Use the graph to answer the question. graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3 Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°. A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0) A′(0, 0), B′(2, −5), C′(−5, −5), D′(−3, 0) A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0) A′(0, 0), B′(−5, −2), C′(−5, 5), D′(0, 3)

Answers

Answer 1

The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3).

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

To find the coordinates of polygon A'B'C'D' after a 180° rotation, we need to reflect each vertex across the x-axis and then the y-axis.

To reflect a point across the x-axis, we change the sign of the y-coordinate.

To reflect a point across the y-axis, we change the sign of the x-coordinate.

Using this method, we can find the coordinates of A'B'C'D':

A(0, 0) reflects to A'(0, 0) (no change)

B(5, 2) reflects to B'(-5, 2) (reflect across y-axis)

C(5, -5) reflects to C'(-5, -5) (reflect across y-axis)

D(0, -3) reflects to D'(0, 3) (reflect across x-axis)

Therefore, the coordinates of polygon A'B'C'D' are:

A'(0, 0), B'(-5, 2), C'(-5, -5), D'(0, 3)

Hence, the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3) and the graph is attached is in the attached image.

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Related Questions

A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results:
• Even number = lose $9.
• 1 or 3 = win $2
• 5 = win $10
What is the expected value of the game?

Answers

I think the expected value is 10$ but I’m just guessing

Linda agreed to lend money to Alex at a rate of 9 percent per year,
contingent he would pay her 300.00 in interest over a four year period. What was the minimum mount Alex could borrow

Answers

Answer:

$731.71

Step-by-step explanation:

300 over 4 years = 75$ per yr

9% per year so 4 years interest = (1+9%)^4 = 1.41

so effective int rate for 4 years is 41%.

41% * x = 300

x = $731.71

(-23u^4 z^2 +32u^7 z^7 -12u^2 z) ÷ -4u^4 z^2

Answers

To simplify the expression, we can factor out -4u^4z^2 from each term in the numerator:

(-23u^4 z^2 +32u^7 z^7 -12u^2 z) / (-4u^4 z^2) = (-4u^4 z^2)(32u^3 z^5 - 8u^2 + 3) / (-4u^4 z^2)

The -4u^4z^2 terms cancel out, leaving:

(32u^3 z^5 - 8u^2 + 3) / u^4z^2

Therefore, the simplified expression is (32u^3 z^5 - 8u^2 + 3) / u^4z^2.

Find the length of CD. The length of BE is 28in

Answers

The length of the segment CD given the length of BE is 42 inches

Finding the length of CD given the length of BE

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

The length of CD = ?The length of BE is 28in

Using the proportional ratio from the triangle, we have

CD = 1.5 * BE

substitute the known values in the above equation, so, we have the following representation

CD = 1.5 * 28

Evaluate

CD = 42

HEnce, the lengtth is 42 inches

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7. El área de un terreno de forma rectangular es 4332 m?. Si de ancho mide la tercera parte de su medida de largo, ¿Cuáles son las dimensiones del rectángulo?

Answers

Sea x la medida de largo del terreno. Entonces, el ancho del terreno es x/3. Como el área del terreno es 4332 m², podemos escribir la ecuación:

x(x/3) = 4332

Resolviendo para x, obtenemos:

x²/3 = 4332

Multiplicando ambos lados por 3, obtenemos:

x² = 12996

Tomando la raíz cuadrada de ambos lados, obtenemos:

x = 114

Por lo tanto, las dimensiones del rectángulo son 114 m de largo y 38 m de ancho.

(AWARDING 90 POINTS!!!) Does this data set have any outliers?

{667, 667, 505, 435, 844, 435, 346, 667, 346, 779, 222}

Yes, 222 is an outlier.

Yes, 667 is an outlier.

Yes, 844 is an outlier.

No, there are no outliers.

Answers

Answer:

Yes, 222 is an outlier

Step-by-step explanation:

{222, 346, 346, 435, 435, 505, 667, 667, 667, 779, 844}

Q1 = 435

Q3 = 667

IQR = Q3 - Q1 = 232

222 is below Q1 - 1.5*IQR (104)

how do you find the perimeter of an object

Answers

Answer:

width*2 +length *2

Step-by-step explanation:

part B write a numerical expression of angle C

Answers

The index of refraction of the second material is 1.27.

