Find the excluded values

Therefore, using algebra, Laura is 14 years old and Juan is 21 years old.

Mathematical symbols and the rules for manipulating them are the focus of the discipline of study known as algebra. In order to express unknowable quantities, it makes use of symbols and variables as well as the study of mathematical equations and their characteristics. In algebra, numbers and mathematical operations are represented by letters and symbols in mathematical expressions and equations.

Let x be Laura's age and y be Juan's age.

Use the given information to set up two equations:

y = x + 7 (Juan is 7 years older than Laura)

xy = 294 (The product of their ages is 294 years)

Substitute the first equation into the second equation to get:

x(x + 7) = 294

Simplify the equation by expanding the left side:

x² + 7x = 294

Move all the terms to the left side of the equation:

x² + 7x - 294 = 0

Solve for x by factoring the left side of the equation or using the quadratic formula. Here, we'll use factoring:

(x + 21)(x - 14) = 0

This gives us two possible solutions for x: x = -21 or x = 14.

Since we're looking for age, we can discard the negative solution, x = -21.

Therefore, Laura's age is x = 14.

To find Juan's age, use the first equation and substitute the value of x:

y = x + 7

y = 14 + 7

y = 21

Therefore, Juan's age is y = 21.

So the ages we're talking about are Laura being 14 years old and Juan 21 years old.

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Your question is in Spanish. The English translation is:

Juan is 7 years older than Laura. The product of their ages is 294 years. What age numbers are we talking about?

The volume of the composite object can be calculated as approximately: 285 ft³.

The composite object is composed of a cylinder and a rectangular prism, therefore:

The volume of the composite object = volume of cylinder + volume of rectangular prism

Volume of cylinder = πr²h

radius (r) = 1/2(4) = 2 ft

height (h) = 5 ft

Volume of cylinder = 3 * 2² * 5 = 60 ft³

Volume of rectangular prism = length * width * height

= 9 * 5 * 5

= 225 ft³

Volume of the composite object = 60 + 225 = 285 ft³.

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The angle taken in a clockwise direction from north to southeast is 135 degrees

When measuring angles, it is common to use a reference direction, such as north, as a starting point. In this case, we are measuring an angle in a clockwise direction from north to southeast. Southeast is located halfway between the directions of south and east, which means it is at a 45-degree angle from each of those directions.

Therefore, the angle from north to southeast is 45 degrees more than a right angle, which is 90 degrees. This gives us a total of 135 degrees. Visualizing this on a compass rose can help to understand the direction and angle more clearly.

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The given question is incomplete, the complete question is:

What is the angle taken in a clockwise direction from north to southeast ?

The effect on the graph of a function when the y-intercept is changed to a smaller positive number depends on the type of function.

If the function is linear and contains the formula y = mx + b, where m denotes the slope and b the y-intercept, then shifting the slope of the y-intercept to a smaller positive value will cause the entire graph to move vertically downward. The magnitude of the change in the y-intercept determines how far the graph goes downward.

On the other hand, since the shape of the function is not linear, changing the y-intercept will typically have a more complicated impact on the graph if the function is a nonlinear function, such as a quadratic or exponential function. The specific form of the function will determine the exact effect.

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Since Diego and Armando were known to have attended the Regional Congress of Indigenous Languages for Latin America as well as the Caribbean, and thus they were able to write the conclusion that is "If people respect differences and act with justice, then human beings will not harm others."

In terms of a) Symbolization:  we can make p to be the proposition that is "people respect differences", and also q to be the proposition that is "people act with justice", and lastly, r can act as the proposition "human beings harm others". Hence the conclusion will be: p ∧ q → ¬r.

In terms of question 2, the Translate situations:

a) The problem scenario is about the Regional Congress of Indigenous Languages that is made for Latin America and the Caribbean, and it is one that is aimed to set up responsible commitments for the promotion, safeguarding, etc.

b) The statement in the underlined text is one tht is said to be: "If people respect differences and act with justice, then human beings will not harm others."

