If the exponential model f(x)=8(9)x is written with the base e, it will take the form A0ekx. What is A0 and what is k?

The equation of line is y = -3x + 2

An equation for two variables is a mathematical statement that relates two variables, typically represented by x and y, using mathematical symbols and operations such as addition, subtraction, multiplication, and division.

To find the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13), we can use the slope-intercept form of the equation of a line:

y = mx + b, where slope of the line is m and y-intercept is b.

First, let's find the slope of the line using two of the points, say (2, -4) and (3, -7). The slope, m, is given by:

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

= (-7 - (-4)) / (3 - 2)

= -3

we know the slope, we can use one of the points, say (2, -4), and the slope to find the y-intercept, b. Use the slope intercept to form the equation of a line:

y = mx + b, and substitute in the slope and coordinates of one of the points:

-4 = (-3)(2) + b

Simplifying this equation, we get:

b = -4 + 6

= 2

Therefore, the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13) is: y = -3x + 2

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When f(x) is divided by x-3 is 27 , then what is the value of k is -3

Remainder Theοrem is an apprοach οf Euclidean divisiοn οf pοlynοmials. Accοrding tο this theοrem, if we divide a pοlynοmial P (x) by a factοr ( x – a); that isn’t essentially an element οf the pοlynοmial; yοu will find a smaller pοlynοmial alοng with a remainder.

When f(x) is divided by x - 3, the remainder is 27, which means that

f(3) = 27.

We can use this fact tο sοlve fοr k as fοllοws:

f(x) = x³ + kx + 9

f(3) = 27

Substituting x = 3 intο the expressiοn fοr f(x), we get:

f(3) = 3³ + k(3) + 9 = 27

Simplifying the left side, we get:

27 + 3k + 9 = 27

Cοmbining like terms, we get:

3k + 36 = 27

Subtracting 36 frοm bοth sides, we get:

3k = -9

Dividing bοth sides by 3, we get:

k = -3

Therefοre, the value οf k is -3.

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1. Use properties of logarithms with the given approximations to evaluate the expression. Use log2=0.693 and/or log6=1.792 to find log12.

Answer: log12 = log6 + log2 = 1.792 + 0.693 = 2.485.

2. Complete parts (a) and (b).

a. Write the inverse of y=8x in logarithmic form.

Answer: log8(y) = x.

b. Graph y=8x and its inverse and discuss the symmetry of their graphs.

Answer: The graph of y=8x and its inverse will have the same shape, but it will be flipped across the line y = x. This is known as the symmetry of their graphs.

3. 2log215 EVALUATE Use properties of logarithms with the given approximations to evaluate the expression. log3≈0.477 and log5≈0.699. Use one or both of these values to evaluate log27. Write as a single logarithm. Assume that variables represent positive numbers. 5log2x+2log2z

Answer: log27 = log5 + log3 = 0.477 + 0.699 = 1.176.

4. On the basis of data for the years 1918 through 1997, the expected life span of people in a country can be described by the function f(x) = 12.576ln x + 17.088 years, where x is the number of years from 1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?

Answer: This model estimates that the life span for people born in 1941 is 70.698 years.

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The solution of the system of equation is (3, 5) and (–4, 12) [option A]

The given system of equations is:

x + y = 8

y = x² – 4

To solve for x and y, we can substitute the second equation into the first equation for y:

x + (x² - 4) = 8

Simplifying, we get:

x² + x - 12 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -12

x = (-1 ± √(1² - 4(1)(-12))) / 2(1)

x = (-1 ± √(1 + 48)) / 2

x = (-1 ± 7) / 2

Solving for x gives us two possible values: x = 3 or x = -4.

To find the corresponding values of y for each value of x, we can substitute them into either of the original equations. Using y = x² - 4:

When x = 3, y = 3² - 4 = 5

When x = -4, y = (-4)² - 4 = 12

Therefore, the solution to the system of equations is (3, 5) and (-4, 12), which is answer choice (a).

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Answer:

? is equal to 8

Step-by-step explanation:

16/20= 0.8

0.8x10= 8

8/10=0.8

OR YOU COUPLE DIVIDED 16 BY TO AND 20 BY 2

Answer:8/10

Step-by-step explanation:when you divide 16 by 20, you get 0.8. So turn 0.8 into a fraction with 10, you get 8/10. (I’m not that smart, mb if I get something wrong.)