We are given that;

Angle= 59°

Randomized Variables 1 = 1.47θ1 = 59°θ2 = 69°

Now,

To find n2, we can rearrange Snell’s law as:

n2 = n1 sin θ1 / sin θ2

Plugging in the given values, we get:

n2 = 1.47 sin 59° / sin 69°

n2 = 1.47 (0.857) / (0.934)

n2 = 1.27 (rounded to two decimal places)

Therefore, by the expression the answer will be 1.27

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Determine the order of the matrix.
VA/L
1
5
-1 1 1 -5
-3 5 7

Answers

The order of a matrix is 2 x 5.

We have,

The order of a matrix is in the form of:

= number of rows x number of columns

Now,

The given matrix has 2 rows.

The given matrix has 5 columns.

Now,

= number of rows x number of columns

= 2 x 5

Thus,

The order of a matrix is 2 x 5.

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Please help asap!!!!!

Answers

Answer:

[tex]f(-1) = -2\\[/tex]

[tex]f(0)=0[/tex]

[tex]f(1)=2[/tex]

Step-by-step explanation:

f(x)=2x

1) f(-1) = 2(-1) = -2

2) f(0) = 2(0) = 0

3) f(1) = 2(1) = 2

Glad for any help, it's a statistics problem and I have the image linked below.

Answers

The 95% confidence interval for the mean time for all players is given as follows:

Between 7.14 minutes and 10.74 minutes.

What is a t-distribution confidence interval?

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 10 - 1 = 9 df, is t = 2.2622.

Inserting the data-set into a calculator, the parameters are given as follows:

[tex]\overline{x} = 8.94, s = 2.52, n = 10[/tex]

Then the lower bound of the interval is given as follows:

8.94 - 2.2622 x 2.52/sqrt(10) = 7.14 minutes.

The upper bound of the interval is given as follows:

8.94 + 2.2622 x 2.52/sqrt(10) = 10.74 minutes.

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Congruent angles. Help me solve!

Answers

angle egf because they are vertical angles

Answer: ∠FGE

Step-by-step explanation:

Congruent: Have the same angle measure

Starting Angle: ∠BGC
Angle Of Congruence: ∠FGE

There's a train going at 96km/h and another at 109km/h, how long will it take them to pass each other?

Answers

The time it would take for the trains to pass each other, would be 58.54 minutes.

How to find the time taken ?

The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.

To find this time, we first need to find the combined speeds of the trains to be :

= 96 + 109

= 205 km / h

With the combined speed, the time till they pass each other would be:

= Distance between trains / Combined speed

= 200 / 205

= 58. 54 minutes

= 0. 98 hours

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The time it would take for the trains to pass each other, would be 58.54 minutes.

How to find the time taken ?

The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.

To find this time, we first need to find the combined speeds of the trains to be :

= 96 + 109

= 205 km / h

With the combined speed, the time till they pass each other would be:

= Distance between trains / Combined speed

= 200 / 205

= 58. 54 minutes

= 0. 98 hours

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I need help with this

Answers

An equation is y = -12/3 when x = 3, y = -4.

What is equation?

An equation is a mathematical statement that indicates that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables that satisfy the given conditions.

If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:

x × y = k

where k is a constant of proportionality. To find the value of k, we can use the given information.

When x = 3, y = -4:

3 × (-4) = k

k = -12

Now we can substitute k into the equation to get:

x × y = -12

This is the equation relating x and y. To find y when x = 3:

3 × y = -12

y = -12/3

Therefore, when x = 3, y = -12/3.

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An equation is y = -12/3 when x = 3, y = -4.

What is equation?

If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:

x × y = k

where k is a constant of proportionality. To find the value of k, we can use the given information.

When x = 3, y = -4:

3 × (-4) = k

k = -12

Now we can substitute k into the equation to get:

x × y = -12

This is the equation relating x and y. To find y when x = 3:

3 × y = -12

y = -12/3

Therefore, when x = 3, y = -12/3.

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Solve for x: x - 2 = 10

A: 2
B:8
C:10
D:12

Answers

Answer:

12 is the answer

Step by step explanation

to get answer move all terms not containing x to the right side of the equation

Which function is represented by the graph below?