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See text below

1. Analiza la situación.

En el mes de septiembre del ano 2019 se llevó a cabo, en el Cusco, el Congreso Regional de Lenguas Indigenas para América Latina y el Ca ribe, cuyo fin era establecer compromisos responsables de promoción, salvaguardia, uso y desarrollo de las lenguas originarias a nivel regio nal. Diego y Armando, estudiantes universitarios, asistieron a dicho evento y al finalizar escribieron algunas conclusiones, entre ellas:

"Si las personas respetan las diferencias y actúan con justicia, enton- ces el ser humano no danara al prójimo".

Simboliza el texto subrayado, elabora su tabla de verdad y determi- na si se trata de una tautologia, contingencia o contradicción.

2. Traduce situaciones.

a. ¿De qué se trata la situación problemática? Explica brevemente.

CONGRESO REGI DE LENGUAS INDIGENA AMERICA LATINA Y EL

b. Identifica, en el texto subrayado, algunos enunciados y escribelos.

3. Comunica su comprensión sobre situaciones.

a. Representa de forma simbólica las proposiciones encontradas.

b. Representa las proposiciones usando los conectivos lógicos.

4. Usa estrategias y procedimientos.

¿Qué estrategia utilizarías para resolver la situación problemática?

5. Argumenta afirmaciones.

a. Explica cómo identificas a una proposición.

b. Una tautologia se reconoce porque todos los valores de verdad de su matriz principal son falsos.

c. ¿Por qué crees necesario saber reconocer una proposición simple de una compuesta?

1. Analyze the situation.

In the month of September of the year 2019, the Regional Congress of Indigenous Languages ​​for Latin America and the Caribbean was held in Cusco, the purpose of which was to establish responsible commitments for the promotion, safeguarding, use and development of native languages ​​to regional level. Diego and Armando, university students, attended said event and at the end they wrote some conclusions, among them:

"If people respect differences and act with justice, then human beings will not harm others."

Symbolize the underlined text, create its truth table, and determine if it is a tautology, contingency, or contradiction.

2. Translate situations.

to. What is the problem situation about? Explains briefly.

REGI CONGRESS OF INDIGENOUS LANGUAGES IN LATIN AMERICA AND THE

b. Identify, in the underlined text, some statements and write them.

3. Communicates understanding of situations.

to. Symbolically represents the propositions found.

b. Represent statements using logical connectives.

4. Use strategies and procedures.

What strategy would you use to solve the problematic situation?

5. Argue affirmations.

to. Explain how you identify a proposition.

b. A tautology is recognized because all the truth values ​​of its main matrix are false.

c. Why do you think it is necessary to know how to recognize a simple proposition from a compound one?

Thus, we get a total of 27 seven-digit phone numbers that begin with a three-digit prefix that has the property you described.

We need to find all seven-digit phone numbers that begin with a three-digit prefix that equals the product of the last four digits.

To do this, we can start by noting that the three-digit prefix can be written as XYZ, where X, Y, and Z are digits. We also know that the last four digits must have a product of XYZ. Let's call the last four digits W, P, Q, and R. Then we have:

W x P x Q x R = XYZ

We can simplify this equation by dividing both sides by XYZ:

(W x P x Q x R) / XYZ = 1

Now we can start counting the number of possible phone numbers that satisfy this equation. We can do this by systematically trying out different values for X, Y, and Z and seeing how many possibilities we get for W, P, Q, and R. Here are the possibilities:

X = 1: In this case, we need to find all four-digit numbers that have a product of 1YZ. The only possibility is 1111, which gives us one seven-digit phone number.

X = 2: In this case, we need to find all four-digit numbers that have a product of 2YZ. The possibilities are 2222, 2211, and 2111. This gives us three seven-digit phone numbers.

X = 3: In this case, we need to find all four-digit numbers that have a product of 3YZ. The possibilities are 3333, 3311, 3222, 3211, and 3111. This gives us five seven-digit phone numbers.

X = 4: In this case, we need to find all four-digit numbers that have a product of 4YZ. The possibilities are 4444, 4322, 4311, and 4222. This gives us four seven-digit phone numbers.

X = 5: In this case, we need to find all four-digit numbers that have a product of 5YZ. The possibilities are 5555, 5422, 5411, 5322, and 5311. This gives us five seven-digit phone numbers.

X = 6: In this case, we need to find all four-digit numbers that have a product of 6YZ. The possibilities are 6666, 6511, and 6422. This gives us three seven-digit phone numbers.

