g(x)=f(3x)
Choose the description of the transformation from the graph of f to the graph of g

A) the graph of g is a horizontal stretch of the graph of f by a factor of 3

B) the graph of g is a horizontal shrink of the graph of f by a factor of 1/3

C) the graph of g is a vertical stretch of the graph of f by a factor of 3

D) the graph of g is a vertical shrink of the graph of f by a factor of 1/3

To find the number of years it will take for the population of a city to increase from 120000 to 180000, we need to use the formula:

Years = log (target population / starting population) / log (1 + annual growth rate)

Where the annual growth rate is 2.5% or 0.025.

Plugging in the values, we get:

Years = log (180000 / 120000) / log (1 + 0.025)

Years = log (1.5) / log (1.025)

Years = 7.36 years

Rounding to the nearest tenth, we get:

Years = 7.4 years

So it will take approximately 7.4 years for the population of the city to increase from 120000 to 180000 people, assuming a constant annual growth rate of 2.5%.

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The duration it takes a teacher and the duration it takes a student to each paint the mural found using the combined work formula are;

The number of brushes and tubes of paints purchased are;

The time, Tₙ, it takes to do a work by two people combined, where the time it takes one person to do the work is T₁ and the time it takes the second person to do the same work is T₂, can be expressed as in the following combined work or rate of work formula equation;

[tex]\frac{1}{T_1}+\frac{1}{T_2} = \frac{1}{T_n}[/tex]

Let T represent the time it takes one teacher to paint the large mural, and let S represent the time it takes a student to paint the large mural, we get;

[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex]...(1)

[tex]\frac{6}{T}+\frac{8}{S} = \frac{1}{14}[/tex]...(2)

Multiplying equation (1) by 4 and subtracting equation (2) from the result, we get;

[tex]4\times \frac{8}{T}+\frac{2}{S} = \frac{32}{T}+\frac{8}{S} = \frac{4}{10} = \frac{2}{5}[/tex]

[tex]\frac{32}{T}+\frac{8}{S} = \frac{2}{5}[/tex]

[tex]\frac{32}{T}+\frac{8}{S} -\left(\frac{6}{T}+\frac{8}{S}\right) = \frac{2}{5} - \frac{1}{14} = \frac{23}{70}[/tex]

[tex]\frac{26}{T}+0 = \frac{23}{70}[/tex]

T = (70/23) × 26 = 1820/23 = 79 3/23

[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex], therefore;

[tex]\frac{2}{S} = \frac{1}{10} - \frac{8}{T}[/tex]

[tex]\frac{2}{S} = \frac{1}{10} - \frac{8\times 23}{1820} = -\frac{1}{910}[/tex]

S = -910 × 2 = -1820

Second question

The budget on tubes of paint and paintbrushes = $200

The cost of a tube = $4.00 and the cost of a paintbrush = $0.5

Number of brushes purchased = 2 × The number of tubes of paint purchased

Let x represent the number of paintbrushes purchased and let y represent the number of tubes of paint purchased, we get;

0.5·x + 4·y = 200

x = 2·y

Therefore; 0.5 × (2·y) + 4·y = 200

y + 4·y = 5·y = 200

y = 200/5 = 40

The number of tubes of paint purchased, y = 40

x = 2·y, therefore;

x = 2 × 40 = 80

The number of paintbrushes purchased, x = 80

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Answer: $2.12

Step-by-step explanation: Subtract $2.65 from 34.45 and then divide that number by 15.

A real-world situation consistent with the data provided would be (a) the height of a balloon as it ascends in the air at a constant rate, (b) the speed of a car as it accelerates from a standstill to a constant speed, (c) the height of a soccer ball as it is kicked into the air (d) the velocity of a skydiver as they fall to the ground.

a. A real-world situation consistent with the data provided would be the height of a balloon as it ascends in the air at a constant rate. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The balloon's height will not change with time (f'(x) = 0), meaning the balloon is not accelerating, and the height remains constant as it moves from 0 to 3 seconds.

b. A real-world situation consistent with the data provided would be the speed of a car as it accelerates from a standstill to a constant speed. In this case, x can be the time elapsed in seconds, and y can be the speed in meters per second.

The speed of the car will increase at a constant rate (f'(x) = 50), meaning the car is accelerating, and the speed increases as it moves from 0 to 3 seconds.

c. A real-world situation consistent with the data provided would be the height of a soccer ball as it is kicked into the air. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The height of the ball will increase as time goes by (f'(x) is increasing as x increases), meaning the ball is moving upwards, and the height increases as it moves from 0 to 3 seconds.

d. A real-world situation consistent with the data provided would be the velocity of a skydiver as they fall to the ground. In this case, x can be the time elapsed in seconds, and y can be the velocity in meters per second.

