La suma de las edades de Andrés, Carlos y Rodolfo es de 90 años. La edad de Andrés excede en 4 años a la edad de Carlos y en 11 a la de Rodolfo. Determina las edades de los tres

Dark chocolate usually takes longer to melt than milk chocolate, as shown by the fact that the median melting time for dark chocolate is higher than the median melting time for milk chocolate.

Based on the given box plots, it is most likely true that after 64 seconds, about half of the brands of milk chocolate are likely to melt, and none of the brands of dark chocolate are likely to melt.

After 259 seconds, none of the brands of milk chocolate are likely to melt, and about a quarter of the brands of dark chocolate are likely to melt.

This conclusion is based on the fact that the box plot for milk chocolate shows a wider spread of melting times, indicating more variation in melting times among the different brands.

while, the box plot for dark chocolate shows a narrower spread of melting times, indicating less variation in melting times among the different brands.

Therefore, Additionally, the median melting time for dark chocolate is higher than the median melting time for milk chocolate, indicating that dark chocolate generally takes longer to melt.

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The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)

A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.

Here is a regular pentagon with side length 21 in.

Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]

Here a= 21 in

So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.

             = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex]     "

             ≈758.73053 square in

              = 758.7 square in. ( rounded to the nearest tenth).

Hence the area of regular pentagon is 758.7 square in.

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Answer:

tesla: y = 25x + 50

acdc: y = 50x

Step-by-step explanation:

Emily paid M = 30 for the ice cream cones.

To find the amount Emily paid (M), we can set up an equation using the given information.
1. The cost of the ice cream cones is 24.
2. She got back 6 in change.
Using these facts, we can write the equation:

M - 24 = 6
Now, let's solve for M:
Step 1: Add 24 to both sides of the equation.
M - 24 + 24 = 6 + 24
Step 2: Simplify.
M = 30.

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Answer:

2) x = 3√5; y = 6;

3) x = 12√2; y = 12;

4) x = 45∘; y = 45∘;

5) x = 60∘; y = 30∘

Step-by-step explanation:

2) Use trigonometry:

[tex] \cos(60∘) = \frac{3}{y} [/tex]

Use the property of the proportion to find y:

[tex]y = \frac{3}{ \cos(60∘) } = \frac{3}{1} \div \frac{1}{2} = \frac{3}{1} \times \frac{2}{1} = 6[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {3}^{2} = {6}^{2} + {3}^{2} = 36 + 9 = 45[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{45} = 3 \sqrt{5} [/tex]

3) Use trigonometry:

[tex] \sin(45∘) = \frac{12}{x} [/tex]

Use the property of the proportion to find x:

[tex]x = \frac{12}{ \sin(45∘) } = \frac{12}{1} \div \frac{ \sqrt{2} }{2} = \frac{12}{1} \times \frac{2}{ \sqrt{2} } = 12 \sqrt{2} [/tex]

Use trigonometry:

[tex] \tan(45∘) = \frac{12}{y} [/tex]

Use the property of the proportion to find y:

[tex]y = \frac{12}{ \tan(45∘) } = \frac{12}{1} = 12[/tex]

4) Use trigonometry:

[tex] \tan(x∘) = \frac{3}{3} = 1[/tex]

x = 45∘

[tex] \tan(y∘) = \frac{3}{3} = 1[/tex]

y = 45∘

5) Use trigonometry:

[tex] \cos(x∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]

x = 60∘

[tex]x = \sin(y∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]

y = 30∘

Unit rate of commercials per hour is 12 commercials per hour based on division in mathematics.

We must divide the number of ads by the number of hours in order to determine the unit rate of commercials per hour.

Wendy watched her favourite television programmes for an hour or an hour and a half. There were 18 advertisements running at this time.

So, the unit rate of commercials per hour can be calculated as:

18 commercials ÷ 1.5 hours = 12 commercials per hour

So, it is possible to compute the number of ads each hour as follows: 18 commercials divided by 1.5 hours equals 12 commercials every hour.

Consequently, 12 commercials are broadcast each hour as the unit rate of commercials.

This indicates that while viewing her favorite television programes, Wendy saw 12 adverts every hour on average.