X = 7: In this case, we need to find all four-digit numbers that have a product of 7YZ. The only possibility is 7777, which gives us one seven-digit phone number.

X = 8: In this case, we need to find all four-digit numbers that have a product of 8YZ. The possibilities are 8644 and 8633. This gives us two seven-digit phone numbers.

X = 9: In this case, we need to find all four-digit numbers that have a product of 9YZ. The possibilities are 9999, 9811, and 9722. This gives us three seven-digit phone numbers.

Adding up all of the possibilities, we get a total of 27 seven-digit phone numbers that begin with a three-digit prefix that has the property you described.

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(a)Probability of landing on A = 3/4 = 0.75 or 75%.

(b)The probability of the spinner landing on A or B is 100%, which means it is certain that the spinner will land on either A or B.

In part (a), we are asked to find the probability that the spinner will land on the letter A. The spinner has 4 sides and 3 of those sides have the letter A on them, so the probability of landing on A is 3/4. We can also express this probability as a percentage by multiplying 3/4 by 100%, which gives us 75%. Therefore, there is a 75% chance that the spinner will land on the letter A.

In part (b), we are asked to find the probability that the spinner will land on A or B. There are 4 sides on the spinner and 3 of them have the letter A, while only 1 of them has the letter B. To find the probability of landing on A or B, we add the number of sides with A or B, which gives us 3 + 1 = 4. Then, we divide this by the total number of sides on the spinner, which is 4. This gives us a probability of 4/4 or 1. We can also express this probability as a percentage by multiplying 1 by 100%, which gives us 100%. Therefore, there is a 100% chance that the spinner will land on either A or B.

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complete question:

Jenny spins a fair 4-sided spinner with the letters A B A and A on it

a) What is the probability that the spinner will land on A?

b) What is the probability that the spinner will land on A or B?​

Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together

Volume is calculated in units cubed because it is a measure of how much three-dimensional space an object occupies.

Volume = Length×Width×Height

=3×3×3

=27 cubic units

Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together.

This is why it is usually represented in units cubed.

Hence, Volume is the amount of space an object takes up, and is calculated by multiplying the object's length, width, and height together

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The quadratic function that could represent p is: [tex]p(x) = x^2 - 9[/tex].

What is quadratic function?

A quadratic function is a function that can be written in the form f(x) = [tex]ax^2 + bx + c[/tex], where a, b, and c are constants, and x is the variable. It is a type of polynomial function of degree 2, which means that the highest power of x in the equation is 2.

If the solutions to the quadratic equation p(x) = 0 are x = -3 and x = 3, we know that the factors of p(x) must be (x + 3) and (x - 3), since these are the expressions that yield zero when evaluated at -3 and 3, respectively. Therefore, a possible quadratic function p(x) that has these solutions is:

p(x) = (x + 3)(x - 3)

Expanding the expression using FOIL method, we get:

[tex]p(x) = x^2 - 9[/tex]

So, the quadratic function that could represent p is:

[tex]p(x) = x^2 - 9.[/tex]

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The data distribution is skewed and the mean of the number of emails is less than the median number of emails.

The median is equal to 22.

The mean is equal to 20.2.

In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the 10 observations from the least to greatest as follows:

15, 16, 18, 19, 22, 22, 22, 22, 23, 23

Median = (22 + 22)/2

Median = 22.

In Mathematics, the mean for a set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Mean = [15+16+18+19+22+22+22+22+23+23]/10

Mean = 202/10

Mean = 20.2

In conclusion, we can logically deduce that the data distribution is skewed to the left because the mean is less than the median.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The value of the standard form for the equation of a circle is,

⇒ (x - 5/2)² + (y - 9/2)² = (3/√2)²

We have to given that;

Circle have a diameter that has endpoints (- 2, 9) and (7, 0).

Hence, The radius of circle is,

We can find the distance the between given points as;

⇒ d = √(7 - (- 2))² + (0- 9)²

⇒ d = √81 + 81

⇒ d = 3√2

Hence, The radius of circle is,

⇒ r = 3√2/2

⇒ r = 3/√2

And, Center of the circle is,

⇒ (- 2 + 7 / 2, 9 + 0/2)

⇒ (5/2, 9/2)

Thus, The value of the standard form for the equation of a circle is,

⇒ (x - 5/2)² + (y - 9/2)² = (3/√2)²

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The mean number of correct answers that the student can expect to guess correctly is 9, and the variance of the number of correct answers is 7.2.

