Calcular las edades de Marcos, Betiana y Sabrina sabiendo que la edad de Sabrina es un tercio de la edad de Betiana más Marcos. La edad de Betiana más la de Sabrina es igual a la edad de Marcos menos 18 y entre los tres suman 72 años

Answer:

gcf is 'x'

Step-by-step explanation:

the common factor to the terms 'x²' and '3x' is 'x'

The solution to the equation 4,300e^(0.07x) - 123 = 5,000 for x is 2.5.

We can solve the equation 4,300e^(0.07x) - 123 = 5,000 for x by first adding 123 to both sides and then dividing both sides by 4,300 and taking the natural logarithm of both sides:

Using the above as a guide, we have the following:

4,300e^(0.07x) - 123 = 5,000

4,300e^(0.07x) = 5,123

e^(0.07x) = 5,123/4,300

e^(0.07x) = 1.1914

0.07x = ln(1.1914)

x = ln(1.1914)/0.07

Using a calculator, we get:

x ≈ 2.50

Rounding to the nearest tenth, the solution to the equation is approximately 2.5.

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Answer:

hope this helps

Step-by-step explanation:

The expression for V(t), the value of Rick's snowmobile, in dollars, after t years can be given by:

V(t) = $10,500 * (1 - 0.14)^t

Simplifying this expression, we get:

V(t) = $10,500 * 0.86^t

So, the required expression for V(t) is:V(t) = 10,500 * 0.86^t

The more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

Let us denote the expected number of times the variable bmax gets updated by E.

We can start by computing the probability that the ith agent updates bmax. This is equal to the probability that agent i has the highest bid among the first i bids. Since all bids are distinct and the order of the agents is chosen uniformly at random, the probability of this event is 1/i.

Therefore, the expected number of updates to bmax is:

E = ∑i=1 to n P(agent i updates bmax)

E = ∑i=1 to n 1/i

This is the harmonic series, which diverges as n approaches infinity. Therefore, as the number of bidding agents increases, the expected number of updates to bmax increases without bound.

In practical terms, this means that the more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

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Answer:

5.5

Step-by-step explanation:

x＋3＝8.5

or，x＝5.5

I hope it helped you

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The IQR (Interquartile Range) of 13 is the most accurate measure of variability to use for this data since the data is skewed and contains outliers. The IQR is less sensitive to outliers than the range and provides a better representation of the spread of the middle 50% of the data.

Variability refers to the extent to which data points in a dataset differ from each other. It is a measure of how spread out or dispersed a set of data is.

In statistics, measures of variability are used to describe how spread out or clustered a set of data is. There are several measures of variability, but the two most common ones are the range and the interquartile range (IQR).

The range is the difference between the maximum and minimum values in a set of data. It is a simple measure of variability that gives an idea of how much the data varies. However, it can be affected by outliers, which are values that are much larger or smaller than the other values in the data set.

The IQR is a more robust measure of variability that is less affected by outliers. It is the difference between the third quartile (the value above which 75% of the data falls) and the first quartile (the value below which 25% of the data falls). The IQR describes the range of the middle 50% of the data and gives an idea of how spread out the data is around the median.

In the case of the charity's donations, the data is skewed towards the higher end, with most of the donations falling between $16 and $20. This means that the range of 13 (20-5) would be affected by the outliers at the high end, and would not accurately represent the variability of the data.

On the other hand, the IQR of 13 (the difference between the third quartile at $20 and the first quartile at $7) would give a more accurate representation of the variability of the data, as it is less affected by the outliers.

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Answer:

75

Step-by-step explanation:

The constant ratio in each representation include the following: r = 3.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio in each representation as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -6/-2 = -18/-6

Common ratio, r = 3.

Based on comparison with the exponential equation, the common ratio is given by;

Common ratio, r = 3.

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A possible story of the graph would be about a student going to school for an important event.

One day, a student named Alex had to go to school for an important event. The graph represents Alex's journey to and from school, with the horizontal axis representing time and the vertical axis representing the distance from school.

