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Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)

The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.

Which graphical representation would be most appropriate for the data, and why?

Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
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The variable “nationality” is a “categorical variable” and the names do not have any order.

Therefore, “option D” is correct.

It is a type of “categorical variable” that cannot be arranged in any “particular order” and it does not have any “numerical” values.

A) The average grade point is a “quantitative variable” and it is not a “categorical variable”.

Therefore, “option A” is incorrect.

B) The variable no. of friends contains the numbers and hence it is a “quantitative variable”.

Therefore, “option B” is incorrect.

C) The variable “birth position” has an order so it is not a “nominal variable”.

Therefore, “option C” is incorrect.

D) The variable “nationality” is a “categorical variable” and the names do not have any order.

Therefore, “option D” is correct.

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The complete question is :

Which of the following student characteristics is an example of a nominal variable?

A)grade point average (3.2, 2.5, etc.)

B) number of friends (0, 1, etc.)

C)birth position in the family (first, second, etc.)

D)nationality (U.S., Japanese, etc

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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Answer: Try to insert 4 on the hypotenuse, or the longer side. Y would be 2 times the square root of 3 (just the symbol)

Step-by-step explanation:

여러가지 보이지 않은 벽들 때문에

한 사람의 외로움과 슬픔을 다 담을 순 없지만, 그래서 더 음악에 매달리게 되는 것

그대의 외로움 내가 다 알 수 없지만

내 표정이던 말투던, 목소리던

너를 안아줄 수만 있다면 참 좋겠다.

To calculate the wavelength λ1 for gamma rays of frequency f1 = 5.60×1021 hz, we can use the formula:
λ1 = c / f1, where c is the speed of light in a vacuum, which is approximately 3.00 × 108 m/s.
Plugging in the values, we get:
λ1 = (3.00 × 108 m/s) / (5.60×1021 hz) = 5.36 × 10^-14 m

Therefore, the wavelength λ1 for gamma rays of frequency f1 = 5.60×1021 hz is approximately 5.36 × 10^-14 meters.
To calculate the wavelength λ1 of gamma rays with frequency f1 = 5.60×10²¹ Hz, we can use the formula:

λ = c / f

Where λ is the wavelength, c is the speed of light (approximately 3.00×10^8 meters per second), and f is the frequency.

Step 1: Write down the given frequency:
f1 = 5.60×10²¹ Hz

Step 2: Write down the speed of light:
c = 3.00×10^8 m/s

Step 3: Use the formula to calculate the wavelength:
λ1 = c / f1
λ1 = (3.00×10^8 m/s) / (5.60×10²¹ Hz)

Step 4: Calculate λ1:
λ1 ≈ 5.36×10^-14 meters

So, the wavelength λ1 for gamma rays of frequency f1 = 5.60×10²¹ Hz is approximately 5.36×10^-14 meters.

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Answer:

Step-by-step explanation:

The solution to the given system of linear equations is (x, y) = (6, 13).

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants.

The given system of linear equations is:

2x - 3y = -27 ...(1)

-3 + 2y = 23 ...(2)

We can rewrite equation (2) as:

2y = 26

y = 13

Now, substitute the value of y = 13 into equation (1):

2x - 3(13) = -27

2x - 39 = -27

2x = -27 + 39

2x = 12

x = 6

Therefore, the solution to the given system of linear equations is (x, y) = (6, 13).

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Answer: B

Step-by-step explanation: a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

Answerits 2

Step-by-step explanation:

did the test

The probability that it will not rain in Switzerland on 1 September = 7/12

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event occurring, first, we should know the total number of possible outcomes.

The probability of rain is 5/12

probability of an event is 1

probability of not rain = 1-5/12

= 7 /12

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Answer:

37.0469 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify

Angle θ = 39°

Opposite Leg = 30

Adjacent Leg = x

Step 2: Solve for x

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.

To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:

Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))

For the first cooler, the probability of selecting a sports drink and a water bottle is:

(19/39) x (20/38) = 0.2498, or about 24.98%

For the second cooler, the probability of selecting a sports drink and a water bottle is:

(14/29) x (15/28) = 0.2586, or about 25.86%

Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.

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What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%

annual interest, compounded monthly?

Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=$120,000

t=12 years

r=14%=14/100=0.14

n=12

substitute in the given formula

Solve for P

Answer

- The solution of this compound inequality is x < 3 OR x ≥ 4

- The graph of this solution is attached below

- The interval notation is (-∞, 3) OR [4, ∞)

Explanation

The compound inequality to be solved is

6x - 3 < x + 12 OR 5x - 6 ≥ 3x + 2

To solve this, we solve each of the pair one at a time for the two-part solution

6x - 3 < x + 12

6x - x < 12 + 3

5x < 15

Divide both sides by 5

(5x/5) < (15/5)

x < 3

OR

5x - 6 ≥ 3x + 2

5x - 3x ≥ 6 + 2

2x ≥ 8

Divide both sides by 2

(2x/2) ≥ (8/2)

x ≥ 4

So, the solution is

x < 3 OR x ≥ 4

So, this solution says that x is less than 3, but greater than or equal to 4.

For the graph, Note that

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

This solution tells us that the wanted parts are numbers less than 3 and numbers greater than 4.