Answers

It would be the second option.

you need 18 lb of peeled and cored apples to make applesauce.apples have a yield percentage of 78%, how many pounds of whole apples are needed

Answers

You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.

Explanation:

To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:

Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage

Plugging in the values we have:

Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)

Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.

how long will it take $5000 to grow to $6000 at an annual rate of 9% compounded monthly

Answers

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

We know that P = $5000, A = $6000, r = 0.09 (9%), and n = 12 (since interest is compounded monthly). We can solve for t algebraically:

A = P(1 + r/n)^(nt)
$6000 = $5000(1 + 0.09/12)^(12t)
$6000/$5000 = (1 + 0.09/12)^(12t)
1.2 = (1.0075)^(12t)
log(1.2) = log(1.0075)^(12t)
log(1.2) = 12t * log(1.0075)
t = log(1.2) / (12 * log(1.0075))
t ≈ 4.58

Therefore, it will take about 4.58 years (or about 55 months) for $5000 to grow to $6000 at an annual rate of 9% compounded monthly.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the amount of money in the account after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

In this case, we want to find the time it takes for an investment of $5000 to grow to $6000 at an annual rate of 9% compounded monthly. So we have:

P = $5000
A = $6000
r = 0.09 (9% annual interest rate)
n = 12 (compounded monthly)

We want to solve for t, the number of years. So we can rearrange the formula to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the values we have:

t = (log(6000/5000)) / (12 * log(1 + 0.09/12))

Simplifying:

t = 3.10 years (rounded to two decimal places)

Therefore, it will take approximately 3.10 years (or about 37 months) for an investment of $5000 to grow to $6000 at an annual rate of 9% compounded monthly.

Please answer this question quickly

FOR 35 POINTS
I WILL GIVE BRAINLIEST

Answers

Answer: 0

Step-by-step explanation:

[tex]log_{3} log_{5} log_{2} 32[/tex]

Let's evaluate

[tex]log_{2}32[/tex] this is the same as

[tex]2^{x}=32[/tex] 2*2*2*2*2=32

you can think of it as 2 to the what power is 32

so x=5

now substitute that in for [tex]log_{2}32[/tex]

[tex]log_{3} log_{5} 5[/tex]

Now evaluate [tex]log_{5}5[/tex]

5 to the what power is 5

substitute into [tex]log_{3} log_{5} 5[/tex]

[tex]log_{3} 1[/tex]

3 to the what power is 1

Anything to the 0 power is 1 (it's a rule)

Refer to the set of data values for Diamonds below
PRICE: 6958,5885,6333,4299,9539,6921,4426,6885,5826,3670,7176,74975170,5547,13596,7521,7260,8139,12196, 14998,9736,9859,12393,25522, 11008,38794,66730,46769,28800,28868
CARATIWEIGHT):1,1,1.01,1.01,1.02,104,104,107,1.07,111,1.12,1 16,1 2,1 23,1.25,129,1.5,1.51,1.67,1.72,1.76,1.8,188,2.03,2.03,2.06,3,4.01,4.01.4.05
COLOR: 3,5, 4, 5, 2, 4, 5, 4, 5, 9,2,5,6,7,1,6,6,6,3,4,8, 5, 6, 2,8,2,1,3,6,7

(a) Use the paired data consisting of the carat weight (x) and the price (y). What is the best predicted price of a diamond with a weight of 1.6 carats?

(b) Use the paired color (x) and the price (y) data. What is the best predicted price of a diamond with a color rating of 37

Answers

linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating.

By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.

What is Equation?
An equation is a mathematical statement that states the equality of two expressions. It is made up of two parts—the left side and the right side—that are separated by an equal sign (=). The left side of an equation is made up of terms, which are numbers and/or variables, and the right side is made up of a single number or variable. Equations are used to solve for unknown values in mathematics, science, and engineering.

The best predicted price of a diamond with a weight of 1.6 carats can be found by using a linear regression equation. This equation uses the paired carat weight (x) and the price (y) data to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the carat weight increases. The equation can then be used to calculate the predicted price of a diamond with a weight of 1.6 carats.

The best predicted price of a diamond with a color rating of 3 can be found by using the paired color (x) and the price (y) data. Using the data, a linear regression equation can be used to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the color rating increases. The equation can then be used to calculate the predicted price of a diamond with a color rating of 3.