It's crucial to remember that unit rate come in handy when comparing two quantities that are measured using various units. In this instance, we were comparing two different units of measurement: the quantity of advertising and the amount of time in hours. By providing the rate at which the quantity is changing per unit of time, the unit rate enables us to meaningfully compare them.

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Let x be the number of weeks it will take Paul to save enough money to buy the skateboard.

In one week, Paul earns $5, so in x weeks he will earn 5x dollars.

Since he already has $25 saved, the total amount of money he will have after x weeks is:

5x + 25

To be able to buy the skateboard that costs $85, Paul needs to save up an additional:

85 - 25 = 60

Therefore, we can set up the following equation to find the number of weeks it will take Paul to save up enough money:

5x + 25 = 60

Simplifying and solving for x:

5x = 35

x = 7

Therefore, it will take Paul 7 weeks to save up enough money to buy the skateboard.

The equation that describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard is:

5w + 25 = 85

Answer:

the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Step-by-step explanation:

The system of linear equations can be written as:

y = (1/3)x

x + 3y = -6

To graph the system, we can graph each equation and find the point of intersection of the two lines.

The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).

The second equation can be written as:

y = (-1/3)x - 2

This has a slope of -1/3 and y-intercept of -2.

To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.

To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.

The graphs of the two equations intersect at the point (-3,-1).

Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Tina and Carl will use 6 and 12 ounces of clay, respectively. Tina uses 3/10 of the 20-ounce bucket and Carl uses 3/5 of the 20-ounce bucket.

To determine how much clay Tina and Carl will use, we need to first find the total amount of clay they will use together.

If 3/10 of the clay is used by Tina and 3/5 of the clay is used by Carl, we can find the total amount of clay used by adding these fractions:

3/10 + 3/5 = (3/10 * 1/2) + (3/5 * 1/2) (we multiply by 1/2 to find the common denominator of 10)

= 3/20 + 6/20

= 9/20

Therefore, Tina and Carl will use a total of 9/20 of the 20-ounce bucket of clay.

To find how much each of them will use, we can multiply the total amount of clay by each person's fraction:

Tina: (3/10) x 20 ounces = 6 ounces

Carl: (3/5) x 20 ounces = 12 ounces

Therefore, Tina will use 6 ounces of clay, while Carl will use 12 ounces of clay.

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Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5, how much of the clay each of them will use?

In order to identify all the prime numbers less than 200, a person will have to eliminate the multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13.

What are multiples?

   Multiples are products that result from multiplying any given number by whole numbers. They are obtained by multiplying a whole number by another whole number. Prime numbers are natural numbers that are greater than 1 and have no positive divisors other than 1 and the number itself.

 The number 1 is not considered a prime number. In order to identify all the prime numbers less than 200, the person will have to eliminate the multiples of the following additional numbers: Multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13

      The person will have to eliminate the multiples of all these numbers to complete the task of identifying all the prime numbers less than 200.

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The expressions, when written as products , would be:

To factor this expression, let's first rearrange the terms:

(81a² - c²) + (6bc - 9b²)

Now, we can see that the first part is a difference of squares, which can be factored as:

(9a - c)(9a + c)

However, the second part (6bc - 9b²) cannot be factored further as a product of binomials. So the expression can be written as:

(9a - c)(9a + c) + 6bc

1 - 25x² + 10xy - y²

This expression remains:

(1 - 5x + y)(1 + 5x + y)

Using the same rule as above.

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1) the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2) the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

Since f is an increasing function over its domain, if a < b, then f(a) < f(b).

We are given the inequality:

f(4x-3) ≥ f(2-x²)

Since f is increasing, this is equivalent to:

4x-3 ≤2-x²

Simplifying, we get:

x² + 4x - 5 ≥ 0

We can factor this inequality as:

(x + 5)(x - 1) ≥ 0

The solutions are x ≤ -5 or x >= 1.

However, we need to ensure that these solutions are within the domain of the function, which is given as (-8, 4).

The solution x ≤ -5 is not within the domain, so we can discard it. Therefore, the solution to the inequality is:

x ≥ 1

To summarize:

f(4x-3) ≥ f(2-x²) is equivalent to x² + 4x - 5 ≥ 0

The solution to x² + 4x - 5 ≥ 0 is x ≥ 1.