Also, in writing inequalities as interval, the signs (< or >) indicate an open interval and is written with the bracket () while the signs [≤ or ≥] denote a closed interval which is denoted by the brackets [].

x < 3, that is, x ranges from negative infinity to just before 3.

x < 3 is (-∞, 3)

x ≥ 4, that is, x ranges from 4 to infinity

x ≥ 4 is [4, ∞)

Hope this Helps!!!

Answer ok i will

Step-by-step explanation:

Answer:

Step-by-step explanation:

if one insect is 2.01 and the other 1.33

2.01-1.33=0.68 cm difference between insects

Answer:

7 m

Step-by-step explanation:

A square has 4 equal sides so the 4 sides must add up to 28.

28 / 4 = 7m

Answer: The tank which has 3 m side.

Step-by-step explanation: A cube is a form that has equal sides. To calculate the volume of it, multiply all three sides:

V = length*width*height

Since they are all the same, volume will be:

V = s³

One tank has a 3 m side, so its volume is:

V = 3³

V = 27 m³

The other has half of the first one side, then s = \(\frac{3}{2}\) and volume will be:

V = \((\frac{3}{2})^{3}\)

V = \(\frac{27}{8}\) m³

As you can see, the volume of the second tank is \(\frac{1}{8}\) smaller than the first one. Therefore, the tank which has 3 m side can store more water than the  tank with side measuring half of the first.

Management by objectives (MBO) is a management system that incorporates goal setting as its central principle.

It emphasizes the establishment of clear, measurable objectives for individuals and teams within an organization, aligning their efforts with overall organizational goals and strategies. MBO provides a framework for performance management and evaluation, allowing managers and employees to work together to define objectives, set targets, and track progress towards achieving those goals.

The goal-setting aspect of MBO is supported by various theories and principles. Firstly, the concept of goal setting itself is a fundamental component of MBO. It is based on the idea that setting specific, challenging, and attainable goals can motivate individuals and enhance performance. The expectancy theory comes into play as well, as MBO assumes that individuals are motivated to achieve their goals when they believe that their efforts will lead to successful performance and desired central outcomes.

Additionally, cognitive dissonance theory suggests that MBO can help reduce cognitive dissonance by providing individuals with clear objectives and performance expectations, minimizing conflicts between their attitudes and behaviors. While hedonism and equity theory are not directly incorporated into MBO, they may indirectly influence individuals' motivation and satisfaction as they work towards their objectives within the MBO framework.

In summary, Management by Objectives (MBO) is a management system that revolves around goal setting. It incorporates various theories and principles such as goal setting theory, expectancy theory, and cognitive dissonance theory. By setting clear objectives, aligning efforts, and tracking progress, MBO provides a structured approach to performance management and encourages individuals and teams to work towards achieving organizational goals.

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Answer:

5

Step-by-step explanation:

As seen in the figure, we know that because ΔABC is isosceles, ∠B = ∠C, so we know that 75 = 3x, x = 15. Next, following the rule that all angles in a triangle sum to 180°, we can set up this equation and solve it:

  4y + 10 + 75 + 75 = 180

                          4y = 180 - 160

                            y = 20

                         ∴ y = 5

Answer:

-60m

Step-by-step explanation:

the fish is 60m below sea level

Answer:

-60 m

Step-by-step explanation:

A fish is 60 m below the surface of the ocean.

Below=(Down/Negative)

Above=(Up/Positive)

(C) "gaffe"

A gaffe is a mistake. The text would read "His conduct at the state dinner was a cavalcade of blunders, one gaffe following another until the evening ended" if this phrase were added. The comma signifies that the word that is missing is equivalent to the word error.

A social misstep can be described using either the words "blunder" or "gaffe." The answer is not (A). A "query" is an enquiry or question. (B) is the wrong answer. Gibe is slang for a mocking comment.

The answer is not (D). Tryst is often used to describe an amorous encounter. The answer is not (E). An expression of appreciation, respect, or admiration is referred to as a "tribute.".

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To verify that g satisfies the hypotheses of the Mean Value Theorem on the interval [0, 8], we need to ensure that two conditions are met:

1. Continuity: We need to check if g is continuous on the interval [0, 8]. This means that there should be no breaks, jumps, or holes in the graph of g over this interval. To verify continuity, we can examine if there are any vertical asymptotes, removable discontinuities, or jumps in the graph of g within the interval [0, 8].

2. Differentiability: We need to check if g is differentiable on the open interval (0, 8). This means that the derivative of g should exist and be finite at every point within the interval (0, 8). To verify differentiability, we can examine if the derivative of g exists and is finite for all values of x in the open interval (0, 8).

To summarize, to verify that g satisfies the hypotheses of the Mean Value Theorem on the interval [0, 8], we need to ensure that g is continuous on [0, 8] and differentiable on (0, 8). If both of these conditions are met, then g satisfies the hypotheses of the Mean Value Theorem on the interval [0, 8].

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The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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Answer:

weight = 57 Kg

Step-by-step explanation:

We require to find the length of the diagonal (d) piece of metal

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )

d = \(\sqrt{100}\) = 10

the length of the 5 pieces is then

8 + 8 + 6 + 6 + 10 = 38 m

the total weight of the 5 pieces is then

weight = 38 × 1.5 Kg = 57 Kg