In the morning, Alex left home (time = 0, distance = 0) and began walking to school. The line on the graph climbs gradually, indicating that Alex was steadily covering the distance to school. Upon reaching school, Alex attended the important event, which lasted for a certain amount of time. During this period, the line on the graph remains flat.

Once the event was over, Alex began their journey back home. The line on the graph starts to decrease gradually until Alex arrived back home, ending up at a distance of zero from the school.

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The circumferences and areas of the circles are:

a)

C =  18.84cm

A = 28.26 cm²

b)

C =  62.8 in

A = 314 in²

c)

C =  75.36 m

A = 452.16 m²

Remember that for a circle of radius R, the circumference is:

C = 2pi*R

The area is:

A = pi*R²

Where pi = 3.14

a) Here we have R = 3cm, replacing that in the formulas above we will get.

C = 2*3.14*3cm = 18.84cm

A = 3.14*(3cm)² = 28.26 cm²

Now let's do that for some more.

b) The radius is 10 inches.

C = 2*3.14*10 in = 62.8 in

A = 3.14*(10in)² = 314 in²

c) The radius is 12m

C = 2*3.14*12m = 75.36 m

A = 3.14*(12 m)² = 452.16 m²

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It is important for researchers to carefully consider these factors when designing studies and analyzing data to ensure that their results are accurate and reliable.

Small Sample Size: With only 40 participants remaining in the experimental group after 6 months, the sample size may have been too small to detect any significant differences between the experimental and control groups.

Sampling Error: Even with random assignment to groups, there is always a chance that the groups will differ on some important characteristic that could affect the results.

Statistical Power: The statistical power of a study refers to its ability to detect a true effect if one exists. With a small sample size, the statistical power of the study may have been too low to detect any real differences between the groups.

Data Analysis: The way in which the data was analyzed could have influenced the results. For example, if the researchers used an inappropriate statistical test or did not correct for multiple comparisons, it could have led to faulty results.

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Answer: 42

Step-by-step explanation: you have to add 9 18 and 15.

Answer: c=a2+b2

Step-by-step explanation:

The odds ratio of 5.91 suggests that vaccination significantly increases the likelihood of remaining healthy and not developing COVID-19 symptoms compared to no vaccination.

Calculate the odds of staying healthy for each vaccination status based on the data provided:

Unvaccinated:

Number of individuals who stayed healthy = 44

Number of individuals who developed COVID-19 = 25

Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 44/25 = 1.76

Vaccinated:

Number of individuals who stayed healthy = 52

Number of individuals who developed COVID-19 = 5

Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 52/5 = 10.4

Next, let's calculate the odds ratio from the odds of staying healthy for each vaccination status:

Odds ratio = Odds of staying healthy for vaccinated / Odds of staying healthy for unvaccinated

= 10.4 / 1.76

= 5.91

Now, let's interpret the odds ratio and answer the research question. An odds ratio of 5.91 indicates that the odds of staying healthy among vaccinated individuals is 5.91 times higher compared to unvaccinated individuals.

This suggests that vaccination is associated with a significantly higher likelihood of staying healthy and not developing COVID-19 symptoms. Therefore, the data collected by the researcher suggests that the vaccine is effective in preventing the development of COVID-19 symptoms.

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Answer:

x >-15

Step-by-step explanation:

Please here is it.

where x >-15

Answer:

The expression that is equivalent to 6c is:

2 x 3 x c

3 x 2 x c

(2 x 3) x c

(3 x 2) x c

6 x c

All of these expressions represent the product of 6 and c, which is the same as multiplying 6 and c together. Therefore, they are equivalent to 6c.

Step-by-step explanation:

The correct option is (a) i.e. The translation direction is downward, and the number of units is 8.

What is translation?

In mathematics, translation refers to the process of moving a geometric object from one location to another, without changing its size, shape, or orientation.

To determine the translation direction and number of units, we need to find the vector between the original point Q(4,3) and the new point Q'(4,-5).

