7. The functions f(x)=2* and g(x)=8(2)* are both shown graphed.
The graph of g is certainly a vertical stretch of the function f by a
factor of 8. But, it is also a shift off by three units left. Can you
explain why this is using an exponent law?

Answers

Answer 1

The function g(x) = 8(2)^x is also a shift left by 3 units of f(x) = 2^x, as 8 = 2³, hence 8(2)^x = 2^(x + 3).

What is a translation?

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.

The functions for this problem are given as follows:

f(x) = 2^x.g(x) = 8(2)^x.

8 is the third power of 2, hence:

8 = 2³.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

8(2)^x = 2³ x 2^x = 2^(3 + x) = 2^(x + 3).

As x -> x + 3, a translation left 3 units happened.

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Related Questions

Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2 ,− 9) and (−6,7). PLSLLSLS

Answers

The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2

What is the slope of the line?

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:

Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )

Midpoint = ( (-2-6)/2 , (-9+7)/2 )

Midpoint = (-4,-1)

Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (7 - (-9)) / (-6 - (-2))

Slope = 4

The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.

Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:

y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.

Plugging in the values we found, we get:

y - (-1) = (-1/4)(x - (-4))

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

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

y = (-1/4)x - 2

Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.

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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 111?

Answers

On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]

What is equation?

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.

Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.

M+D = 82 marbles

[tex]M= 82- D[/tex]

[tex]D= 4M+2[/tex]

[tex]D= 4(82-D) +2[/tex]

[tex]D= 328 - 4D+2[/tex]

[tex]5D = 330[/tex]

[tex]D= 66[/tex]

Therefore, Don has 66 and Mark has 82-66 = 16

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A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.

Answers

Weight is 0.229 pounds after 4 weeks.

As a young channel catfish only weights 0.1 pounds,

It gains weight over the following 8 weeks at a rate of roughly 23% every week.

In this case, the exponential growth function is as follows:

Exponential formulas are provided by.

[tex]y=a(1+r)^{x}[/tex]

where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.

Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.

As a result,

[tex]y=0.1(1+0.23)^{4} \\[/tex]

y = 0.1(2.289)

y = 0.229

Consequently, the weight at 4 weeks is 0.229 pound.

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Complete question:

A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.

Graph the line with slope -1 passing through the point (1,-5)

Answers

Answer:

please review the attachment

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called

Answers

Answer:

sampling distribution

Step-by-step explanation:

:)

The ratio of first- class, second- class and third-class passengers who survived the ship wreak is
101:59:89. How many passengers were saved if the total number of first-class passengers were 202?

Answers

Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.

If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.

Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.

Step-by-step explanation:

Find the value of x that makes each sentence true.
If (5 1/5)^5=25x then x =
If (8 1/3)^2= 4x, then x =

Answers

The first equation is:

(5 1/5)^5 = 25x

To solve for x, we need to simplify the left side of the equation first.

(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776

So,

7776 = 25x

Therefore,

x = 7776/25 = 311.04

For the second equation:

If (8 1/3)^2 = 4x, then x =

We need to simplify the left side of the equation first.

(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81

So,

81 = 4x

Therefore,

x = 81/4 = 20.25

So the values of x that make each sentence true are 311.04 and 20.25, respectively.

rj and is 2 brother are given php2000 weekly allowance they have allocoted 60% for food 8% for fare 15% for school needs and the remaining 17% for savings how much is allocoted for the following

Answers

Answer:

RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.

For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.

For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.

For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.

For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.

So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 21 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.)

Answers

A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.

Is a high standard deviation desirable?

The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.

The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.

The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.

In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.

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Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5

Answers

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]

Jonathan is a single taxpayer. His taxable income before deductions was $63,110. He was able to reduce his taxable income by $10,312 when he filled out Schedule A and Schedule 1.
a. How much did he save in tax by using Schedule A?

Answers

In a linear equation. , $12,215 did he save in tax by using Schedule A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given,

      Taxable income with out deductions = $63,110

                     total deductions = $10,312

       the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is

                          tax = $12,215

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Suppose you invest $500 into an account earning simple interest. The APR is 2% and you invest it for 5 years. Choose two answers: How much would your investment be worth at the end? What equation should you use to calculate this?
1a. $2500.10
2a. $550
3a. $1000
4a. $2550
5a. $5500
1b. A = 500 ( 1 + 2(5))
2b. A = 500 (1 + 0.2(5))
3b. A = 500 (1 + 0.02(5))

Answers

Answer:

a=1000.10

Step-by-step explanation:

The width of a table is 4 2/5
feet. The length of the table is 2 1/5
times as long as its width.

Which equation shows the length of the table?

Please answer ASAP

Answers

The equation that shows the length of the table is  length = 11/5 × 22/5

What is a fraction?