Answer:

3*C

Step-by-step explanation:

We can Frame an equation, taking the previous temperature as "x" and adding 2 by every hour.

Previous Temprature + 2 = New Temprature

Therefore by this equation:

at 8AM , the Temperature is -5 + 2 = -3*c
at 9AM , the Temperature is -3 + 2 = -1*c
at 10 AM, the Temperature is -1 + 2 = 1*c


Therefore at 11AM , the Temperature will be 1 + 2 = 3*c

Hope it helps.

Answer: y=28

Step-by-step explanation:

The coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

To find the coordinates of the foci of the ellipse given by the equation 4x² + y² = 64, we can compare it to the standard form of an ellipse:

(x²/a²) + (y²/b²) = 1

In this case, the equation 4x² + y² = 64 can be rewritten as:

x²/(8²) + y²/(8²) = 1

Comparing the equation to the standard form, we find that a = 8 and b = 8. The foci of the ellipse can be calculated using the formula:

c = sqrt(a² - b²)

For our ellipse, c = sqrt(8² - 8²) = sqrt(64 - 64) = 0.

Since c = 0, the foci coincide with the center of the ellipse. Thus, the coordinates of the foci are the same as the center of the ellipse.

Therefore, the coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

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The probability of drawing the blue and even-numbered marble from the given jar is 3/10.

The given problem can be solved using the concept of Probability. Let's see how to solve it.

Step 1: Total Number of Marbles in the Jar

Number of red marbles in the jar = 3

Number of blue marbles in the jar = 7

Total number of marbles in the jar = 3 + 7 = 10

Step 2: Find the Probability of Marble is Blue and Even Numbered

Number of blue marbles which are even-numbered = 3 (Blue marbles numbered 2, 4, and 6 are even-numbered marbles)

Total number of marbles in the jar = 10

Probability of marble is blue and even-numbered = Number of blue marbles which are even-numbered / Total number of marbles in the jar = 3/10

So, the required probability of drawing the blue and even-numbered marble is 3/10.

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Answer:

52.08 Euros

Step-by-step explanation:

21.70 euros / 20 uk pounds = 1.085 per pound

so 48 euro x 1.085 pounds = 52.08 euros

The trinomial( consists three different terms), 2x² + 13x + 6, has a linear factor of (x + 6) and the linear factor of (x+6) is equals to a (2x+1).

We have, a trinomial 2x² + 13x + 6 has a linear factor of x + 6 and we have to determine that linear factor of (x + 6). To determine the linear factor of (x + 6) either dividing the trinomial by (x+6) or factorization of this trinomial. Factoring a trinomial means expanding an equation into the product of two or more binomials. Here, middle term of trinomial, b = 13

last term, c = 6

Using spliting middle term method for factorization, 2x²+ 13x + 6 = 2x² + 12x + x + 6

=> 2x² + 13x + 6 = 2x( x + 6) + 1(x + 6 )

Common factor from binomials,

=> 2x² + 13x + 6 = (x + 6)(2x + 1)

Thus, the linear factor of (x+6) is (2x +1).

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Answer: x = 24

Step-by-step explanation:

To solve for x, we need to simplify the left side of the equation first by combining like terms:

4x - 2 + 3x + 14 = 180

7x + 12 = 180

Next, we will isolate the variable by subtracting 12 from both sides:

7x + 12 - 12 = 180 - 12

7x = 168

Finally, we will solve for x by dividing both sides by 7:

7x/7 = 168/7

x = 24

Therefore, the solution to the equation 4x-2+3x+14=180 is x = 24.

The length of each side of the hexagon is 13 units long, which is equal to length of the park.

In order to determine the length of every side of the hexagon, it is necessary to compute the distance between each pair of neighboring vertices.

This can be accomplished by employing the distance formula, which is represented as follows:

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² ).

To facilitate the process, we will designate the vertices as A, B, C, D, E, and F in sequence, with A being the vertex at the top.

