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The critical values of the function are x = 0 and x = 4.

The critical values of a function f(x) are the values of x for which f'(x) = 0.

In this problem, the function is:

f(x) = [tex]\frac{x^4}{5(x-2)^2}[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{2x^3(x-4)}{5(x-2)^3}[/tex]

The zeros of the function are the zeros of the numerator, thus:

2x³(x-4) = 0

∴ x = 0, 4

Hence, the critical values of the function are x = 0 and x = 4.

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Answer:

To find the population of Brazil in 10 more years, we can use the formula for exponential growth:

A = P(1 + r)^t

where A is the final amount, P is the initial amount, r is the annual growth rate as a decimal, and t is the number of years.

We know that the current population of Brazil is 205,822,685, and the annual growth rate is 0.9%. We want to find the population in 10 more years, so t = 10. Plugging in these values, we get:

A = 205,822,685(1 + 0.009)^10

Simplifying this expression, we get:

A = 205,822,685(1.009)^10

A = 237,832,190.44

Rounding this to the nearest whole number, we get:

A = 237,832,190

Therefore, the population of Brazil in 10 more years will be approximately 237,832,190.

Step-by-step explanation:

The solution is the value of X is, x = 2.

Here, we have,

from the given diagram,

we get,

from triangle ABC,

AB = 5, AC = 6

and, From triangle ADE,

AD = 10, AE = 12

and, both has same angle A,

so, by SAS rule, both are congruent.

we get,

triangle AED ~ triangle ABC

now, we know that,

here, DE = 2 BC

so, x+12 = 2( 4x-1)

or, x+ 12 = 8x -2

or, x = 14/7

or. x= 2

Hence, the value of X is, x = 2.

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The requried line of reflection is the x-axis.

To determine the line of reflection, we need to find the line that maps each vertex of the first polygon to the corresponding vertex of the second polygon.

We can start by reflecting the first polygon across the x-axis. This will map V to V', W to W', X to X', Y to Y', and Z to Z', as shown below:

First Polygon (VWXYZ) Second Polygon (V'W'X'Y'Z')

(3, 2) V (3, -10) V'

(3, 0) W (3, -8) W'

(6, -7) X (6, -1) X'

(9, 0) Y (9, -8) Y'

(9, 2) Z (9, -10) Z'

Next, we can compare the coordinates of each vertex in the first and second polygons to determine the line of reflection. We notice that reflecting the first polygon across the x-axis negates the y-coordinates of all vertices. Therefore, the line of reflection must be the x-axis.

Therefore, the line of reflection is the x-axis.

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Answer:

three

Step-by-step explanation:

All other numbers are even except three

The probability that a day in Dayton will include rain or snow is 38%.

Let's assume that there are 365 days in a year (not considering leap years), and we are aware that Dayton typically experiences 25 days of snow per year, in addition to 110 days of rain. We can add the total number of rainy and snowy days in Dayton and then divide that total by the number of days in a year to determine the likelihood that a given day will be either one of those things:

probability of rain or snow = [tex]\frac{110+25}{365}[/tex]

                                             =0.38

The probability that a day in Dayton will have rain or snow is 0.38 or 38%.

The question is incomplete, complete question is " Dayton is a small town in Ohio, which receives  110 days of rain and 25 days of snow per year. Ignoring leap years, Find the probability that a day in Dayton will include rain or snow."

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The function that are vertical translations of f(x) are; (B), (C), and (D).

Given that f(x) = √x is the square root function.

We know that vertical translation of a function is a transformation that shifts the graph of the function up or down without changing its shape.

Option (A) K(x)=√√√-5+x is a vertical translation of f(x) because it shifts the graph of f(x) to the right by 5 and then applies three square root operations. so, it is not a vertical translation that shifts the graph up or down.

Option (B) n(x) = -7+ √x is a vertical translation of f(x) due to it shifts the graph of f(x) down by 7 units.

Option (C) g(x)=√x -4 is a vertical translation of f(x) since it shifts the graph of f(x) down by 4 units.