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractions

From the information given, we have that;

Length = 2 1/5 × Width

Width = 4 2/5 feet

Turn into improper fractions

Width = 22/5 feet

Then, length = 11/5 × 22/5

Hence, the equation is 11/5 × 22/5

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The value of a machine, V , at the end of t years

Answers

The value of machine after 2 years is $346.4.3

What is Rate of Depreciation?

Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.

Given:

C = $707 (the original cost),

r = 0.3 (the rate of depreciation),

and t = 2 (years that have gone by)

Using the Formula

V = C [tex](1-r)^t[/tex]

V = (707)(1 - 0.3)²

V = (707)(0.7)²

V = (707)(0.49)

V = 346.43

Thus, the value of machine is $346.43

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Place the following set of scores in a frequency distribution table.

7, 5, 6, 4, 4, 3, 8, 9, 4, 7, 5, 5, 6

9, 4, 7, 5, 10, 6, 8, 5, 6, 3, 4, 8, 5
Are the scores clustered together, or are they spread out across the scale? a. Most of the scores are clustered within 1 or 2 points of X = 6. b. The scores are spread out fairly evenly across the scale. c. Most of the scores are clustered within 1 or 2 points of X = 8. d. The scores are clustered in two peaks near X = 3 and near X = 9.

Answers

GIven the set of scores, it is seen that a. Most of the scores are clustered within 1 or 2 points of X = 6.

What is a Frequency Table?

A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.

Here is a frequency distribution table for the given set of scores:

Score Frequency

3 2

4 5

5 5

6 5

7 2

8 3

9 2

10 1

You can see that the scores are clustered around X = 6, with the highest frequency (5) at score 6 and the next highest frequency (5) at score 5.

The scores are not evenly spread out across the scale.

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Solve the equations for x

Answers

Answer:

Step-by-step explanation:

5=cx-ax=x(c-a)

x(c-a)/5=1

(c-a)/5=1/x

x=5/(c-a)

what is the least common denominator for 5/18, 11/12, and 6/13

Answers

Answer:

LCD → 468

Step-by-step explanation:

[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]

[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]

[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]

Hence, the least common denominator for these three fractions would be 468.

Use calculator to find 61.6 to the nearest hundredth

Answers

Answer : 61.60

Step-by-step explanation:

Answer:61.60

Step-by-step explanation:

i just typed it in

Circles and please answers please just need help Thank you so much

Answers

The area of the shaded region is given as follows:

As = 324(2π - 1) in².

What is the area of the shaded region?

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:

A = π x [tex](18\sqrt{2})²[/tex]

A = 648π in².

The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:

A = 18²

A = 324 in².

Hence the area of the shaded region is given as follows:

As = 648π - 324

As = 324(2π - 1) in².

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Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.

Answers

The ratio of the amounts of money that they each get:

1 : 3 : 3/2

What is the ratio?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Let's represent the amount of money that Jan gets as x.

Then, the amount of money that Freda gets is 3x,

and the amount of money that Pieter gets is:

= (1/2) x 3x

= 3/2 x (x)

The ratio of the amounts of money that they each get can be written as:

⇒ x : 3x : 3/2 x (x)

⇒ 1 : 3 : 3/2

So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.

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Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y=x-2
y=x-1

Answers

The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.

What are parallel lines?

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

No matter how far we extend a parallel line, it will never meet another parallel line.

Given that,

y=x-2

y=x-1

For x = 1:

y = x - 2 = 1 -2 = -1

y = x - 1 = 1 - 1 = 0

For x = 2:

y = 2- 2 = 0

y = 2 -1 = 1

Plot the graph using the points.

The two lines have the same slope hence they are parallel lines.

Since, the two lines are parallel the system has no solutions.

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if an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s what is the value of V0y?​

Answers

The value of the final velocity before striking the ground will be 9.899 meters per second.

What is a vector?

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.

We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.

The speed of the object before striking the ground is given as,

v² - u²= 2gh

v² - 0² = 2 × (9.8) × (5)

v² = 98

v = 9.899 meters per second

The value of the final velocity before striking the ground will be 9.899 meters per second.

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Choose all of the values that are solutions to inequality x < -2

Answers

Answer:

The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.

So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).

Therefore, the values that are solutions to the inequality x < -2 are:

• all real numbers less than -2, such as -3, -4, -5, etc.

Note that -2 itself is not part of the solution set, since it is not less than -2.

Which of the following is an example of a continuous random variable?a. A Bernoulli trial
b. Binomial random variable
c. Normal random variable
d. Discrete uniform random variable

Answers

An example of a continuous random variable is a Normal random variable.

What is a normal random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).

Here, we have

We have to determine the example of a continuous random variable.

