are 8,192 players in a Rock Paper Scissors tournament. In each round half the players ar d to find the number of players remaining in the tournament at the end of x rounds? f(x)=8192(0.05)^(x) B

So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

Question 1: Use the following functions to evaluate each expression f(x) = 1/(x + 2) and g(x) = 3x + 7.

a.) f(g(-2)) = f(3(-2) + 7) = f(1) = 1/(1 + 2) = 1/3

b.) g(f(1)) = g(1/(1 + 2)) = g(1/3) = 3(1/3) + 7 = 1 + 7 = 8

So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

In summary, to evaluate the expression f(g(x)) or g(f(x)), we need to first find the value of the inner function and then substitute it into the outer function. This process is called function composition. It is important to follow the order of operations and simplify the expression as much as possible.

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1 and 3

Step-by-step explanation:

pick one from the junior side and 3 from seniors because the senior is more that the junoir

Answer:

990 different combinations

Step-by-step explanation:

There are 6 juniors and 12 seniors for a total of 16 students

Out of 6 juniors we have to pick 2 juniors

Out of 12 seniors we have to pick 2 seniors

The number of items r that we can pick from a larger set of n items is given by C(n, r) pronounced n choose r.. This is sometimes written as nCr

The formula forC(n, r) is

[tex]\boxed{C(n,r) = \dfrac{n!}{r! (n - r)! }}[/tex]

where n! = n factorial = n x (n-1) x (n-2) x .... x 3 x 2 x 1

We can choose 2 juniors out of 6 juniors in C(6, 2) ways
and
2 seniors out of 12 seniors in C(12, 2) ways

[tex]C(6, 2) = = \dfrac{6!}{ 2! (6 - 2)! }\\\\= \dfrac{6!}{2! \times 4! }\\\\= 15[/tex]

[tex]C(12, 2) = \dfrac{12!}{ 2! (12 - 2)! }\\\\ = \dfrac{12!}{2! \times 10! }\\\\= 66[/tex]

Therefore the total number of ways you can select 2 juniors and 2 seniors from a pool of 6 juniors and 12 juniors

= 15 x 66 = 990

Answer:

First Option, (A) $29,922.

Step-by-step explanation:

To calculate the future value of Heather's savings account after 5 years, we can use the formula for compound interest:

FV = P((1+i)^n - 1)/i

where:

FV = future value

P = principal (the initial amount Heather deposits)

i = interest rate per period (monthly in this case)

n = number of periods (months in this case)

P = $75 (the amount of Heather's monthly payments)

i = 3.6% / 12 = 0.003 (the monthly interest rate, calculated by dividing the annual interest rate by 12)

n = 5 x 12 = 60 (the total number of months in 5 years)

Substituting these values into the formula, we get:

FV = $75((1+0.003)^60 - 1)/0.003

FV = $75(1.21879)/0.003

FV = $29,922.02 (rounded to the nearest cent)

Therefore, Heather will have approximately $29,922.02 in her savings account after the 5 year period. The answer is option A: $29,922.

Therefore, the answers are:
a. 0.0498
b. 0.8008
c. 0.7745

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

a. The probability that none is sold on a particular day can be calculated using the formula:
P(X = 0) = (e^-λ)(λ^0) / 0!
Where λ is the mean and e is the base of the natural logarithm.
Substituting the values, we get:
P(X = 0) = (e^-3)(3^0) / 0!
P(X = 0) = (0.0498)(1) / 1
P(X = 0) = 0.0498

b. The probability that at least 2 automobiles are sold on a particular day can be calculated using the formula:
P(X ≥ 2) = 1 - P(X < 2)
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X ≥ 2) = 1 - ((e^-3)(3^0) / 0! + (e^-3)(3^1) / 1!)
P(X ≥ 2) = 1 - (0.0498 + 0.1494)
P(X ≥ 2) = 1 - 0.1992
P(X ≥ 2) = 0.8008

c. The probability that for five consecutive days at least one automobile is sold can be calculated using the formula:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - (e^-3)(3^0) / 0!
P(X ≥ 1) = 1 - 0.0498
P(X ≥ 1) = 0.9502
The probability that for five consecutive days at least one automobile is sold is:
P(X ≥ 1)^5 = 0.9502^5 = 0.7745

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The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".