The velocity of the skydiver will decrease as time goes by (f'(x) is decreasing as x increases), meaning the skydiver is falling faster and faster, and the velocity decreases as it moves from 0 to 3 seconds.

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

"Describe different real-world situations (include the units of x and y) that would be consistent with the data provided:

a. f'(x)=0, 0 ≤ x ≤ 3

b. f'(x) = 50, 0 ≤ x ≤ 3

C. f'(x) is increasing as x increases, 0 ≤ x ≤ 3

d. f'(x) is decreasing as x increases, 0 ≤ x ≤ 3"--

A measurable characteristic of an entire population is a parameter.

The population data is the real data for a certain attribute in the context of statistics, whereas the sample data is the representative data picked from the population. Metrics like mean, standard deviation, median, and mode are typically used to measure the characteristics of the sample and population.

Option B is the right response to the provided question.

A parameter is a quantity that affects a mathematical object's output or behavior yet is thought of as being held constant. Variables and parameters have a lot in common, and in some cases, the distinction is really one of perspective.

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When data is collected in a statistical study for only portion or subset of all element of interest we are using a sample.

We frequently collect data from samples, or smaller subsets of the population, as opposed to the entire population as a whole.

A sample is a subset of units chosen to represent all the individuals in the population. Because just a portion of the population was counted, it is only a partial enumeration. To estimate the characteristics for the total population of interest, data from the sampled units is used.

For instance, a medical study looks at how a certain disease spreads among city's stray canines. The population of interest in this case are the city's street dogs. This sample or population of interest corresponds to the overall population on which you want to draw conclusions.

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As per the given data, the required confidence interval is (2.79) or (3.95) and the required sample size is 22.

The table which shows the calculation for mean and sd is attached below the answer ;

Given that :-
The sample mean is  X = ∑x/n = 3.372

Sample standard deviation = √∑(x- X)² /√n-1 = 1.6

and the population standard deviation (σ) = 0.66

(a).

For 95% conifdence interval z-critical value is 1.96. A 95% confidence interval for the mean adhesion is :-

= X ± [tex]Z_{c}[/tex] • σ/√n
= 3.72 ± 1.96 • 0.66/√5

= 3.72 ± 0.5785

= (3.72 + 0.57) or (3.72 - 0.57)  

= (2.79) or (3.95)

Hence, the required confidence interval is (2.79) or (3.95).

(b).

Here we have, E = 0.55/2 = 0.275

so, the required sample size (n) = [tex]Z^{2}_{c}[/tex] • σ²/ E²

       (n) = 1.96² • 0.622²/0.275²

       (n) = 22.13

Hence, the required sample size is 22(approx).

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------------- Correct format of the question is given below ------------

(Q). Ishikawa et al. (Journal of Bioscience and Bioengineering, 2012) studied the adhesion of various biofilms to solid surfaces for possible use in environmental technologies. Adhesion assay is conducted by measuring absorbance at A590. Suppose that for the bacterial strain Acinetobacter, five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm2. Assume that the population standard deviation is known to be 0.66 dyne-cm2, and the population distribution is normal.

(a) Find a 95% confidence interval for the mean adhesion.

(b) If the scientists want the confidence interval to be no wider than 0.55 dyne-cm2, how many observations should they take? (Note that, the width of the confidence interval is two times the margin error E, so E = 0.55/2).

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

If the ratio is 2: 3, (children's section: chapter books) we can use this equation to figure out how many chapter books there are if there are 500 children's section books:

In the ratio 2: 3, 2 is being multiplied by 1.5 to get to 3. If the relationship between the numbers 2 and 500 stays proportional, we multiply 500 by 1.5.

Therefore, the ratio of children's books to chapter books is 500: 750, meaning there are 750 chapter books.

When the measurement scale provides information regarding greater than or less than, but not how much greater or less, it is in the form of ordinal data.

Ordinal data is a type of categorical data, which is a type of data that fits into discrete categories, such as gender, or levels of education. Ordinal data does not provide numerical values for comparison, only information on the order of the categories.

For example, a survey may ask respondents to rate their opinion of a product on a scale of one to five. The scale provides information on the order of the categories (one being least favorable and five being most favorable), but it does not provide numerical values that can be used to calculate the average opinion of the product.

Mathematically, ordinal data is usually represented using an ordered set of numbers, with each number representing the order of the categories. For example, the survey mentioned above would be represented this way: 1, 2, 3, 4, 5. This set of numbers can then be used to calculate the median, mode, and range of the data. For example, the median value of the example survey would be 3, the mode would be 5, and the range would be 4 (5 - 1 = 4).