The mean and variance of this binomial distribution can be calculated using the formula:

where n is the number of trials, and p is the probability of success (i.e. guessing the correct answer) on each trial.

In this case, n = 45 (the number of questions) and p = 1/5 (the probability of guessing the correct answer on each question, assuming all choices are equally likely).

Thus, the mean is:

mean = n * p = 45 * (1/5) = 9

And the variance is:

variance = n * p * (1 - p) = 45 * (1/5) * (4/5) = 7.2

Therefore, the mean number of correct answers that the student can expect to guess correctly is 9, and the variance of the number of correct answers is 7.2.

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The required plant grew 9 centimeters in the sixth week.

Let x be the number of centimeters the plant grew in the sixth week.
To estimate x, we can use the formula for the mean (average) of a set of numbers:

mean = (sum of numbers) / (number of numbers)

We know the mean for 6 weeks is 9, so we can write:

9 = (13 + 6 + 10 + 5 + 11 + x) / 6

Multiplying both sides by 6, we get:

54 = 45 + x

Subtracting 45 from both sides, we get:

x = 9

Therefore, the plant grew 9 centimeters in the sixth week.

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The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

To solve for x in the measures of the exterior angles of a triangle, use the formula 180°=6x°+8x°+10x°. Rearranging to isolate x, we get x=180°/24x°=7.5. Therefore, x=7.5°.

Conclusion: The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

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The triangle has exterior angles measuring 90°, 120°, and 150° and value of x is 15.

What is Angle?

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

The sum of the exterior angles of any triangle is always 360 degrees.

Therefore, we can set up the equation: 6x° + 8x° + 10x° = 360°

Simplifying the left side of the equation, we get: 24x° = 360° Dividing both sides by 24, we get: x° = 15°

Therefore, the measures of the exterior angles of the triangle are: 6x° = 6(15°) = 90°

8x° = 8(15°) = 120°

10x° = 10(15°) = 150°

So the triangle has exterior angles measuring 90°, 120°, and 150°.

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The equivalent expression of the function using the distributive property is determined as  x² + 11x + 18.

The equivalent expression can be obtained by using distributive property as shown below;

The given expression = ( x + 2 ) ( x + 9 )

Using distributive property, we will have the following;

( x + 2 ) ( x + 9 ) = x ( x + 9 ) + 2 ( x + 9 )

x ( x + 9 ) + 2 ( x + 9 ) = x² + 9x + 2x + 18

x² + 9x + 2x + 18 = x² + 11x + 18

Thus, the equivalent expression is determined using  distributive property.

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Required sum of interior angles of the kite is 360°.

What is kite?

A quadrilateral with two pairs of adjacent sides which are congruent is called kite. Total number of sides are four.

Let the kite has vertices A, B, C,D and the lengths of its diagonals are d_1 and d_2.

The interior angles of a kite can be found using the following formulas:

[tex]∠A = ∠C = \frac{(180° - ∠B - ∠D)}{ 2} \\ ∠B = ∠D = \frac{(360° - (∠A + ∠C)) }{2}[/tex]

We know sum of interior angles = (n-2) × 180°

Where n is number of sides.

Here number of sides are 4.

So, sum of interior angles of kite = (4-2)×180° = 2×180° = 360°

Therefore required sum of interior angles is 360°.

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Correct question is " What is the sum of interior angles of a kites for A,B,C,D ?"

In the variation, the value of z is -6, when x = 10 and y = -7.

The value of z is calculated as follows;

x = ky/z

where;

k = xz/y

k = (20 x 6 ) / 14

k = 8.5714

In the variation, the value of z, when x = 10 and y = -7 is calculated as follows;

z = (ky) / x

z = (-8.5714 x 7 ) / (10)

z = -6

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The answer of the given question based on the Scale factor is , Part (a) the dimensions of the print are 3.51 feet by 6 feet. , Part (b) the area of the print is 21.06  feet².

Dimension refers to the measurement or size of an object in terms of length, width, and height. It can also refer to the number of parameters or variables that are required to describe a system or phenomenon.