In conclusion, linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating. By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.

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what is the best measure of sensors to use in the set of data below 12, 8, 15, 45, 7, 13 mean, median, mean or median, mode?

Answers

Answer:

The best measure of central tendency to use in a set of data depends on the characteristics of the data and the specific objective of the analysis. Let's examine the given data set: 12, 8, 15, 45, 7, 13.

Mean: The mean, also known as the average, is calculated by summing up all the values in the data set and dividing by the total number of values. The mean is sensitive to extreme values and can be influenced by outliers. In this case, the mean is calculated as (12 + 8 + 15 + 45 + 7 + 13) / 6 = 100 / 6 ≈ 16.67.

Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. The median is not affected by extreme values and is a good measure to use when there are outliers or when the data is not symmetrically distributed. In this case, when the data set is arranged in ascending order, the median is 13, as it is the middle value.

Mode: The mode is the value that appears most frequently in a data set. It is a useful measure when we want to identify the most common value in the data set. In this case, the mode is not applicable as there are no repeated values in the data set.

Based on the characteristics of the given data set, the median is a good measure to use as it is not affected by extreme values and provides a central value that represents the middle of the data set. The mean may be influenced by the outlier value of 45, and the mode is not applicable in this case. So, the best measure of central tendency to use in this data set would be the median.

limh→0(5e^x−5e^(x+h))/3h

Answers

We define ln(x)=int[(1 , x)(1/t)dt], then (ln(x))’=1/x . Define e^x as the inverse of ln(x) .

Then lim [ln(1+x)/x] =lim 1/(1+x) =1 as x approaches to 0 (using the Hp rule). Let ln(1+y)=x then y=e^x-1 and lim[ln(1+y)/y]=lim[x/e^x-1]=1 as x approaches to 0. then limit[(e^h-1)/h]=1 as h approaches to 0 . We have

lim[(5e^x-5e^(x+h))/3h]=(5/3)lim[(e^x-(e^x)(e^h))/h]=(5/3)e^xlim[(1-e^h))/h]=

-(5/3)e^xlim[(e^h-1))/h]=-(5/3)e^x as h approaches to 0.

find the circumference of a circle circumscribed about a right triangle with legs 5 centimeters and 3 centimeters

Answers

Answer:

Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).

Step-by-step explanation:

To find the circumference of a circle circumscribed about a right triangle with legs 5 cm and 3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse, which is also the diameter of the circle.

Using the Pythagorean theorem, we have:

c^2 = 5^2 + 3^2

c^2 = 25 + 9

c^2 = 34

c = sqrt(34)

So the diameter of the circle is sqrt(34) cm, and the radius is half of the diameter, or sqrt(34)/2 cm.

The circumference of a circle is given by the formula:

C = 2 * pi * r

where pi is approximately 3.14 and r is the radius of the circle.

Substituting the value of the radius, we get:

C = 2 * 3.14 * sqrt(34)/2

C = 3.14 * sqrt(34)

Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).

Indirect measurement, pls help, I am stuck on this question.

Answers

The building is 246 feet tall.

What are similar triangles?

Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.

To determine the height of the building, we have;

height of pole = 7 ft

total length of the building's shadow = 167 ft

the length of the shadow of the pole = 4.75 ft

Let the height of the building be represented by h. On comparison, we have;

4.75/ 167 = 7/h

4.75h = 167 x 7

= 1169

h = 1169/ 4.75

= 246.11

The building is 246 ft. tall.

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What questions please help me thanks

Answers

1. The monthly payment for Loan A is roughly $516.40.

2. The total interest for Loan A is roughly $1590.4

How do we calculate the monthly payment and total interest?

We've been given the formula: PMT = (P(r/n)) / [1 - (1 + r/n)^-nt] to calculate the monthly payment loan.

If we should insert the figures given to the formula, it should be

PMT = (17000(0.059/12)) / [1 - (1 + 0.059/12)^(-12*3)]

PMT = 516.40

To calculate total interest for loan A, we use the formula (PMT x n x t) - P.

If we insert the figure provided, it should be;

(598.87 x 12 x 3) - 17000

= $1590.4

The above answer is in response to the question below as seen in the picture;

Suppose that you decide to borrow $17,000 for a new car. Installment loan A: 3 years at 5.9%. Use PMT = (p(r/n))/ [1 - (1 + r/n)^-nt]

Find the monthly payment and the total interest for loan A. The monthly payment for Loan A is $..............

