En un bufete de abogados se tiene que el costo fijo mensual es de 200 dólares, los costos unitarios que demanda cada caso atendido y resuelto es de 100 dólares y el ingreso mensual está modelado por la siguiente función i(x)= 200x -x2 -160 en dólares, donde x es el número de casos atendidos y resueltos. Responda: ¿a qué razón cambia la utilidad respecto al nivel de casos atendidos y resueltos x cuando se atienden 20 casos? ¿qué ingreso se espera obtener cuando x se aproxima a 10 y 20 casos atendidos y resueltos?

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

y = 2x + 3

Step-by-step explanation:

y = ?x + 3

(0,2)

+4 +2

(4,5)

mx = 4/2 = 2

y = 2x + 3

hope this helps :)

Step-by-step explanation:

m=3-5/0-4 = 1/2

5=1/2(4)+c

c=3

y=mx+c

y=1/2x+3

The expression that matches the simplified form is 7x^5 - 6x + 5x^3 - x^2 + 4x. Option D.

To simplify the given expression, we can combine like terms by adding or subtracting coefficients of the same degree.

The given expression is:

3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x + 7x - 3x^3

Combining like terms, we get:

(3x^4) + (2x^3 - 3x^3) + (-5x^2 + 4x^2) + (6x - 2x - 3x + 7x) - 3x

Simplifying further, we have:

3x^4 - x^3 - x^2 + 12x - 3x

Now, let's arrange the terms in descending order of their exponents:

3x^4 - x^3 - x^2 + 9x

Therefore, the simplified form of the given expression is:

3x^4 - x^3 - x^2 + 9x Option D is correct.

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Answer:

x=8.5

Step-by-step explanation:

3x+31=14+5x

17=2x

x=8.5

According to the given information, (yn) is convergent.

What is the convergence and divergence of the sequence?

Convergence: A sequence approaches a fixed number as the number of terms increases.

Divergence: A sequence does not approach a fixed number as the number of terms increases.

Yes, (yn) is convergent.

Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.

Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.

Combining these two inequalities, we have:

|yn - L| = |yn - xn + xn - L|

≤ |yn - xn| + |xn - L|

< ε + ε (for all n ≥ M)

Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.

Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).

Hence, (yn) is also convergent.

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If a data set has an outlier, the median would be the best measure of central tendency to use as it is less sensitive to extreme values compared to the mean.

The presence of an outlier can heavily skew the mean in the direction of the outlier, causing it to become an inaccurate representation of the center of the data. On the other side, the median is less sensitive to extreme values and represents the middle value of the dataset. It is calculated by finding the middle value in a dataset after arranging it in numerical order.

Therefore using the median as the measure of central tendency in a dataset with an outlier can provide a better indication of the typical value compared to the mean.

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The inequality for the statement:-2/7 is at most the product of a number and -4/5. is --4x/5 ≤ -2/7

Information from the question

the statement: -2/7 is at most the product of a number and -4/5

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to

at most means the highest value hence the answer is either the number or less.

let the number be x

x * -4/5 ≤ -2/7

--4x/5 ≤ -2/7

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The original price of the novel is $21.5

The first step is to write out the parameters given in the question

Last year, Gloria buys a novel for $18.70

This price is with a discount of 15% form the original price

The original price of the novel can be calculated as follows

15/100 × 18.70

= 0.15 × 18.70

= 2.805

The next step is to add 2.805 to the price of the novel last year($18.70)

= 18.70 + 2.805

= 21.5

Hence the original price of the novel before the addition of the discount is $21.5

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The system of equations that can be used to determine the amount each player earned, in million of dollars is the option;

(4) m + f = 3.95

f + 0.005 = m

A system of equation consists of two or more equations that have the same variables.

The details in the question indicates;

The earnings of football player McGee's in 2010, m = 0.005 million dollars more than those of his teammate Fitzpatrick's earnings, f

The amount earned by the two players = 3.95 million dollars

Therefore, we get;

m + f = 3.95

f + 0.005 = m

The correct option is therefore, option 4

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Answer:

Infinite Solutions

Step-by-step explanation:

To solve for this problem, we want to isolate x on one side of the equation.

Apply the distributive property on the right side:

\(3x - x - 5 = 2x+4 -9\)

Combine like terms:

\(2x - 5 = 2x - 5\)

Woah, we have the exact same thing on both sides of the equation. This means that we have infinite solutions, aka any value of x will satisfy this equation.

Test it out! Any value of x, whether its 1, 5, or 10000 will satisfy the equation.

So this has infinite solutions.

Hope this helped!