Then, the length of side AB is calculated as follows:

|AB| = √((38.5-26.5)² + (7-12)²)

|AB| = √((12)² + (-5)²)

|AB| = √(144 + 25)

|AB| = √169

|AB| = 13

Similarly, we can calculate the length of each side:

|BC| = √( (26.5-38.5)² + (2-7)² ) = 13

|CD| = √( (13.5-26.5)² + (2-2)² ) = 13

|DE| = √( (1.5-13.5)² + (7-2)² ) = 13

|EF| = √( (13.5-1.5)² + (12-7)² ) = 13

|FA| = √( (26.5-13.5)² + (12-12)² ) = 13

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Answer:

13 units

Step-by-step explanation:

d^2 = (x2 – x1)^2 + (y^2 – y^1)^2

Now we calculate the distance between 2 points:

d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2

d^2 = 169

d = 13

Therefore the length of each side of the park is 13 units.

(13/4)z^(5)x^(2) - 6/x

The given expression is: (13z^(5)x^(5)-24zx^(5))-:(-4x^(3)x^(4)) To simplify the given expression, we will use the rules of division of two algebraic expressions. The division of two algebraic expressions is equal to the multiplication of the first expression with the reciprocal of the second expression. The reciprocal of an expression is the inverted expression of that expression. So, (13z^(5)x^(5)-24zx^(5))-:(-4x^(3)x^(4))=(13z^(5)x^(5)-24zx^(5)) x ( -1/4x^(3)x^(4))Simplify the above expression by combining the like terms as follows:(13z^(5)x^(5)-24zx^(5)) x ( -1/4x^(3)x^(4))=(13z^(5)x^(5) x (-1/4x^(3)x^(4))) + (-24zx^(5) x (-1/4x^(3)x^(4)))=-(13/4)z^(5)x^(2) - 6/x Therefore, the simplified form of the given expression is -(13/4)z^(5)x^(2) - 6/x.

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The volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm.

Volume is a measure of the quantity or amount of space an object occupies. It is measured in cubic units, such as cubic meters, cubic centimeters, and cubic feet. Volume is also used to measure the amount of liquid or gas in a container. Volume is an important concept in mathematics, science, engineering, and other subject areas. It can be used to calculate the mass, weight, density, and other physical properties of a substance or object.

The volume of water that can be enclosed in the outside layer of the glass is equal to the volume of the plastic material that encloses the glass. Since the thickness of the plastic is 0.25 cm, the volume of the plastic material is equal to its surface area multiplied by the thickness. The surface area of the glass can be calculated using the equation 4πr², where r is the radius of the glass.

Therefore, the volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm. This is equal to the volume of the plastic material that encloses the glass. It should be noted that this volume of water is only an approximation since other factors such as the porosity of the plastic material must be taken into account.

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The volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm.

Volume is a measure of the quantity or amount of space an object occupies. It is measured in cubic units, such as cubic meters, cubic centimeters, and cubic feet. Volume is also used to measure the amount of liquid or gas in a container. Volume is an important concept in mathematics, science, engineering, and other subject areas. It can be used to calculate the mass, weight, density, and other physical properties of a substance or object.

The volume of water that can be enclosed in the outside layer of the glass is equal to the volume of the plastic material that encloses the glass. Since the thickness of the plastic is 0.25 cm, the volume of the plastic material is equal to its surface area multiplied by the thickness. The surface area of the glass can be calculated using the equation 4πr², where r is the radius of the glass.

Surface area = 4πr², where r is the radius of the glass. Therefore, the approximate volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm, where r is the radius of the glass.

Therefore, the volume of water that can be enclosed in the outside layer of the glass is 4πr² x 0.25 cm. This is equal to the volume of the plastic material that encloses the glass. It should be noted that this volume of water is only an approximation since other factors such as the porosity of the plastic material must be taken into account.

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Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). The coordinates of the intersection point are (1,3).

What is rhombus?

A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.

Since ABCD is a rhombus, its diagonals AC and BD are perpendicular bisectors of each other, and they intersect at their mutual midpoint M.

The midpoint M of AC is the average of the coordinates of A and C, namely:

M = ((-1+3)/2, (2+4)/2) = (1, 3)

Similarly, the midpoint of BD is the average of the coordinates of B and D. Since we don't know the coordinates of B and D, we need to find them first.

The other two vertices of the rhombus are obtained by reflecting A and C about the midpoint M, since opposite sides of a rhombus are parallel and equal in length. To do this, we subtract the coordinates of M from those of A and C, and then add them to M:

B = 2M - A = 2(1,3) - (-1,2) = (3,4)

D = 2M - C = 2(1,3) - (3,4) = (-1,2)

Now we can find the midpoint of BD:

N = ((3-1)/2, (4+2)/2) = (1, 3)

Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). Therefore, the coordinates of the intersection point are (1,3).