To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.

So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)

Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.

The denominator can be factored as (z+6)(z+2).

So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)

Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.

So, the final simplified answer is 1/(z+6).

Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).

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The area of shaded region is 0.15 ft².

The area of the shaded region is calculated by subtracting the area of the triangle from the area of the entire sector.

The angle subtended by the sector is calculated as;

θ = ¹/₂ (55⁰)

θ = 27.5⁰

The area of the triangle is calculated as;

A₁ = ¹/₂r² sinθ

where;

A₁ = ¹/₂ x 4² sin(27.5)

A₁ = 3.69 ft²

Area of the sector is calculated as;

A_t = θ/360 x πr²

A_t = ( 27.5 / 360) x π x 4²

A_t = 3.84 ft²

Area of shaded region = 3.84 ft² - 3.69 ft² = 0.15 ft².

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Answer:

Yes they are similar since it is a regular shape

Yes, the red outer shape is a regular hexagon. the hexagons are similar. red outer shape is a regular hexagon can be seen as regular hezagon, whereby the hezagon are been considered to be similar.

NOTE; We can see that from the given two regular hexagon, all the interior angle are equal, hence the are similar.

A regular hexagon is a polygon with six equal sides and six equal angles. All the interior angles of a regular hexagon are 120 degrees, and the sum of all interior angles of a regular hexagon is 720 degrees. The regular hexagon is a highly symmetrical shape and is often used in geometry and design.

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Answer:

He realizes the casino is a trap when he found out people from 1977 are in the casino. They wasted five days in the casino.

The solution of the radical expression will be y⁴√(39y).

Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.

The given expression is √39y⁹. The radical expression can be simplified as below,

E = √39y⁹

E = √( 39 x y² x y² x y² x y² x y )

E = y⁴√39y

Therefore, the expression will have the simplified solution as E = y⁴√39y.

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The diameter of the circle is 28 inches.

Formula for the area of a circle is:

A = πr²

Where A represents the area, r denotes the radius, and π is a mathematical constant approximately equal to 3.14.

To find the diameter of the circle, we can use the formula:

D = 2r

in the given formula D is the diameter and r is the radius.

We know that the area of the circle is 615.44 sq. inches. So, we can use the area formula to find the radius:

615.44 = πr²

615.44 = 3.14r²

r² = 615.44/3.14

r² = 196

r = √196

r = 14

Now that we know the radius is 14 inches, we can use the diameter formula to find the diameter:

D = 2r

D = 2(14)

D = 28

Therefore, the diameter of the given circle is 28 inches.

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Answer:

y = 0.8x

Step-by-step explanation:

y = x-0.2x

y=x(1-0.2)

y=x(0.8)

hence y = 0.8x

With these informations you can now do a graph !

In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.

It seems like there are a lot of typos and irrelevant information in this question, making it difficult to understand what is being asked. However, I will do my best to provide an answer based on the key terms provided.

In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.

For the final aubmision, it is important to make sure that your work is accurate and complete before converting it to a PDF. This will ensure that your modified portfolio is professional and easy to understand.

Once you have completed your work, you can download it as a PDF and submit it in your portfolio. This will allow you to keep a record of your work and show your understanding of trigonometry and teffeeratures.

I hope this helps! If you have any further questions, please feel free to ask.

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The soap from Seventh Generation brand cost less than Method brand.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

The Method brand that is $5. 49 for 36 oz

So, the unit rate of soap

= 5.49 / 36

= $ 0.1525

and, The Seventh Generation brand that is $3. 39 for 25 oz

So, the unit rate of soap

= 3.39/ 25

= $0.1356

So, the soap from Seventh Generation brand is cheaper.

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31, 87, 90 are the numbers which are considered possible outliers.

An outlier is an observation or data point that is significantly different from other observations in a dataset. In other words, it is an unusual or extreme value that is much higher or lower than most other values in the data.