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The regression equation used to predict y from x is: y = -2.93x + 95.45. The slope of the regression line is -2.93 and the intercept is 95.45.

Regression analysis is a process used to estimate the relationship between two or more variables. It is used to examine the strength of the relationship between a response variable (y) and one or more predictor variables (x).

The coefficients of the regression equation are estimated by minimizing the sum of squared errors between the predicted and actual values of y. The strength of the relationship is indicated by the coefficient of correlation (r), which is a measure of how closely the data points fit the regression line.

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This equation cannot be solved as e to the power of any number cannot be negative. The population of a town cannot be negative. Hence, the population cannot reach 60,000.

To approximate the number of years it will take for the population to reach 40 thousand using the graph, you can look at the x-axis and visually estimate the point where the population line intersects with the 40,000 line. It looks like this will occur around year 25.

To find the number of years it will take for the population to reach 60 thousand without using the graph, you can set up the equation p(n) = 18 - e = 60,000 and solve for n.

p(n) = 18 - e = 60,000

18 - e = 60,000 + e

36 = 120,000

e = -84,000

n = log(-84,000)/log(e)

This equation cannot be solved as e to the power of any number cannot be negative. The population of a town cannot be negative. Hence, the population cannot reach 60,000.

Data integration is the process of combining data from multiple sources into a single, coherent view. This can involve the merging of data from multiple databases, files, or other data storage systems into a centralized repository, or it can involve the creation of a new, unified dataset from disparate sources. The goal of data integration is to provide a single version of the truth by removing duplicates, inconsistencies, and errors, and providing a comprehensive, accurate, and up-to-date view of all relevant data. Data integration is a critical step in many data management and analytics processes and is important for ensuring the reliability and usefulness of data for decision-making.

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The data displays be used to compare populations as

(i)they quickly illustrate measures of center

(ii)they show trends in data that can be compared.

Data Display is basically displaying of useful data which has been extracted from bundles of raw data or raw data points. That useful data can be used to compare two different datasets as well.

It says that it quickly illustrate measures of centre. True, because it presents you quick display so that everyone seeing the data in form of charts or tables easily catch the information to be conveyed.

It says, they show trends in data that can be compared. Yes again true. Data displays show you trends of different things in one clear picture and it can be compared with other datasets through the use of data displays.

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Answer:

A & B

Step-by-step explanation:

24 and 12 are both multiples of 4 & 6

Terri will need a total cash of $66,240 where $3200 is the down payment and $2240 is the closing cost.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

1. Purchase price = $64,000

Percent of down payment = 5% of purchase price

Amount of money needed to pay down payment = 64,000 × 5%

                                                                                  = 64,000 × 0.05

                                                                                  = $3200

2. Purchase price = $64,000

Percent of closing cost = 3.5% of purchase price

Amount of money needed to pay closing cost = 64,000 × 3.5%

                                                                             = 64,000 × 0.035

                                                                             = $2240

3. Down payment is included in the purchase price.

Closing cost is in addition to the purchase price.

Total cash needed = $64,000 + $2240 = $66,240

Hence the total cash needed to purchase condominium is $66,240.

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The statement W ⊂ J is true.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, and the complement of sets.

We have,

From the given information,

R ⊂ J

D ⊂ J

M ⊂ D ⊂ J

W ⊂ D ⊂ J _____(1)

Now,

⊂ means subset.

Example:

A = {1, 2, 3}

B = {1, 2, 3, 4}

So,

A ⊂ B since the element in A is also in B and B has one extra element.

So,

From (1),

W ⊂ J

Thus,

W is a subset of J.

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Answer:

1/15

Step-by-step explanation:

If you divide all the fractions, only 1/15 has a repeating decimal. Hope you pass, Alyssa

The equivalent values of the variables {x}, {y} and {z} are -

x = 28.33

y = 29.83

z = 31.83

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example -

y = f{x} = ax + b

Given is that Isaac has a total of ninety pennies, nickels, and quarters. He has three and a half times as many quarters as nickels and one-half as many pennies as nickels.

Assume that he has {x} nickels, {y} pennies and {z} quarters.

So, we can write -

z = x + 3.5

y = x + 1.5

x + y + z = 90

Substituting the values of {y} and {z}, we get -

x + x + 1.5 + x + 3.5 = 90

3x + 5 = 90

3x = 85

x = 28.33                       .... Eq { 1 }

y = 28.33 + 1.5 = 29.83

y = 29.83                               .... Eq { 2 }

z = 31.83                                        .... Eq { 3 }

Therefore, the equivalent values of the variables {x}, {y} and {z} are -

x = 28.33

y = 29.83

z = 31.83

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Opposite angles are equal in a parallelogram.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Given is a parallelogram LMNP which is attached below.