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the high-temperature range which is most likely represented by the shaded area labeled 1 is 90°F to 99°F.\

Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).

In Science, the temperature is measured by using a thermometer and its units include the following:

Celsius (°C)

Kelvin (K)

Fahrenheit (°F)

Based on the weather map shown in the image attached below, we can deduce that the high-temperature range which is most likely represented by the shaded area labeled 1 is 90°F to 99°F.

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The area of the garden is given as follows:

A = 20.6925 ft².

The garden has a rectangular format, hence it's area is given by the multiplication of it's length l by it's width w, as follows:

A = lw.

From the image, converting the mixed numbers to decimal, the dimensions of the garden are given as follows:

Hence the area in feet squared is given by the multiplication of these two dimensions, as follows:

A = 7.75 x 2.67

A = 20.6925 ft².

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a. The perimeter in the scale is 36 centimeters

The area in the scale drawing is 80 square centimeters.

b.  The actual perimeter is 40 millimeters.

The actual area is 937.5 square millimeters. ​

To find the perimeter of the icon in the scale drawing, you need to add up the length of all its sides. Using the ruler provided, measure the length and width of the icon and round them to the nearest half centimeter. Then, add up the length and width and multiply by 2 to get the perimeter.

a. Assuming the scale of the drawing is 1 cm : 2 units, the length of the icon in the drawing would be 2 x 5 = 10 units and the width would be 2 x 4 = 8 centimeters.

The perimeter in the scale drawing would be 2 x (length + width) = 2 x (10 + 8) = 36 cm (rounded to the nearest half-centimeter).

The area in the scale drawing would be length x width = 10 x 8 = 80 square cm.

b. Assuming the scale of the drawing is 1 cm : 2 units, the actual length of the icon would be 2.5 cm / 2 = 1.25 units and the actual width would be 1.5 cm / 2 = 0.75 units.

The actual perimeter would be 2 x (length + width) = 2 x (1.25 + 0.75) = 4 cm = 40 mm.

The actual area would be length x width = 1.25 x 0.75 = 0.9375 square cm = 937.5 square mm.

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The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

A reflection across the x-axis is a transformation that flips an object across the line x = 0. This means that the points in the object will be reflected across the x-axis. The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis .Let us consider the original quadrilateral, ABCD, with coordinates A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). Then, the coordinates of the reflected quadrilateral A'B'C'D are A'(-x1, y1), B'(-x2, y2), C'(-x3, y3) and D'(-x4, y4).For example, if the coordinates of quadrilateral ABCD are A(3, 5), B(7, 6), C(4, 8) and D(9, 2), then the coordinates of the reflected quadrilateral A'B'C'D will be A'(-3, 5), B'(-7, 6), C'(-4, 8) and D'(-9, 2).Therefore, the coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

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Answer:

x = 6

Step-by-step explanation:

Solve for x

[tex]11+x=7-4x[/tex]

Add 7 on both sides

[tex]18+x=4x[/tex]

Subtract x on both sides (same as 1x)

[tex]18=3x[/tex]

Divide by 3

[tex]6=x[/tex]

The area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:

Area = (1/2) * perimeter * apothem

The perimeter of the polygon can be found by multiplying the number of sides by the length of each side. Since the polygon is regular, all sides are of equal length. Let's call this length "s".

s = 2 * r * sin(π/n) where r is the radius and n is the number of sides

s = 2 * 4 * sin(π/12)

s = 1.38 (rounded to two decimal places)

The perimeter of the polygon is:

P = 12 * s

P = 16.56 (rounded to two decimal places)

To find the apothem, we can use the formula:

apothem = r * cos(π/n)

apothem = 4 * cos(π/12)

apothem = 3.77 (rounded to two decimal places)

Now we can calculate the area of the polygon:

Area = (1/2) * P * apothem

Area = (1/2) * 16.56 * 3.77

Area = 31.28 square units (rounded to two decimal places)

Therefore, the area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

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Answer: 45 ml/h

Step-by-step explanation: that is  s/t graph

read in any point on the part of graph  distance , and divide

it with time .