A box and whisker plot is used to easily detect outliers. In this figure, the outliers are shown as black circles or dots. These are the data points that are distant from other observations.

Therefore, the numbers which are considered possible outliers are 31, 87, and 90.

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13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.

To solve this word problem on proportions using a unit rate, we need to first find the unit rate for the cost of the wire. The unit rate is the cost per one inch of wire.

We can find this by dividing the cost by the number of inches:

Unit rate = 72 cents / 18 inches = 4 cents per inch

Now that we have the unit rate, we can use it to find the cost of 13 inches of wire.

We simply multiply the unit rate by the number of inches:

Cost = 4 cents per inch × 13 inches = 52 cents

Therefore, 13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.

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Answer:

16,500 miles

Step-by-step explanation:

In 12 minutes, the satellite travels 3,300 miles around Earth. To find how far the satellite travels around Earth in 1 hour, we can use unit conversion:

1 hour = 60 minutes

So, the number of 12-minute intervals in 1 hour is:

1 hour / 12 minutes = 5 intervals

Therefore, in 1 hour, the satellite travels:

3,300 miles/interval × 5 intervals = 16,500 miles

So the satellite travels around Earth at a distance of 16,500 miles in 1 hour.

The discriminant is positive (D = 8), the equation x² - 6x + 7 = 0 has two distinct real solutions, which supports Jason's claim.

The quadratic equation's roots are represented geometrically by the discriminant. The equation has two separate real roots if the discriminant is positive, and as a result, the graph of the quadratic function meets the x-axis twice. The quadratic function's graph crosses the x-axis precisely one time if the discriminant is zero, which indicates that the equation has one real root.

To find the discriminant of the given equation, we can substitute the values of a, b, and c into the formula:

D = (-6)² - 4(1)(7) = 36 - 28 = 8

Since the discriminant is positive (D = 8), the equation x² - 6x + 7 = 0 has two distinct real solutions, which supports Jason's claim.

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The complete question is:

The possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.

The possible rational zeros of a polynomial function can be determined using the Rational Zero Theorem. This theorem states that if a polynomial function has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In the given polynomial function, P(x)=21x^(3)-38x^(2)+44x-10, the constant term is -10 and the leading coefficient is 21. The factors of -10 are ±1, ±2, ±5, ±10 and the factors of 21 are ±1, ±3, ±7, ±21.

Using the Rational Zero Theorem, the possible rational zeros are:

p/q = ±1/1, ±2/1, ±5/1, ±10/1, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21

Simplifying these fractions gives us the possible rational zeros:

±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21

Therefore, the possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.

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The slope-intercept form of the equation of the line that passes through the point P (5, 4) and makes an angle, θ = 30°, with the x-axis is the option A.

A. y = ((sqrt(3))/3)·x - ((5·sqrt(3))/3 - 4)

The slope-intercept form of linear equation is an equation of the form; y = m·x + c, where;

m = The slope of the graph of the equation

c = The y-intercept of the graph of the equation.

The point through which the line passes, P = (5, 4)

The angle θ the line makes with the positive x-axis = 30°

The slope of the line = The tangent of the angle the line makes with the positive x-axis, therefore;

(y - 4)/(x - 5) = tan(30°) = 1/√3

y - 4 = (x - 5)/√3 = (x - 5)/√3 × (√3/√3) = (x - 5)·√3/3

y = (x - 5)·√3/3 + 4

The above equation can be converted into the slope-intercept form of a linear equation; y = m·x + c by simplifying the equation and rearranging the equation, into the required form;

y = (x - 5)·√3/3 + 4

y = (√3/3)·x - 5·√3/3 + 4 = (√3/3)·x - (5·√3/3 - 4)

y = (√3/3)·x - (5·√3/3 - 4)

The equation in slope-intercept form, is therefore;

A. y = (sqrt(3))/3)·x - (5·sqrt(3))/3 - 4)

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The equivalent expression to the given one is:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

We start with the expression:

y⁸*y³*x⁰*x⁻²

Remember the exponent rule for products of powers with the same base, it says that we can write:

xᵃ*xᵇ = xᵃ⁺ᵇ

So we just add the two exponents.