Option (D) h(x)=3+√x is a vertical translation of f(x) since it shifts the graph of f(x) up by 3 units.

Option (E)  m(x)=√5x is not a vertical translation of f(x) since it involves multiplying the input of f(x) by a constant factor of 5.

Therefore, the options that are vertical translations of f(x) are; (B), (C), and (D).

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A system of linear equations that describes this situation include the following;

x = 5y

x + y = 24

In order to write a linear equation or function to describe this situation, we would assign variables to the length of the longer piece and the length of the shorter piece in feet respectively, and then translate the word problem into a linear equation as follows:

Since one piece is five times as long as than the other and the length of the longer piece plus the length of the shorter piece equals 24 feet, a system of linear equations or function to describe this situation can be written as follows;

x = 5y

x + y = 24

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Answer:Assuming that the number on the end of the number line is a 1 (I cant read it too clearly), this number line goes to 7/7ths so that means A would be 1/7th and B would be 4/7th

Step-by-step explanation: thats how Number lines work

We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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Answer: image below

Step-by-step explanation:

Since r is a positive rational number, an inequality must also be true include the following: A.) q < 0.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

Next, we would solve the given inequality in order to determine all of the solutions that satisfies the variable q. This ultimately implies that, we would simplify the inequality by cancelling out the variable r as follows;

r × q/r < 0 (r is a positive rational number).

q < 0

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Complete Question:

An inequality is given, where r is a positive rational number.

r • q/r < 0

Which inequality must also be true?

A.) q < 0

B.) q > 0

C.) q < - r

D.) q/r < - r

Diameter is the segment whose end points are on the circle and passing through the center of the circle.

Given a statement.

We have to find the term defined for the statement.

Given a circle.

The end points of the circle are on the circle.

Any line segment whose end points are on the circle is defined as the chord.

If a chord passes through the center of the circle, then it is called the diameter.

Hence the correct term is diameter.

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Your question is incomplete. The complete question must be probably the on as given below.

Identify the term.

A _____ is a segment whose end points are on the circle and passing through the center of the circle.

Answer:

Step-by-step explanation:

Blue line: 0 + -4<x

Black line: 8 - 7<7

Orange: 0=0>y

Green: 1-9<y

Starting points and ending

a) From the box plot of Dwayne's data, the measure of center = 9 and the measure of spread = 5

b)  From the box plot of Mitchell's data,  the measure of center = 10 and the measure of spread = 2

c)  From the box plot of Terry's data,  the measure of center = 10 and the measure of spread = 2

We know that in the box plot the measures of spread include the interquartile range and the mean of the data set.

Whereas, the measures of center include the mean or average and median.

For the Dwayne's box plot the interquartile range is 11 - 6 = 5

And the median is 9

So, the measure of center = 9 and the measure of spread = 5

For the Mitchell's box plot the interquartile range is 11 - 9 = 2

And the median is 10

So, the measure of center = 10 and the measure of spread = 2

For the Terry's box plot the interquartile range is  11 - 9 = 2

And the median is 10

So, the measure of center = 10 and the measure of spread = 2

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If the Lions in their "seventh-game" scored 14 runs, then the true statement is (b) The mean increases and the median remains the same.

To determine how the additional 14 runs affect the mean and median, we need to calculate the original mean and median.

The mean is the sum of all the runs divided by the number of games:

So, Mean = (5 + 8 + 1 + 5 + 2 + 7)/6 = 28/6 = 4.67,

The median is defined as "middle-value" when data is arranged in order. In this case, the data in order is : 1, 2, 5, 5, 7, 8

So, the median is 5.

If the Lions scored 14 runs in their seventh game, the total number of runs for seven games is:

⇒ 5 + 8 + 1 + 5 + 2 + 7 + 14 = 42,

The new mean is the sum of all the runs for seven games divided by the number of games:

⇒ Mean = 42/7 = 6,

The new data in order is : 1, 2, 5, 5, 7, 8, 14,

So, the new median is also 5.

Comparing the original mean and median to the new mean and median, we can see that:

⇒ The median remains the same.