Therefore, the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2)
Since g is a decreasing function over its domain, if a < b, then g(a) > g(b).

We are given the inequality:

g(3² - 2x) ≥ g(3x - 2)

Since g is decreasing, this is equivalent to:

3² - 2x ≤ 3x - 2

Simplifying, we get:

11 ≤ 5x

The solution is x ≥ 11/5.

To summarize:

g(3² - 2x) ≥ g(3x - 2) is equivalent to 11 ≤ 5x.

The solution to 11 ≤ 5x is x ≥ 11/5.

Therefore, the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

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Thus, the two digits are 9 and 11.

Two-variable equations are algebraic equations that involve two variables, typically x and y, and describe a relationship between them.

Let's call the tens digit "T" and the ones digit "O". Based on the problem, we know that:

T = 2 + O

Then substitute this equation in 10T + O = 10O + T + 27 i.e.

10T + O = 10O + T + 27

10T - T = 10O - O + 27

9T = 9O + 27

9(2 + O) = 8O + 27

9(2 + O) = 8O + 27

18 + 9O = 8O +  27

9O - 8O =  27 - 18

O = 9

Then,

T = 2 + 9

T = 2 + 9

T = 11

Thus, the two digits are 9 and 11.

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The statements that describe the graph of f function are A) Asx → ∞, f(x) → -4 and C) The y-intercept is (0, -3).

Let's analyze the given function:

f(x) = 9(1/3)ˣ⁺² - 4

Now, let's analyze the properties of the graph:

A) As x → ∞, f(x) → -4.

As x → ∞, the exponential term ((1/3)ˣ⁺²) approaches 0, so f(x) = 9(0) - 4 = -4. This statement is correct.

B) As x → -∞, f(x) → -∞.

As x → -∞, the exponential term (1/3)ˣ⁺² approaches ∞, so f(x) = 9(∞) - 4 → ∞, not -∞. This statement is incorrect.

C) The y-intercept is (0, -3).

To find the y-intercept, we can plug x = 0 into the function:

f(0) = 9(1/3)ˣ⁺² - 4 = 9(1/9) - 4 = 1 - 4 = -3

The y-intercept is (0, -3), so this statement is correct.

D) The domain is {x | x > -2}

This is incorrect. The domain of the given function is all real numbers because there is no restriction on the value of x.

E) The range is the set of real numbers.

This is incorrect. The range of the given function is {y | y > -4} since the function approaches -4 as x goes to ∞, but never reaches -4, and it increases as x goes to -∞.

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Image transcribed:

Identify the statements which describe the graph of f(x) = 9(1/3)ˣ⁺² - 4.

Select all that apply.

A) Asx → ∞, f(x) → -4.

B) Asx → -∞, f(x) →-∞.

C) The y-intercept is (0, -3).

D) The domain is {xlx > -2}

E) The range is the set of real numbers.

The probability that the sample mean cholesterol value be between 145 and 165 mg/dl is   0.288893452 or 28.89% .

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We first get the z score for the two values. As z =[tex]\frac{x-\mu}{\sigma}[/tex] , then as            

x1 = lower bound =     145        

x2 = upper bound =     165        

μ= mean =  155        

σ = standard deviation =     27        

Thus, the two z scores are            

=> [tex]z_1[/tex] = lower =>z score = [tex]\frac{X_1-\mu}{\sigma}[/tex] =     -0.37037037        

=> [tex]z_2[/tex]= upper => z score = [tex]\frac{X_2-\mu}{\sigma}[/tex] =     0.37037037        

Using table/technology, the left tailed areas between these z scores is            

=>P(z < z1) =     0.355553274        

=>P(z < z2) =     0.644446726        

Thus, the area between them, by subtracting these areas, is            

=>P(z1 < z < z2) =     0.288893452 or 28.89%.

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Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.

Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.

[tex]Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25[/tex]

Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.

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Answer:

Only Z

Step-by-step explanation:

Supplementary angles are angles whose sum up to 180 degrees.

Answer: 3.04

Step-by-step explanation:

3.04

Answer:

a) 10^4/4^10

Step-by-step explanation:

10^-2 = 1/10^2

4^5 x 1/10^2 = 4^5/10^2

(4^5/10^2)^-2 = (10^2/4^5)^2 = 10^4/4^10

By following these steps, you can use the unit circle to define the trigonometric functions of any angle.