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How do I find the squareroot?

Answers

Answer:

Step-by-step explanation:

Factoring a square root means that you are finding the closest numbers that multiply together. The easiest square roots are ones that factor directly into squares, such as √100, but more complicated ones involve several square roots, such as √225. Here are the steps to finding the square root using factoring:

1. Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. For √100, the factors would be √(10 x 10). The factors of √225 would be √(25 x 9).

2. Separate the factors into their own square roots. Because both factors of √100 are 10, the square root of 100 is 10. For √225, you would separate the factors under their own square root signs, so the formula would be √25 x √9.

3. Solve for the individual squares. Next, you would find the squares of each of the individual factors. √25 = 5 and √9 = 3. The remaining formula will look like 5 x 3.

4. Finish solving the equation. Now that you know what the simplified squares are, you will find that 5 x 3 = 15. So, √225 = 15.

Hope that helps!

b: if jen and ricky each randomly select an egg from their farm, who is more likely to select an egg classified as medium

Answers

Rick is more likely to select a large egg. Jens probability for a large egg is87.5 ricks is 90.7

What is Probability?

Probability is a fundamental concept that gauges the plausibility of an event taking place. It is expressed numerically within the range of 0 to 1, with values corresponding to complete impossibility and absolute certainty respectively.

When probability values take on an exact midpoint value such as 0.5, they indicate equal probabilities for both possible outcomes. Experts use probability models before making significant decisions in fields such as science, engineering, finance, and speculative markets like gambling.

The study of these apprehension methods and their application form the foundation of probability theory, which helps analyze chance events' rules and guidelines.

Answers

Answer:

-1.82

Step-by-step explanation:

It won't let me write the explanation for some reason. I'll put it in the comments below

NO LINKS!! URGENT HELP PLEASE!!!

Movies generally lose 23% of its audience for each week it is in the theatre. A movie STARTED with an audience of 196 people per viewing.

a. Equation: ________________

b. Make a chart and fill in the table for the first ten weeks.

c. Graph the function. Label each axis with a title and scale

Answers

Answers:

a) The equation is y = 196(0.77)^x

b) The chart is shown below

c) The graph is shown below

================================================

Explanation:

Part (a)

One template of an exponential equation is y = ab^x

a = starting valueb = connected to the growth rate or decay rate

In this case

a = 196b = 1-0.23 = 0.77

If 23% of the audience leaves, then 77% remains. This is another way to see where b = 0.77 comes from. Exponential decay will have 0 < b < 1.

Therefore, the equation is y = 196(0.77)^x

Other equations are possible.

-------------------

Part (b)

I'll be using LibreOffice spreadsheet to make the table. Any spreadsheet software will do.

Type x into cell A1

Type 0 and 1 into cells A2 and A3 in that order.

Select cells A2 and A3. Pull down the small marker at the bottom right corner. Pull this marker down to cell A12 to get values 2 through 10 (which will be in cells A4 to A12).

Now move to cell B1. Type in y = 196(0.77)^x in this cell.

In cell B2, type in "=ROUND(196*(0.77)^A2)" without quotes. As you can probably guess, the ROUND function will round to the nearest whole number. The calculation 196*(0.77)^A2 computes the result of y = 196*0.77^x when plugging x = 0 which is in cell A2.

Do not forget about the equal sign up front.

After cell B2 is filled in, hit enter. Then pull down the smaller marker at the bottom right corner to cell B12. A bunch of whole numbers should fill in cells B3 to B12

This is what you should get for your table

[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{y} = 196(0.77)^{\text{x}}\\\cline{1-2}0 & 196\\\cline{1-2}1 & 151\\\cline{1-2}2 & 116\\\cline{1-2}3 & 89\\\cline{1-2}4 & 69\\\cline{1-2}5 & 53\\\cline{1-2}6 & 41\\\cline{1-2}7 & 31\\\cline{1-2}8 & 24\\\cline{1-2}9 & 19\\\cline{1-2}10 & 14\\\cline{1-2}\end{array}[/tex]

x = week number

y = viewer count (approximate)

Example calculation:

Plug in x = 5 to get y = 196*0.77^5 = 53.05297 approximately which rounds to y = 53. Therefore, we estimate there would be about 53 people in the audience for week 5.