⇒ The mean increases from 4.67 to 6.

Therefore, the correct option is (b).

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The number of people who ate at neither McDonald's or Wendy's is given as follows:

D) 30.

Before obtaining the number of people who ate at neither place, we must obtain the number of people who ate at least one place, as follows:

At least one = McDonald's + Wendy's - (McDonald's and Wendy's).

Replacing the values given in this problem, we have that:

At least one = 55 + 35 - 20

At least one = 70.

Considering that 100 students were surveyed, the number of students who ate at neither place is given as follows:

Neither = 100 - At least one

Neither = 100 - 70

Neither = 30 students.

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Answer:

Step-by-step explanation:

V≈448.92in³

r Radius = 4.75
V=4/3πr3=4/3·π·4.753≈448.9205in³

Step-by-step explanation:

k = a constant of proportionality

Putting m = 1kg, a = 1 ms-2

F becomes 1 N.

So, 1 N = 4 × 1kg × 1 ms-2

∴ k = 1

From equation (1), we have

F = ma

Answer: 525 jumping jacks

Step-by-step explanation:

she does 25 x 3 = 75 jumping jacks per day.

so in a week, (7 days) she will do 7 x 75 = 525 jumping jacks

To Graph the equation using the slope and the​ y-intercept is discussed below.

let us consider a equation of line slope intercept form is y= -1/2x - 1.

As, the general form of equation is

y= mx+ b

where m is the slope and b is y intercept

Here in the equation slope= -1/2 and intercept is -1.

To y intercept is value of y when x= 0 then the coordinate in the graph should be (0, -1).

Now, the slope show the change in y wrt to x here if 2 unit in x then 1 unit.

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The best option among the rest is

A. This data fits a linear model because the growth rate is constant.

The justification for this is that a linear model is suitable when the growth rate of the data remains constant, suggesting that the relations between the independent and dependent quantities are relative and does not differ through time or with modifications in the input figures.

It would cause a straight-line graph to appear, where the dependent elements change linearly comparable to alterations in the independent variable.

All other selections, B, C, D, and E, aren't applicable according to the given information. As a result, the optimal conclusion is A, conveying that the data abides by a linear model derivable from an unchanging growth rate.

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It is used in various fields, such as healthcare, marketing, and social sciences.

False. Logistic regression is used when the dependent variable is binary or categorical (i.e., a nominal or ordinal variable). It is not appropriate for continuous dependent variables.

Logistic regression models the probability of an event occurring, where the event is represented by a binary variable (such as yes/no, success/failure, etc.). The output of the logistic regression model is the probability of the event occurring given the values of the independent variables. This probability can take any value between 0 and 1.

The logistic regression model assumes that the log odds of the event occurring (i.e., the logarithm of the probability of the event divided by the probability of its complement) can be modeled as a linear function of the independent variables. The coefficients of this linear function are estimated using maximum likelihood estimation.

Overall, logistic regression is a commonly used technique in statistics and data analysis for modeling the probability of a binary or categorical outcome. It is used in various fields, such as healthcare, marketing, and social sciences.

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I don't have access to the applet you are referring to. Can you please provide more information or context about the applet so I can better assist you?

Answer: A: 50 ft

Step-by-step explanation:

We need to find the height of this composite figure. We can do so by using the volume formulas, (which include height).

Volume of Figure = Volume of Cylinder + Volume of Hemisphere

26,225.3 = pi r^2 h   +     2/3 pi r^3

26,225.3 = pi 12^2 h + 2/3 pi 12^3

(26,225.3 - 2/3 pi 12^3)/pi 12^2 = h

this simplifies to about 50.

Hence your answer is A

The probability of selecting a citizen, aged 25 or over, who had 4 years of college will be 0.2455.

Given that:

The table below shows the educational attainment of a​ country's population, aged 25 and over.

The probability is given as,

P = (Favorable event) / (Total event)

The probability of selecting a citizen, aged 25 or over, who had 4 years of college will be given as,

P = 41 / 167

P = 0.2455

The probability will be 0.2455.

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The complete question is given below.