Part A:

To find the dimensions of the print in feet, we need to first find the dimensions of the original painting in feet, and then multiply them by the scale factor of 3.

The width of the painting in feet is 14 inches divided by 12 inches/foot, which is:

14/12 = 1.17 feet

The length of the painting in feet is 24 inches divided by 12 inches/foot, which is:

24/12 = 2 feet

Multiplying these dimensions by the scale factor of 3, we get:

Width of print = 1.17 feet x 3 = 3.51 feet

Length of print = 2 feet x 3 = 6 feet

Therefore, the dimensions of the print are 3.51 feet by 6 feet.

Part B:

To find the area of the print in square feet, we need to multiply the width and length of the print together. Using the dimensions we found in Part A, we get:

Area of print = width x length

Area of print = 3.51 feet x 6 feet

Area of print = 21.06  feet²

Therefore, the area of the print is 21.06 feet².

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Expressing the function F(2x - 1) in the form ax² + bx + c when F(x) = x² - 3x - 5 we get,

F(2x - 1) = 4x² - 10x - 3 and here  a = 4, b = -10 and c = -3

Given that the standard function is given by,

F(x) = x² - 3x - 5

We have to express the F(2x - 1) in the form ax² + bx + c.

In order to find F(2x - 1) we have to replace x with 2x - 1.

So, F(2x - 1) = (2x - 1)² - 3(2x - 1) - 5

F(2x - 1) = (2x)² + 1² - 2*2x*1 - 3*2x - 1*(-1) - 5

F(2x - 1) = 4x² + 1 - 4x - 6x + 1 - 5

F(2x - 1) = 4x² - 10x - 3

So comparing it with ax² + bx + c we get, a = 4, b = -10 and c = -3.

Hence, F(2x - 1) = 4x² - 10x - 3

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In conducting a regression analysis, extrapolation is performed when one whishes to (A) predict beyond the limit of the sample

Extrapolation is the process of using a regression equation to make predictions beyond the range of the observed data. It involves extending the regression line or curve beyond the observed data points and predicting the values of the dependent variable for values of the independent variable that are outside the range of the observed data.

Determining cause and effect involves testing a hypothesis or theory about the relationship between variables. Lag variables are used as explanatory variables when there is reason to believe that the effects of a variable on the dependent variable are delayed or occur over time. Filling in gaps for missing observations involves imputing values for missing data points in the observed data set.

Therefore, the correct option is (A) predict beyond the limit of the sample.

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The given question is incomplete, the complete question is:

In conducting a regression analysis, extrapolation is performed when one whishes to :

A. predict beyond the limit of the sample

B. determine cause and effect

C. use a lag variable as an explanatory variable

D. fill in gaps for missing observations

The fraction which is greater then "3/8" by using "8" in denominator is "1/2", and the process to check that the answer is correct is explained below.

To write a fraction that has a value greater than 3/8 using 8 as the denominator, we need to find a fraction whose numerator is greater than 3.

One possible fraction is 4/8, which simplifies to 1/2.

To check why this fraction is greater than 3/8, we compare the sizes of the equivalent fractions with a common denominator:

⇒ 3/8 = 3/8, and

⇒ 1/2 = 4/8,

Since, fraction "4/8' is greater than "3/8", we can say that "1/2" is greater than "3/8".

Another way to check is to convert both fractions to decimals:

⇒ 3/8 = 0.375,

⇒ 1/2 = 0.5,

Since 0.5 is greater than 0.375, we confirm that 1/2 is greater than 3/8,

Therefore, one fraction that has a value greater than 3/8 using 8 as the denominator is 1/2.

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If in a family one of children is a boy, then probability that both children are boys is 1/3.

Let the child born is a boy be denoted as "b" and

Let the child born is a girl be denoted as "g",

Let "S" = event that a family has "two-children",

So, "S" is = {(g, b), (b, g), (g, g), (b, b)},

The number of elements in "S" is ⇒ n(S) = 4,

Let "A" denote the event that "at-least" single-child is a boy.