The vector between two points is found by subtracting the coordinates of the initial point from those of the final point. Therefore, we have:

Q'Q = (4,-5) - (4,3) = (0, -8)

This tells us that the new point Q' is 8 units down (in the negative y-direction) from the original point Q. Therefore, the translation direction is downward, and the number of units is 8.

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Answer: We can begin by factoring the quadratic expression in the numerator and denominator of the left-hand side of the inequality:

x^2 - 1 = (x + 1)(x - 1)

x^2 + 5x + 4 = (x + 1)(x + 4)

Substituting these expressions into the inequality, we get:

(x + 1)(x - 1)/(x + 1)(x + 4) ≤ 0

We can simplify this expression by canceling out the common factor of (x + 1) from both the numerator and the denominator:

(x - 1)/(x + 4) ≤ 0

To solve this inequality, we can use a sign chart or test values. Here's a sign chart:

x x - 1 x + 4 (x - 1)/(x + 4)

-4 -5 0 +

-1 -2 3 -

1 0 5 0

4 3 8 +

The inequality is satisfied when (x - 1)/(x + 4) is less than or equal to 0, which occurs when x is between -4 and -1, or when x is equal to 1. Therefore, the solution to the inequality is:

-4 ≤ x < -1 or x = 1

Step-by-step explanation:

Answer:

the answer of the question is

104+8x

The slope of the second line is also positive, as it is parallel to the first line which has a positive slope.

Slope is a measure of how steep a line is, and is defined as the ratio of the change in the y-coordinate (vertical change) to the change in the x-coordinate (horizontal change) between any two points on the line. It represents the rate at which the line is rising or falling as it moves from left to right. Slope can be positive, negative, or zero. A positive slope indicates that the line is increasing as it moves from left to right, a negative slope indicates that the line is decreasing as it moves from left to right, and a zero slope indicates that the line is horizontal.

Here,

When two lines are parallel, they have the same slope. In this case, the first line has a positive slope of "a," which means that it is increasing as it moves from left to right. Since the second line is parallel to the first line, it will also have the same slope as the first line. Therefore, the slope of the second line will also be positive, indicating that it is increasing as it moves from left to right.

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The base area, the lateral area and the surface area of the prism are 124.8 cm², 288 cm² and 412.8 cm², respectively.

In this problem we need to compute three kinds of areas in a prism with a triangular base. The base area, that is, the sum of the areas of the two triangles, the lateral area, that is, the sum of the areas of the three rectangles and the surface area, that is, the sum of the base and lateral areas.

The area formulas of the triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine each kind of area:

Base area

A = 2 · 0.5 · (12 cm) · (10.4 cm)

A = 124.8 cm²

Lateral area

A = 3 · (8 cm) · (12 cm)

A = 288 cm²

Surface area

A = 124.8 cm² + 288 cm²

A = 412.8 cm²

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Experimental studies involve the manipulation of variables, and quasi-experimental studies involve some level of intervention but lack full control or randomization.

An observational study.

In an observational study, researchers collect data without intervening or manipulating any variables.

The study evaluated the association between exposure to anticholinergic drugs and dementia risk using existing data collected from an anonymized research database of more than 30 million individuals in over 1500 general practices. The data includes demographic information, medical diagnoses, prescriptions, referrals, laboratory results, and clinical values.
Case patients were those diagnosed with dementia during follow-up, and each case patient was matched to 5 controls by age, sex, general practice, and calendar time.

The study used information on prescriptions for 56 drugs with strong anticholinergic properties to calculate measures of cumulative anticholinergic drug exposure.

The data were analyzed from May 2016 to June 2018.
Since the researchers did not manipulate any variables or treatments and only analyzed existing data, it is considered an observational study.

The study uses data collected from a research database of routine healthcare, rather than manipulating variables in a controlled setting.

The researchers observed the exposure to anticholinergic drugs in patients and followed them over time to evaluate the association with dementia risk.

The study did not involve the manipulation of any variables, which is characteristic of experimental or quasi-experimental studies.

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This is an observational study which we can infer from the given data in the question.