95:2 hours,  

The first five terms of the sequence given the definition are -1, 0, 1, 2 and 3

To find the first five terms of the sequence {an}, we can use the recursive definition of the sequence and compute each term one by one:

a1 = -1

For n = 2, we have:

a2 = a1 + (-1)² = -1 + 1 = 0

For n = 3, we have:

a3 = a2 + (-1)³ = 0 - (-1) = 1

For n = 4, we have:

a4 = a3 + (-1)⁴ = 1 + 1 = 2

For n = 5, we have:

a5 = a4 + (-1)⁵ = 2 - (-1) = 3

Therefore, the first five terms of the sequence {an} are:

a1 = -1

a2 = 0

a3 = 1

a4 = 2

a5 = 3

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Answer:

Step-by-step explanation:

Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).

Answer: u = 2.83, -2.83.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two sides separated by an equals sign (=). The expressions on both sides of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The goal in solving an equation is to find the value or values of the variable(s) that make the equation true.

The real numbers are a set of numbers that includes all rational and irrational numbers. Real numbers can be represented on the number line, where every point corresponds to a unique real number. The real number system is denoted by the symbol R.

In the given question,

To solve the equation 7u² - 56 = 0, we can start by isolating the variable u by adding 56 to both sides of the equation:

7u² - 56 + 56 = 0 + 56

Simplifying the left side, we get: 7u² = 56

Dividing both sides by 7, we get: u² = 8

Taking the square root of both sides, we get: u = ±√8

Simplifying the square root, we get: u = ±2.83

Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).

Answer: u = 2.83, -2.83.

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The growth rate given by value of dR / dc at C = 2 is 0.0021 (approx).

The given formula is, R(C) = 1.35c / (0.29 + c)

=> R(C) = 1.35c / 0.29 + 1.35c / c

Take the derivative of R with respect to c: R(C) = 1.35c / 0.29 + 1.35c / c

Differentiating with respect to c, dR / dc = 1.35(0.29 + c) - 1.35c / (0.29 + c)2dR / dc

= 1.35(0.29 + c - c) / (0.29 + c)2dR / dc

= 1.35(0.29) / (0.29 + c)2

At C = 2,dR / dc = 1.35(0.29) / (0.29 + 2)2= 0.002129

A bacterial growth rate is given by the equation R(C) = 1.35c / (0.29 + c).

We know that R(C) = 1.35c / (0.29 + c) dR / dc = 1.35(0.29 + c - c) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + 2)2dR / dc = 0.002129

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Answer:

function not defined for x = 2

Step-by-step explanation:

The open circle at x = 2 shows that the function is not defined for x = 2.

The religious make-up of the United States Congress is reflective of that in the general population.

Answer:Yes, the religious make-up of the United States Congress is reflective of that in the general population.The steps to test whether the distribution of religion among U.S. adults differs significantly from that among the 114th U.S. Congress with an α = 0.01 level of significance are given below:First, calculate the expected frequencies for Mormon and Unaffiliated using the formula:Expected frequency = (total sample size) x (proportion)Expected frequency of Mormons = (1500) x (0.030) = 45Expected frequency of Unaffiliated = (1500) x (0.019) = 28.5Next, calculate the chi-square statistic using the formula:Chi-square = ∑ [(observed frequency - expected frequency)² / expected frequency]To find the observed frequency - check the frequency table below.Religion Frequency Expected Contribution Protestant 772 858.0 8.620 Catholic 368 460.5 18.580 Mormon 34 45.0 8.690 Orthodox 12 13.5 0.167 Jewish 46 78.0 13.128 Other 61 16.5 120.015 Unaffiliated 207 28.5 149.969The degrees of freedom for the chi-square test = (number of categories - 1) = 7 - 1 = 6Finally, compare the calculated chi-square statistic with the critical value from the chi-square distribution table with 6 degrees of freedom at α = 0.01 level of significance. If the calculated chi-square statistic is greater than the critical value, then the null hypothesis is rejected and we conclude that the distribution of religion among U.S. adults is significantly different from that among the 114th U.S. Congress. If the calculated chi-square statistic is less than or equal to the critical value, then the null hypothesis is accepted, and we conclude that the distribution of religion among U.S. adults does not differ significantly from that among the 114th U.S. Congress.

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