So, "A" = {(g, b), (b, g), (b, b)} and

The number of elements in "A" is ⇒ n(A) = 3,

Let "B" denote the event that both child are boys,

So, "B" = {(b, b)},

The probability that one is a boy is ⇒ P(A) = n(A)/n(S),

⇒ P(A) = 3/4,

The probability that both are boys is given as P(B) = n(B)/n(S),

⇒ P(B) = 1/4,

We see that, A∩B = {(b, b)},

So, number of elements in event-set "A∩B" is = n(A∩B) = 1,

The probability of "event-A" occurring and "event-B" occurring is :

⇒P(A∩B) = n(A∩B)/n(S)

⇒ P(A∩B) = 1/4,

By conditional probability, we know that probability of "B" given that "A" is happening is given as : P(B|A) = P(A∩B)/P(A), where P(A∩B) is = probability of "A" and "B" both happening and P(A) is probability of "A" happening.

⇒ P(B|A) = (1/4)/(3/4),

⇒ P(B|A) = 1/3.

Therefore, the required probability is 1/3.

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The amount of income tax for a couple claiming married filing jointly status for a year would be = $108,124.75

To calculate the income tax first determine the range where the salary of the each individual falls using the table given above.

That is;

For Mr Slater, his salary income of $57,235, fell within $18,501 to $75,300 and the percentage tax income = 15%

That is, 15/100 × 57,235/1

= 858525/100

=$8,585.25

Therefore the income of Mr Slater after tax = 57,235- 8,585.25 = $48,649.75

For Mrs Slater, her salary income of $79,300 fell within range of $75,301 to $151,900 and the tax percentage = 25%.

That is , 25/100 × 79,300

= 1982500/100

= $19,825

Therefore the income of Mrs Slater after tax = 79,300-19,825 = $59,475

Therefore, the amount of income tax for a couple claiming married filing jointly status for a year would be =$48,649.75+$59,475

= $108,124.75

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The parallelogram with the given vertices is a,

7. None of the shapes.

8. Rectangle.

7. Parallelogram with vertices A(-2, -2), B(-3, 3), C(2, 0), D(-1, -5)

Using the distance formula,

AB = √(-3 + 2)² + (3 + 2)² = √1 + 25 = √26

BC = √(2 + 3)² + (0 - 3)² = √25 + 9 = √34

Adjacent sides are not equal.

So this is not a square or a rhombus.

AC = √(2 + 2)² + (0 + 2)² = √20

BD = √(-1 + 3)² + (-5 - 3)² = √68

This is not a rectangle since the diagonals are not equal.

8. L(-3, -4), M(3, 3), N(4, -3), O(-2, -2)

Using the distance formula,

LM = √36 + 49 = √85

MN = √1 + 36 = √37

Not a square or a rhombus.

LN = √49 + 1 = √50

MO = √25 + 25 = √50

Diagonals are equal, so it is a rectangle.

Hence the first one is none and the second one is a rectangle.

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Answer:

3/1

Step-by-step explanation:

3/1 the ratio is 3:1

Using combination, there are 424,110 ways to form a committee consisting of 4 teachers and 5 students.

This is a combination problem, as we are selecting a group of individuals from a larger set.

The number of ways to select 4 teachers from the 11 eligible teachers is:

C(11,4) = 11! / (4! * 7!) = 330

Similarly, the number of ways to select 5 students from the 13 eligible students is:

C(13,5) = 13! / (5! * 8!) = 1287

To find the total number of ways to form the committee, we need to multiply these two values:

330 * 1287 = 424,110

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The total number of kilometres that Calvin has swum in these competitions would be = 3 kilometres.

The total number of 400 meters races he covered = 5

The total number of 200 meters races he covered = 5

Therefore the total meters he swum;

= (400×5) + (200×5)

= 2000+1000

= 3000m

But 1 km = 1000m

3000m = 3km

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14/42, 21/63 and  70/210 are the three fractions proportional to the fraction of sharpened pencils.

If Gary has a box of pencils and in the box, 7/21 of the pencils have been sharpened, the three fractions are proportional to the fraction of sharpened pencils in Gary's box by multiplying the numerator and denominator by the same value as  shown:

For the first fraction

7/21 * 2/2= 14/42

For the second fraction

7/21 * 3/3= 21/63

For the third fraction

7/21 * 10/10= 70/210

Hence the three fractions are proportional to the fraction of sharpened pencils in Gary's box are 14/42, 21/63 and  70/210

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