Using exponent rules, we can rewrite the product as

y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²

That is the equivalent expression.

Then we can write:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

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Answer:

6

Step-by-step explanation:

First, we need to calculate the average number of toys produced per hour during the busy season and the regular season.

During the busy season, the factory operates for 2 x 30 = 60 days or 60 x 12 = <<2*30=60>>720 hours.

The average number of toys produced during this time is 528 toys per 12-hour shift, or 528/12 = <<528/12=44>>44 toys per hour.

During the regular season, the factory operates for the rest of the year, which is 12 - 2 = 10 months, or 10 x 4 = 40 weeks, or 40 x 5 = <<1045=200>>200 days, or 200 x 8 = <<200*8=1600>>1600 hours.

The average number of toys produced during this time is 304 toys per 8-hour shift, or 304/8 = <<304/8=38>>38 toys per hour.

The difference between the average number of toys produced per hour during the busy season and the regular season is:

44 - 38 = <<44-38=6>>6 toys per hour.

Therefore, the factory produces 6 more toys per hour during the busy season than during the regular season. Answer: 6.

Answer:

To calculate the number of more toys the factory produces in an hour during the busy season than during the regular season, we can divide the difference between the two shifts by the total hours of each shift:

More toys per hour = (528-304)/(12-8) = 224/4 = 56 toys per hour

The most accurate comparison is that a gamma ray has more energy than a radio wave because it has a shorter wavelength and higher frequency.

The most energetic and high frequency particles are gamma rays. On the other side, radio waves are the EM radiation types with the lowest energies, longest wavelengths, and lowest frequencies.

All electromagnetic radiation travels in a vacuum at the speed of light (c), which is the same for all electromagnetic radiation types, including microwaves, visible light, and gamma rays.

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The answer is V equals 355 over 113 times 6 squared times 8.

What is the volume of the cylinder?

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder, and h is the height of the cylinder.

Alternatively, the volume of a cylinder can be found by multiplying the area of the base (πr²) by the height (h).

The correct method to calculate the number of cubic units of cake batter needed to fill the mold is:

[tex]V = \pi r^2h[/tex], where r is the radius and h is the height of the cylinder.

The diameter of the cake mold is 12 inches, so the radius is half of that, which is 6 inches.

Therefore, the volume of the cake batter needed is:

V = (355/113) x 6² x 8

V = (355/113) x 36 x 8

V = 904.96 cubic inches

So the answer is: V equals 355 over 113 times 6 squared times 8.

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(i)  If Jane's assumption is correct, she will not get 15 tomatoes.

(ii) If Jane's supposition about the body mass of the each tomato is wrong, she could not obtain 15 tomatoes to 1 kg of tomatoes.

What types of things are assumptions?

An presumption is something you believe to be true despite the lack of evidence. People might presume, for instance, that you are a geek if you wear spectacles, even though that is untrue.

(b) (i) If Jane's assumption is correct, then the weight of 15 tomatoes would be:

15 tomatoes × 75 g/tomato = 1125 g

Since 1 kg is equal to 1000 g, Jane would need to buy at least:

1125 g / 1000 g/kg = 1.125 kg of tomatoes

Therefore, Jane would need to ask for at least 1.125 kg of tomatoes to get 15 tomatoes if her assumption about the weight of each tomato is correct.

(b) (ii) If Jane's assumption about the weight of each tomato is not correct, it is possible that she could get 15 tomatoes with 1 kg of tomatoes, depending on the actual weight of each tomato.

For example, if each tomato actually weighs 67 g, then 15 tomatoes would weigh:

15 tomatoes × 67 g/tomato = 1005 g

This is less than 1 kg, so Jane would get 15 tomatoes with 1 kg of tomatoes.

On the other hand, if each tomato actually weighs 100 g, then 15 tomatoes would weigh:

15 tomatoes × 100 g/tomato = 1500 g

This is more than 1 kg, so Jane would not get 15 tomatoes with 1 kg of tomatoes if her assumption about the weight of each tomato is incorrect.