Answer:

\( \sf \: 12th \: term = 37\)

Step-by-step explanation:

Common difference (d) is,

→ d = a2 - a1

→ d = -3 - (-7)

→ d = -3 + 7

→ [ d = 4 ]

Now the 12th term will be,

→ a1 + (d × (n - 1))

→ -7 + (4 × (12 - 1))

→ -7 + (4 × 11)

→ -7 + 44

→ 37 => 12th term

Hence, the answer is 37.

The value of result in the following expression will be 0 if x has the value of 12:

result = x > 100 ? 0 : 1.

The expression given is known as a ternary operator.

It's a short form of if-else.

The ternary operator is written with three arguments separated by a question mark and a colon:

`variable = (condition) ? value_if_true : value_if_false`.

Here, `result = x > 100 ? 0 : 1;` is a ternary operator, and its meaning is the same as below if-else block.if (x > 100)  {  result = 0; }  else {  result = 1; }

As per the question, we know that if the value of `x` is `12`, then the value of `result` will be `0`.

Hence, the answer is `0`.

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Answer:

\(2x^2+x-5\)

Step-by-step explanation:

(x+3)(2x−5)

=(x+3)(2x+−5)

=(x)(2x)+(x)(−5)+(3)(2x)+(3)(−5)

=\(2x^2+x-5\)

Answer:

I think it is 0

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

To find the y-intercept from a table all you have to do is find when x is 0 because the y-intercept is (0,5) on a graph

Answer:

512

Step-by-step explanation:i think so

Answer:

The second one

Step-by-step explanation:

I got it right

It is given that the radius increases at the rate of 7 cm per second, that is 7 cm in 1s.

It follows that after 4s since backing away, the increase in radius is:

Add the increase to the initial length of the radius:

Hence, the radius 4s after you start backing away is 33 cm.

After 7s, the increase in radius will be:

Add this increase to the initial length of the radius:

Hence, the radius 7s after you start backing away is 54 cm.

Answer:

the mean is 6

the median is 6

the mode there is none

the range is 6.

Answer:

There is no mode. (they all appear once)

The lowest number is 3 and the highest is 9, so the range is 6.

The mean is the average, add them all up (30) and divide by the number of data sets (5). The average is 6.

I have to go to dinner so maybe let someone else help with the median? The median is the middle, so you have to order them and find the middle. Hope it helped!

Answer:

2m - 3

Step-by-step explanation:

We know that Jim ran m miles. Twice that amount is simply 2 times that, or 2 * m which simplifies to 2m. 3 miles fewer means that we have to subtract 3 from that quantity, so the answer is 2m - 3.

Answer:

2m - 3

Step-by-step explanation:

Distance ran by Jim = m

Twice as far as Jim : 2 * m = 2m

3 miles fewer than '2m' = 2m - 3

Distance ran by Kelly = 2m - 3

Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

The height of the parallelogram is 10 cm and its base is 20 cm.

Let's denote the base of the parallelogram as 'b' and its height as 'h'. According to the given information, the height is half the base.

We know that the formula to calculate the area of a parallelogram is:

Area = base * height

Given that the area is 200 cm^2, we can write the equation as:

200 = b * h

Since the height is half the base, we can substitute 'h' with 'b/2' in the equation:

200 = b * (b/2)

To solve this equation, we can multiply both sides by 2 to eliminate the fraction:

400 = b^2

Taking the square root of both sides, we find:

b = √400

b = 20 cm

So, the base of the parallelogram is 20 cm.

Since the height is half the base, we can calculate the height by dividing the base by 2:

h = 20 / 2

h = 10 cm

Therefore, the height of the parallelogram is 10 cm and its base is 20 cm.

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Answer:

Step-by-step explanation:

let the no of girls be x

ratio of boys to girls=4:7

4/7=16/x

do cross multiplication

7*16=x*4

112=4x

112/4=x

28=x

therefore there are 28 no of girls.

To determine the total grade we mutiply each one by the percentage it represents of the overall grade in decimal form and add them, that is:

Therefore, the overall grade is 69

Answer:

50.65 grams

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total amount of salt =  38.1 + 12.55 = 50.65 grams

38.10 +

12.55

50.65

The probability that the bus arrives early or on time is 11/14.

We will denote probability of the bus arriving early as P(E) and the probability of the bus arriving on time as P(T).

We are given that P(E) = 3/7 and P(T) = 5/14.

The probability that the bus arrives early or on time will be found using the formula:

P(E or T) = P(E) + P(T)

P(E or T) = 3/7 + 5/14

P(E or T) = (6/14) + (5/14)

P(E or T) = 11/14.

Full:

The probability that a bus arrives early at a bus stop is (3)/(7). The probability that it arrives on time is (5)/(14). Calculate the probability that the bus arrives early or on time. Give your answer as a fraction in its simplest form.