-------------------

Part (c)

You could use a spreadsheet to make the graph, but I find GeoGebra is more friendly for graphing. But we'll be using the data we just made in the spreadsheet.

Select cells A2 through B12. This is the 11 row by 2 column block of x,y data pairs. Do not select the headers at the top.

Copy that data and paste it into GeoGebra's spreadsheet mode.

Then select that same block of data in GeoGebra. Right-click to go to "create" then to "list of points". It will do as it describes. Eleven points will show up in the graph window. Resize and adjust the window if needed.

I'm using the following window parameters

xMin = -5xMax = 20yMin = -20yMax = 220

The graph is shown in the screenshot below.

Answer:

[tex]\textsf{a.} \quad \textsf{Equation:} \;\;\;y=196(0.77)^x[/tex]

b. See below.

c. See attachment.

Step-by-step explanation:

We can model the given situation using an exponential decay equation since the weekly change in audience is a constant percentage change.

Exponential decay formula

[tex]\boxed{y=a(1-r)^x}[/tex]

where:

a is the initial value.r is the percentage decrease (in decimal form).x is the time period.

Given the movie started with an audience of 196 people viewing, a = 196.

Given the movie loses 23% of its audience each week, r = 0.23.

As the movie loses a constant percentage of its audience each week, let x be the number of weeks.

Substitute the values of a and r into the formula and simplify:

[tex]y=196(1-0.23)^x[/tex]

[tex]y=196(0.77)^x[/tex]

Therefore, the equation that models the given scenario is:

[tex]\boxed{y=196(1-0.23)^x}[/tex]

Create a table for the first ten weeks by substituting the values of x from zero through 10 into the equation. Round each number to the nearest whole number.

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}$Weeks$\;x&$Audience$\;y\\\cline{1-2}\vphantom{\dfrac12}0&196\\\cline{1-2}\vphantom{\dfrac12}1&151\\\cline{1-2}\vphantom{\dfrac12}2&116\\\cline{1-2}\vphantom{\dfrac12}3&89\\\cline{1-2}\vphantom{\dfrac12}4&69\\\cline{1-2}\vphantom{\dfrac12}5&53\\\cline{1-2}\vphantom{\dfrac12}6&41\\\cline{1-2}\vphantom{\dfrac12}7&31\\\cline{1-2}\vphantom{\dfrac12}8&24\\\cline{1-2}\vphantom{\dfrac12}9&19\\\cline{1-2}\vphantom{\dfrac12}10&14\\\cline{1-2}\end{array}[/tex]

The graph of the function is an exponential decay curve, which starts at (0, 196) and approaches zero as x approaches infinity.

The x-axis represents the number of weeks and the y-axis represents the audience size.

Use a scale of x : y = 1 : 10.

Plot the points from the table and draw a smooth curve through them that approaches zero as x approaches infinity.

find dy/dx of y= ln(1-x^2/1+x^2)

Answers

The derivative of y with respect to x is:

[tex]dy/dx = -4x / (1 - x^4)[/tex]

How to find derivative ?

The chain rule and the quotient rule must be utilized in order to determine the derivative of y with respect to x.:

First, we can rewrite y as follows:

[tex]y = ln[(1 - x^2)/(1 + x^2)][/tex]

Let's define two functions:

[tex]u = 1 - x^2[/tex]

[tex]v = 1 + x^2[/tex]

Then, y can be rewritten in terms of u and v as:

y = ln(u/v)

Now, we can use the chain rule to find the derivative of y with respect to u and v, respectively:

[tex]dy/du = 1/u\\dy/dv = -1/v[/tex]

Using the quotient rule, we can find the derivative of y with respect to x:

[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)[/tex]

[tex]du/dx = -2x\\dv/dx = 2x[/tex]

Substituting in the values we get:

[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)\\= (1/u) * (-2x) + (-1/v) * (2x)\\= -2x/(1 - x^2) - 2x/(1 + x^2)\\= -4x / (1 - x^4)[/tex]

Therefore, the derivative of y with respect to x is:

[tex]dy/dx = -4x / (1 - x^4)[/tex]

know more about differentiation visit :

https://brainly.com/question/24898810

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