This is an observational study. In this study, the researchers evaluated the association between exposure to anticholinergic drugs and dementia risk using data collected from a large database. They identified case patients with dementia and matched them with controls based on age, sex, general practice, and calendar time. The researchers did not manipulate any variables or randomly assign participants to groups, which is characteristic of an observational study.

When conducting an observational study, researchers observe and gather data on a group of people or subjects without interfering or changing any of the factors. An observational study's objective is to identify and evaluate patterns, behaviours, or occurrences without modifying or altering them.

Observational studies can be carried out in a variety of locations, including the outdoors, businesses, homes, and communities. The social sciences, epidemiology, psychology, and medicine are just a few of the disciplines in which they might be applied.

The two subtypes of observational studies are prospective and retrospective. In a prospective observational study, a group of people is tracked over time as information is gathered on their behaviours, exposures, and results. On the other hand, a retrospective observational study looks back in time and gathers information.

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a) The probability of him answering all seven questions correctly is [tex](1/4)^7[/tex]or approximately 0.000019%.

b) Therefore, the probability of him answering exactly three questions correctly is [tex]35 * (1/4)^3 * (3/4)^4[/tex]or approximately 19.7%.

c) The probability of him answering at least three questions correctly is the sum of these probabilities, which is approximately 71.5%.

Since each question has four choices and only one is correct, the probability of guessing the correct answer for any one question is 1/4.

a) To answer all seven questions correctly, Edward must guess the correct answer for each question.

Therefore, the probability of him answering all seven questions correctly is [tex](1/4)^7[/tex] or approximately 0.000019%.

b) To answer exactly three questions correctly, Edward must guess the correct answer for three questions and the incorrect answer for the remaining four questions.

The number of ways in which he can do this is given by the binomial coefficient C(7,3) = 35.

The probability of him guessing three questions correctly and four questions incorrectly is [tex](1/4)^3 * (3/4)^4.[/tex]

Therefore, the probability of him answering exactly three questions correctly is [tex]35 * (1/4)^3 * (3/4)^4[/tex]or approximately 19.7%.

c) To answer at least three questions correctly, Edward must either guess three, four, five, six, or seven questions correctly.

We have already calculated the probability of him guessing exactly three questions correctly.

The probability of him guessing exactly four questions correctly is [tex]C(7,4) * (1/4)^4 * (3/4)^3 = 35 * (1/4)^4 * (3/4)^3[/tex]or approximately 34.7%.

The probability of him guessing exactly five questions correctly is [tex]C(7,5) * (1/4)^5 * (3/4)^2 = 21 * (1/4)^5 * (3/4)^2[/tex] or approximately 16.3%.

The probability of him guessing exactly six questions correctly is[tex]C(7,6) * (1/4)^6 * (3/4)^1 = 7 * (1/4)^6 * (3/4)^1[/tex] or approximately 0.82%. Finally, the probability of him guessing all seven questions correctly is (1/4)^7 or approximately 0.000019%.

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The average value of the function f(x,y) = sin(x+y) over the rectangle 0 ≤ x ≤ π/3, 0 ≤ y ≤ 5π/3 is -27√(3) / (40π^2).

To find the average value of the function ​f(x,y)=sin(x+y) over the given rectangle, we need to integrate the function over the rectangle and then divide by the area of the rectangle.

So, we have:

average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle

where the limits of integration are

0 ≤ x ≤ π/3

0 ≤ y ≤ 5π/3

The area of the rectangle is

Area = (π/3 - 0) × (5π/3 - 0) = 5π^2 / 9

Now, we can integrate the function f(x,y) over the rectangle

double integral of f(x,y) over the rectangle = integral from 0 to π/3 of integral from 0 to 5π/3 of sin(x+y) dy dx

= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+y)] evaluated from y=0 to y=5π/3 dx

= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+5π/3) + cos(x)] dx

= [tex]\int\limits^{\pi /3}_0[/tex]  [-1/2cos(x) - 1/2cos(x+π/3)] dx

= [-1/2sin(x) - 1/4sin(x+π/3)] evaluated from x=0 to x=π/3

= [-1/2sin(π/3) - 1/4sin(2π/3)] - [-1/2sin(0) - 1/4sin(π/3)]