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The probability that a student plays either baseball or soccer is 0.4296 (or 42.96%).This is the long answer.

Percentage of students that play baseball = 18%Percentage of students that play soccer = 32%Probability of a student playing baseball given that the student plays soccer = 22%We need to find the probability that a student plays either baseball or soccer (or both).Let the probability of a student playing baseball be P(B)Let the probability of a student playing soccer be P(S)Using the formula of conditional probability:P(B|S) = P(B ∩ S) / P(S)Where P(B ∩ S) is the probability that a student plays both baseball and soccerP(B ∩ S) = P(B) + P(S) - P(B ∪ S) (Using the formula of probability of the union of two events)Where P(B ∪ S) is the probability that a student plays either baseball or soccer or bothP(B ∪ S) = P(B) + P(S) - P(B ∩ S)Now substituting the values in the formula:P(B|S) = P(B ∩ S) / P(S) => 0.22 = P(B) + P(S) - P(B ∪ S) / 0.32

Now we need to calculate the probability that a student plays either baseball or soccer or both. Using the formula of probability of the union of two events. P(B ∪ S) = P(B) + P(S) - P(B ∩ S)We know :P(B) = 0.18P(S) = 0.32We need to calculate P(B ∩ S) which can be calculated as follows :P(B|S) = P(B ∩ S) / P(S)0.22 = P(B ∩ S) / 0.32 => P(B ∩ S) = 0.22 x 0.32 = 0.0704Now substituting the values in the formula :P(B ∪ S) = P(B) + P(S) - P(B ∩ S)P(B ∪ S) = 0.18 + 0.32 - 0.0704 = 0.4296

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Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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Answer:

afjhs

Step-by-step explanation:

The population mean is greater than $12.5, assuming that we know the population standard deviation is equal to 6.75.

To test whether we can infer at the 5% significance level that the mean fee for car washers (including tips) is greater than $12.5, we need to perform a one-sample t-test with the following hypotheses:

Null hypothesis: μ ≤ $12.5

Alternative hypothesis: μ > $12.5

We will use a t-distribution with degrees of freedom (df) equal to n-1 = 15-1 = 14.

The test statistic is given by:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (14.9 - 12.5) / (6.75 / sqrt(15)) = 2.28

The critical value for a one-tailed test with α = 0.05 and df = 14 is 1.761. Since our calculated t-value (2.28) is greater than the critical value (1.761), we reject the null hypothesis and conclude that we can infer at the 5% significance level that the mean fee for car washers (including tips) is greater than $12.5.

To test whether we can infer at the 5% significance level that the population mean is greater than $12.5, assuming that we know the population standard deviation is equal to 6.75, we need to perform a z-test with the following hypotheses:

Null hypothesis: μ ≤ $12.5

Alternative hypothesis: μ > $12.5

We will use a standard normal distribution.

The test statistic is given by:

z = (x - μ) / (σ / sqrt(n))

where σ is the population standard deviation, which is given as 6.75.

Substituting the given values, we get:

z = (14.9 - 12.5) / (6.75 / sqrt(15)) = 2.28

The critical value for a one-tailed test with α = 0.05 is 1.645. Since our calculated z-value (2.28) is greater than the critical value (1.645), we reject the null hypothesis and conclude that we can infer at the 5% significance level that the population mean is greater than $12.5, assuming that we know the population standard deviation is equal to 6.75.

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Answer:

median=10

mode=8

mean=42,63

Answer:

Mean:7

Median:8

Mode:8

Mean: The sum of all observation divided by several observation

Median: it is the middlemost observation of data arraged in increasing or decreasing order of values

Mode: it is the value that accurs most frequently in a set of data

Hope it helps!!

It is highly unlikely that a firm in this industry will earn less than 103 million dollars.

z = (x - μ) / σ

z = (103 - 9090) / 1515 = -5.38

The probability of a firm earning less than -5.38 standard deviations from the mean is very low, approximately 0.00000003. This means that the probability of a randomly selected firm earning less than 103 million dollars is extremely low, less than 0.00000003 or 0.000003%.

Probability is a mathematical concept that measures the likelihood of an event occurring. It is a way to quantify uncertainty and express it as a numerical value between 0 and 1. A probability of 0 indicates that the event is impossible, while a probability of 1 indicates that the event is certain.

Probabilities can be calculated using various methods, including the classical, empirical, and subjective approaches. The classical approach is based on the assumption that all outcomes are equally likely, while the empirical approach is based on observed data. The subjective approach involves using personal beliefs and opinions to estimate the probability of an event.

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