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The probability that this really contains a letter just after an odd number is one-half. D's likelihood of being in the program but not at the first place is 1/4.

A possibility which deals with the possibility of random occurrences is referred to as probability. All occurrences must have a chance of occuring at least once, or 1.

The possibility or possibility of an incident occurrence is known as probability. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of coin flipping and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.

The size of the sample space is (8, 16, 20, and 24)

If a code is chosen at random,

The probability that it has a letter that immediately follows an odd number (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/2

If a code is chosen at random,

The probability that D is in the code but is not in the first position (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/4

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Using the zero product property

To use the zero product property to determine the values of x for which the expression equals 0, we need to set each factor equal to 0 and solve for x.

Setting each factor equal to 0 gives us:

x+7 = 0 or x-2 = 0

Solving each equation for x, we get:

x = -7 or x = 2

Hence, the values of x are x=-7 and x=2.

Setting each factor equal to 0 gives us:

2x+7 = 0 or x-6 = 0

Solving each equation for x, we get:

x = -7/2 or x = 6

Hence, the values of x  are x=-7/2 and x=6.

Setting each factor equal to 0 gives us:

-3x+11 = 0 or 4x+18 = 0

Solving each equation for x, we get:

x = 11/3 or x = -9/2

Hence, the values of x  are x=11/3 and x=-9/2.

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The measurement of variability that would be best to use for the distribution is Interquartile Range, the correct option is (b).

The best measurement of variability to use depends on the distribution of the data and the purpose of the analysis.

If the distribution is skewed or contains outliers, the median and interquartile range would be better measures of variability than the mean and standard deviation.

The median is less affected by extreme values, and

The interquartile range is a robust measure of spread that is not influenced by outliers.

The mean and mean absolute deviation may be appropriate if the data are approximately symmetric and do not contain outliers.

Therefore, The best measurement of variability is (b) Interquartile range.

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Answer:

a) 0.32 = 32/100 = 8/25

b) 3.003 = 3 + 3/1000 = 3000/1000 + 3/1000 = 3003/1000

c) 13.134 = 13 + 134/1000 = 13000/1000 + 134/1000 = 13134/1000

d) 5.2303 = 5 + 2303/10000

The image after the rotation would be X(2, 1) Y(0,-2) and Z(-2, 1) according to the graph below.

An ordered graphical depiction of numbers or variables is how this is described.

180 degrees in each direction results in (x,y) becoming (-x,-y). The coordinates are thus inverted to either positive or negative values depending on their respective signs.

A graph is a mathematical structure made up of a set of lines linking some pairs of VERTICES that may or may not be empty and a collection of points called VERTICES. Graphs are a common method for displaying the relationships between data. Although taking up less space, a graph accomplishes the goal of presenting data that are either too many or complex to be adequately described in the text.

There are eight different types: linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.

Hence, it means  X(−2, −1), Y(0, 2), and Z(2, −1) = X(2, 1) Y(0,-2) and Z(-2, 1).

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Complete question -

Mr. Morris should expect around 3672 books in the collection to have minor or major damage.

What is proportion ?

Proportion is a relationship between two quantities that expresses the fraction of one quantity in terms of the other. In other words, a proportion is a statement that two ratios are equal.

To estimate the number of books in the collection that have minor or major damage, we first need to find the proportion of books in the sample that have such damage. We can then use this proportion to estimate the number of damaged books in the entire collection.

The total number of books in the sample is:

Total number of books = 737 + 67 + 31 = 835

The proportion of books in the sample that have minor or major damage is:

Proportion of damaged books = (67 + 31) / 835 = 0.108

To estimate the number of damaged books in the entire collection, we can multiply the proportion of damaged books by the total number of books in the collection:

Number of damaged books in collection = 0.108 x 34,000 = 3672

Rounding this answer to the nearest whole number, we get:

Therefore, Mr. Morris should expect around 3672 books in the collection to have minor or major damage.

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