A graph titled Monthly Sales and Advertising Costs has Advertising Costs (1,000 dollars) on the x-axis and sales (1,000 dollars)

Each 16-ounce serving contains 330 mg of caffeine. For 8-ounce servings:
330 mg divided by 2 equals 165 mg.
The limit for caffeine intake is capped at 600 mg.
Calculating for three servings: 165 mg * 3 = 495 mg, which is under the limit.
Calculating for four servings: 165 mg * 4 = 660 mg, exceeding the maximum amount.
Thus, a person can consume 3 full 8-ounce servings daily while remaining within the safety limit.

<span>9 ten thousandths equals 0.0009, which can be expressed as 9 × 10 to the power of -4</span>

Response:

A) The preferred colors of kindergarten students

B) The growth heights of tomato plants that were all planted on the same day

E) The age ratings (G, PG, PG-13, R) assigned to films released in 2019

Clarification:

A normal distribution is characterized by a bell-shaped curve where a majority of data points cluster near the average. Instances pertaining to intelligence, height, blood pressure, student evaluations, shoe sizes, birth weights, citizen incomes, stock market data, and random events like rolling dice or flipping coins, are examples that can be well-described using a normal distribution. The central limit theorem is applicable here, considering that various independent factors impact a particular characteristic.

Response:

Anna's walk represented as a vector is shown in , please refer to the attachment.

Explanation:

Assuming the origin is point 1, where Anna begins her walk.

She walks 80 meters in a straight line at an angle of 33° north of east from point 1, as illustrated below.

Breaking this down into vector components, the vertical component amounts to 80Sin33°, and the horizontal component to 80Cos33°, as depicted in figure (2).

Anna's walk represented as a vector is

Therefore, Anna's walk can be illustrated as a vector depicted in .

Answer:

a) True

b) True

c) False

d) True

e) True

f) True

g) True

Step-by-step breakdown:

Let A denote a set. The element a is part of A if and only if a∈A.

a) The sole element of {∅} is ∅, so it follows that ∅∈{∅}.

b) The elements of {∅, {∅}} are ∅ and {∅}, thus ∅ ∈ {∅, {∅}}.

c) As {∅} solely contains ∅, it is clear {∅}≠∅ due to {∅} having one element while ∅ has no elements. Hence, {∅} ∉ {∅} since {∅} is not an element of {∅}.

d) The one element in {{∅}} is {∅}. Thus, {∅} ∈ {{∅}}.

e) The items in {∅, {∅}} include ∅ and {∅}. The only element of {∅} is ∅. Thus, every element of {∅} appears in {∅, {∅}} too, leading to {∅} ⊂ {∅, {∅}}.

f) With elements of {∅, {∅}} being ∅ and {∅}, and since the only element of {{∅}} is {∅}, we determine that {{∅}} appears in {∅, {∅}}, which means {{∅}} ⊂ {∅, {∅}}.

g) The only element of {{∅}, {∅}} equals {{∅}} which is {∅}. Each element of {{∅}} is also within {{∅}}, therefore {{∅}} ⊂ {{∅}, {∅}}={{∅}}.