Steps: Draw a unit circle,  place the angle, Identify the point of intersection, Define the trigonometric functions.

To use the unit circle to define the trigonometric functions of any angle, follow these steps:
1. Draw a unit circle: This is a circle with a radius of 1, centered at the origin (0, 0) of the coordinate plane.

2. Place the angle: Position the angle in standard position, which means that the initial side (starting side) of the angle is along the positive x-axis and the terminal side (ending side) is formed by rotating the initial side counterclockwise to a certain position.

3. Identify the point of intersection:

Determine the point where the terminal side of the angle intersects the unit circle.

This point will have coordinates (x, y).
4. Define the trigonometric functions:

Using the coordinates (x, y), define the six trigonometric functions as follows:
  - Sine (sin): sin(angle) = y
  - Cosine (cos): cos(angle) = x
  - Tangent (tan): tan(angle) = y/x
  - Cosecant (csc): csc(angle) = 1/y
  - Secant (sec): sec(angle) = 1/x
  - Cotangent (cot): cot(angle) = x/y.

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Answer:

B. $50,000

Explanation:

4%=.04

50,000 x .04=2000

48000/12=4000

She makes $4000 off of her salary each month.  Then because she only gets 4% of her commissions you multiply the 50000 by .04 and you get 2000.  So she gets $2000 in commissions and $4000 off of her salary.

The value of a₅ is 688. The problem provides us with a recursive formula that relates each term of the sequence to the previous term.

We can use this formula to find the value of any term in the sequence, given the value of the previous term.

The recursive formula is:

aₙ = -3aₙ₋₁ - 2

This formula tells us that to find the value of aₙ, we need to take the previous term aₙ₋₁, multiply it by -3, and then subtract 2.

The problem also provides us with the value of the first term a₁, which is 8. Using the recursive formula, we can find the value of the second term a₂:

a₂ = -3a₁ - 2 = -3(8) - 2 = -26

We can repeat this process to find the value of the third term a₃:

a₃ = -3a₂ - 2 = -3(-26) - 2 = 76

Continuing in this manner, we can find the values of a₄ and a₅:

a₄ = -3a₃ - 2 = -3(76) - 2 = -230

a₅ = -3a₄ - 2 = -3(-230) - 2 = 688

Therefore, the value of a₅ is 688.

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If a₁ = 8 and aₙ = -3aₙ₋₁ - 2, then what is the value of a₅?

Probability distribution after two battles: Dark 1/3, Psychic 1/3, Fighting 1/3 Steady-state probability distribution: Dark 1/3, Psychic 1/3, Fighting 1/3. Probability distribution after two battles: Dark 1/4, Psychic 1/4, Fighting 1/4, Ghost 1/4. Steady-state probability distribution: Dark 1/6, Psychic 1/6, Fighting 1/2, Ghost 1/6

If Kecleon starts as the Fighting type and battles twice, the probability distribution of Kecleon's type is (1/3, 1/3, 1/3).

After many battles, the steady-state probability distribution of Kecleon's type is (1/3, 1/3, 1/3). This is because Kecleon has an equal chance of winning and losing battles against each of the other types, and so over time its type will converge to a uniform distribution.

If Kecleon starts as the Fighting type when Ghost Pokémon arrive and battles twice, the probability distribution of Kecleon's type is (1/4, 1/4, 1/4, 1/4).

After many battles, the steady-state probability distribution of Kecleon's type is (1/6, 1/6, 1/2, 1/6). This is because the presence of Ghost Pokémon alters the dynamics of the battles, causing Kecleon's type to converge to a non-uniform distribution where it is more likely to become a Psychic type due to the dominance of Ghost-type Pokémon over Fighting and Dark types.