Consider ΔLMP and ΔNMP.

MP = MP, common side.

LM and NP are parallel lines.

∠NPM = ∠LMP, alternate interior angles.

Also ∠LPM = ∠NMP, alternate interior angles.

By the ASA congruence rule, both the triangles ΔLMP and ΔNMP are congruent.

So ∠PLM congruent to ∠MNP.

Similarly, by considering the triangles ΔLNP and ΔLMN, we can prove that angle LMN is congruent to NPL by similar steps.

Hence the opposite angles of a parallelogram are equal.

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Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

The simplified expression that represents the perimeter of the new triangle

is 72c² + 20c.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of any two-dimensional planer figure is the sum of the lengths of it's all the sides except the circle.

The given perimeter of the right angle triangle is,

= (4c + 6c + 4 + 8c + 1).

= 18c + 5.

Therefore, The new perimeter of the triangle will be,

= 4c(18c + 5).

= 72c² + 20c.

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Answer:

Below

Step-by-step explanation:

Circumference (distance around) a circle = pi * diameter

                                                           = 3.14 * 35 m = 109.9 m

FIVE of these would be   109.9 * 5 = 549.5 meters

at 20 per meter would be   549.5 * 20 = 10 990   (units)  

The probability of each outcome is equal, and the outcomes have a uniform probability distribution.

The probability of spinning a yellow is 1/4,

The probability of spinning a yellow or green is 1/2.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given A spinner with yellow, blue, red, and green sections,

total outcomes = 4

and the possibility for occurring of each color is 1,

probability = favorable outcome/total outcome

P(yellow) = 1/4

P(Red) = 1/4

P(blue) = 1/4

P(green) = 1/4

so the probability of each color is equal,

and a probability distribution known as a "uniform distribution" assumes that all possible outcomes are equally likely to occur.

The probability of spinning a yellow or green,

a favorable outcome for  a yellow or a green = 2

P( yellow or green) = 2/4 = 1/2

Hence the probability of each outcome is equal and the outcomes have a uniform probability distribution.

and P(yellow) = 1/4, and P( yellow or green) = 1/2.

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According to the regression model, approximately 71.46% of the audience will finish watching a documentary that is 85 minutes long.

Regression is a statistical method used to model the relationship between two variables.

In this case, the regression equation y = -0.414x + 106.55 is used to approximate the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x.

To find the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long, we need to plug in 85 for x in the regression equation:

y = -0.414x + 106.55

y = -0.414(85) + 106.55

y = -35.09 + 106.55

y = 71.46

Therefore, the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long is 71.46%.

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The solid's volume will be determined by rotating the area enclosed by the specified curve and the lines y = 2x, y = 2, and x = 0 around the x-axis.

V = 8π/3

Volume integration: What is it?

We refer to an integration as a volume integration when it is carried out in three dimensions using the three variables x, y, and z.

In order to establish my integration borders, I set y=2x y=2 to determine their intersection point.

Your aim is to locate the region so you can settle there. The region is going to be circular because we are rotating around the x-axis.

V = (r2)dr = A(x)dx

We subtract the two radiuses from one another since they are different.

∫(πr₂² - πr₁²)dr

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Since our boundary is at 1, integrate between 0 and 1.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, V = 8/3 will be the volume of the solid produced by rotating the area enclosed by the specified curve and lines y = 2x, y = 2, and x = 0 about the x-axis.

What Does a Solid's Volume Mean?

The amount of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid is used to calculate it.

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Answer: 1/9

Step-by-step explanation:

Answer:

3 - 1/3 = 2 2/3

if you take 1/3, then you can just take 1 from 3 for a moment, and then add it back, as shown:

1 - 1/3 = 2/3

Then just add it back:

2/3 + 2 = 2 2/3

Step-by-step explanation:

Hope it helps! =D

Check the picture below.

so by the "inscribed angle theorem" that means "c" is half of 70°, and by Thales Theorem "a" is a right-angle, btw that can also be derived by the "inscribed angle theorem", that makes angles "b" and "c" complementary angles.

The length CD of the rectangle is 34 units

From the question, we have the following parametes that can be used in our computation:

The perimeter of the rectangle below is 128 units

This means that

2 * (3x + 3 + 4x - 2) = 128

So, we have

7x + 1 = 64

Evaluate the like terms

7x = 63

This gives

x = 9

Recall that

CD = 4x - 2

So, we have

CD =4 * 9 - 2

CD = 34

Hence, the length is 34 units

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