms vitamin D₃ under UV light.

Steroid Hormones:

Cholesterol is the backbone for:

• Sex hormones (testosterone, estrogen, progesterone).
• Adrenal hormones (cortisol, aldosterone).

Explanation

Step 1: Evaluate the expression inside the parentheses

0.3 + 0.3 = 0.6

Step 2: Multiply 2 by the result

2 × 0.6 = 1.2

Step 3: Multiply 1.2 by 2

1.2 × 2 = 2.4