= (-√(3)/4) - (1/4 × √(3)/2) = -3sqrt(3)/8

Therefore, the average value of f(x,y) over the rectangle is

average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle

= (-3sqrt(3)/8) / (5π^2 / 9)

= -27sqrt(3) / (40π^2)

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The given question is incomplete, the complete question is:

Find the average value of ​f(x,y)=sin(x+y) over the rectangle 0≤x≤π/3​, 0≤y≤5π/3.

The statement "Poisson distributions are useful to model any variables positive or negative as long as they are integer values" is false because Poisson distributions are specifically used for modeling the number of events occurring in a fixed interval of time or space, given a fixed average rate of occurrence (λ).

The key characteristics of a Poisson distribution are:

1. The events are independent, meaning the occurrence of one event does not influence the occurrence of another event.
2. The average rate of occurrence (λ) is constant throughout the interval.
3. The probability of more than one event occurring in an infinitesimally small interval is negligible.

Given these characteristics, Poisson distributions are not suitable for modeling any variables, positive or negative, as long as they are integer values. Instead, they are applicable for modeling non-negative integer values (0, 1, 2, ...) representing the number of events occurring in a specific context. Negative integer values are not applicable in this distribution since it would be illogical to have negative events occurring in a fixed interval.

In summary, Poisson distributions are only useful for modeling non-negative integer values representing the number of events in a fixed interval of time or space, given a fixed average rate of occurrence.

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The simplified expression is: 2√3

To simplify the given radical expression √363 - 3√27, we first need to simplify each square root term individually.

Simplify √363:

We need to find the prime factorization of 363 and look for pairs of identical factors.

363 = 3 × 121

363 = 3 × 11 × 11

There is a pair of 11's, so we can simplify the square root:

√363 = √(3 × 11 × 11)

√363 = 11√3

Simplify 3√27:

We need to find the prime factorization of 27 and look for pairs of identical factors.

27 = 3 × 3 × 3

There is only one pair of 3's, so we can simplify the square root:

3√27 = 3√(3 × 3 × 3)

3√27 = 3(√(3 × 3) × √3)

3√27 = 3(3√3)

Now we can substitute the simplified expressions for the original terms in the expression:

(11√3) - (3(3√3))

To further simplify, we need to combine like terms. In this case, we have two terms with the same radical (√3), so we can combine them:

11√3 - 9√3 = (11 - 9)√3

11√3 - 9√3 = 2√3

The simplified expression is: 2√3

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Answer:

20

Step-by-step explanation:

So start with the ones you know like 2+2. So what I did is add the 2,s and then add the 4,s then I added 3,s which then added the 6,s the 8+12= 20 and that's how I got my answer.

0.5 is used as a conservative estimate of p in determining the minimum sample size for a proportion confidence interval to account for maximum uncertainty.

In statistical hypothesis testing and estimation, we often need to make inferences about population parameters based on a sample. One of the parameters of interest is the proportion of successes in a population.

When we construct a confidence interval for a proportion, we need to specify the desired level of confidence and the desired margin of error. The margin of error depends on the sample size and the standard error of the sample proportion.

The standard error of the sample proportion is estimated using the population proportion, p, which is unknown. Since we don't know the true value of p, we typically use the sample proportion, p-hat, as an estimate. However, using p-hat alone can lead to an overly optimistic estimate of the standard error and, therefore, an overly narrow confidence interval.

To account for this uncertainty, we use a conservative estimate of the standard error that assumes a worst-case scenario for p. The worst-case scenario is when p is 0.5, which corresponds to maximum uncertainty or variability in the estimate of the proportion. This is why 0.5 is often used as a conservative estimate of p when determining the minimum sample size necessary for a proportion confidence interval. By assuming p = 0.5, we ensure that our sample size is large enough to account for the worst-case scenario and provide a reliable estimate of the proportion.

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