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--The given question is incomplete, the complete question is given

" In a particular region of the Pokémon world, there are just three types of Pokémon: Dark, Psychic, and Fighting. Kecleon, the Color Change Pokémon, has the ability to change its type to blend into its surroundings. Its goal is to become the best type. It seeks to accomplish this goal by choosing a type of Pokémon to battle uniformly at random; it may choose a Pokémon of its own type. If it wins the battle, it will keep its old type. If it loses, it will take on the type of the Pokémon that defeated it. It continues this process indefinitely. For all questions assume that Dark Pokémon always defeat Psychic Pokémon, Psy- chic Pokémon always defeat Fighting Pokémon, and Fighting Pokémon always defeat Dark Pokémon. If two Pokémon of the same type battle, each has an equal chance of winning. a) Suppose that Kecleon starts as the Fighting type. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) b) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) A nearby graveyard is haunted! Ghost-type Pokemon invade the population. Assume that Ghost Pokémon always lose to Dark Pokémon, and always win against Psychic Pokémon and Fighting Pokémon. c) Suppose that Kecleon starts as the Fighting type when the Ghost Pokémon arrive. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.) d) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.)"--

The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.

In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.

By applying direct proportion to the given information, we have the following mathematical equation:

15 gallons of gasoline = 214.5 miles

X gallons of gasoline = 111.54 miles

By cross-multiplying, we have the following:

214.5x = 15 × 111.54

x = 1,673.1/214.5

x = 7.8 gallons of gasoline.

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Answer:

It earned $60 in interest

Step-by-step explanation:

The uniform probability distribution is option (c) The probabilities of drawing any individual card in a deck with one draw

The uniform probability distribution is a probability distribution where all outcomes are equally likely. Out of the options provided, (c) The probabilities of drawing any individual card in a deck with one draw is an example of a uniform probability distribution. This is because each card in a deck is equally likely to be drawn, assuming that the deck is well-shuffled.

The other options are not examples of a uniform probability distribution.

(a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO is not a uniform distribution because the probability of reaching 75F is not the same throughout the year, and is influenced by many factors like seasonal variation, climate changes, etc.

(b) A time period in which it rained 25% of the time and did not rain 75% of the time is not a uniform distribution since the probability of rain is not equally likely across the time period.

(d) Flipping a coin two times and recording whether heads or tails is also not a uniform distribution as the probability of getting heads or tails is not the same, it is 0.5 for each individual flip, but the probability of getting two heads, two tails or one head and one tail are different.

Therefore, the correct option is (c) The probabilities of drawing any individual card in a deck with one draw

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The given question is incomplete, the complete question is:

Which would be a uniform probability distribution? a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO  b) A time period in which it rained 25% of the time and did not rain 75% of the time c) The probabilities of drawing any individual card in a deck with one draw d) Flipping a coin two times and recording whether heads or tails

The function that represents the total cost f(x) to send a letter that is x ounces can be calculated as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

The total cost to send a letter that is 1 ounce is $0.50, and the total cost to send a letter that is 3 ounces is $0.92. Since the postal service calculates the weight to the whole ounce, if we send a 2-ounce letter, we can consider it as sending two 1-ounce letters.

Therefore, the total cost of sending a 2-ounce letter will be twice the cost of sending a 1-ounce letter.

Let f(x) be the total cost to send a letter that is x ounces.

Then,f(1) = 0.50f(2) = 2f(1) = 2(0.50) = 1.00f(3) = f(2) + 0.42 = 1.00 + 0.42 = 1.42

Hence, we can represent the function as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

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Answer:

Step-by-step explanation:

425 - 59 is 366

:)

Answer:

366.

Step-by-step explanation:

Answer: 1. 37.5%,

Step-by-step explanation:

1. we can solve this using a proportion, 10/13.75 = 100/x

a. using cross multiplication we get 10x = 1375

b. when you simplify you get x= 137.5, the percent it was of the whole

c. then subtract the original 137.5-100, and you get 37.5%

The rest of the problems follow a similar fashion

15 is the distance of the equation of a line passing through the points.

What is distance ?

Distance is the separation between two objects. Moreover, it serves as a gauge for the distance between two objects. It is measurable along any route. So even though his position does not change, a person who circles about has moved a certain amount of distance.

the points (4,-3) and (16, 6)

D = √(x₂ - x₁)² + (y₂ - y₁)²

     = √(16 - 4)² + (6 -(-3)²

     = √(12)² + (9)²

      = √144 + 81

       = √225

       = 15

Learn more about distance

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