We concluded that the example of a continuous random variable is a normal random variable.

Hence, an example of a continuous random variable is a Normal random variable.

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Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°.

Find the distance he swam across the lake.

Hint: hypotenuse = 2shortleg )

Answers

The length of the lake is 100 ft

Finding the length of the lake:

Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.  

From the trigonometric ratio table,

Tan 30 = 1/√3

Here we have

Yoshi swam across a lake but did not know how far he swam.

He found that it was 100√) feet from point A to point C.

Angle C was a right angle and angle A is 30°.

We represent the given scenario in the form of a right angle triangle as shown in the picture.

Let 'B' be the point where Yoshi swam started and  BC be the length of the lake.  

From the triangle,  

Tan A = BC/AC

From the given data,

Tan 30° = BC/100√3

=> BC = Tan 30°(100√3)

=> BC = (1/√3)(100√3)  

=> BC = 100 ft

Therefore,

The length of the lake is 100 ft

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(c) 10:35 f the foll ing ratio​

Answers

The ratio 10:35 can be simplified to 2:7.

What is a Ratio?

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

The ratio 10:35 can be simplified to 2:7.

To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.

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Simply the following ratio 10:35

Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?

Answers

For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.

So, the domain of the function is all real numbers greater than 2, or -

Domain: x > 2

Now let's consider the range of the function.

The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.

Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.

So, the range of the function is -

Range: -∞ > f(x) > ∞

Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.

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What is the image of (1, 0) after a dilation by a scale factor of 4 centered at the
origin?

Answers

Answer:

  (4, 0)

Step-by-step explanation:

You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.

Dilation

When the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.

  (1, 0) ⇒ 4(1, 0) = (4, 0)

The image of the point is (4, 0).

Consider a function f(x) = x ^2 . A second function h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).

Answers

Answer:

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Step-by-step explanation:

Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:

The x-coordinates of f(x) and h(x) are the same, so x is unchanged.

The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.

The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.

Given the equation of f(x) = x^2, the equation of h(x) can be written as:

h(x) = -x^2 + 3

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?

Answers

Answer:

3 lunch specials are possible.

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at the instant , the athlete is running with a constant speed of 2 m/s. determine the angular velocity at which the camera must turn in order to follow the motion. in the hecksher-ohlin model, a change from autarky to trade will hurt the owners of group of answer choices labor technology the relatively scarce factor of production the relatively abundant factor of production capital within order of magnitude, approximate time of appearance of: prokaryotes, eukaryotes, multicellular eukaryotes, animals, land plants, humans Dark moths began to outnumber white moths in cities after the Industrial Revolution. What is the most likely reason for this change?answer choicesLight-colored moths mutated into dark colored moths.Light-colored moths began to die due to overpopulation.Light-colored moths were less favored for survival in the new environment.Light-colored moths began to turn black because of factory pollution. Jordan Peele- what inspired them to get involved (why they do what they do)- what they are advocating for/their message- why it is important to them and/or everyone- position(s) or role(s) they are or have been in (e.g.; one person on the list is a UNICEF ambassador)- organizations that they belong to and/or started- area of the country (or world) that they focus on if any- one famous quote from your selected individual - why you or your group chose this person mathematics 20 points a young woman who believes she is overweight begins to starve herself in the hopes of becoming more attractive. a sociologist would explain the woman's behavior in terms of: group of answer choices what is social force and rise of sociology? What are three functions of simple columnar epithelium? Why would a population have a trait controlled by only one allele? Select all that apply.Having a single allele makes it more likely that the population can survive environmental changes.That exact trait is necessary in order for the organism to function properly.The allele makes the population more diverse.A small group of organisms becomes isolated and forms a new population.is it a and c Which property of real numbers is shown below?3 + ((-5) + 6) = (3 + (-5)) + 6O commutative property of additionO identity property of multiplicationassociative property of additioncommutative property of multiplication 3. Farmhouse in Provence by Vincent van Gough demonstrates the artist's post-impressionist style becauseO A. it depicts reality as it's seen in real life.OB. it doesn't attempt to represent reality accurately but rather uses shapes, colors, and forms to achieve an effectOC. it's characterized by distorted shapes and thrilling colors.O D. it creates dreamlike and bizarre scenes dominated by symbolism. How did the Trail of Tears affect native populations in the future? which country was not interested in establishing colonies in the smaller caribbean islands under favorable circumstances including reaction time the world project is a massive and ongoing cross-cultural investigation of nine cultural dimensions involved in leadership and organizational processes. true/false Under the communist party, organized religion in the soviet union was officially_____. What is the story of Judith Slaying Holofernes about? PLEASE ANSWER hurry i need the answer See question in the picture below , will give brainliest for correct answer