The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.

To show that the properties of a probability distribution for a discrete random variable are satisfied, we need to verify that the probability distribution function (PDF) satisfies, The PDF must be non-negative for all values of the random variable and The sum of the probabilities for all possible values of the random variable must be equal to 1.

Let X be a discrete random variable taking values x1, x2, ..., xn, and let P(X) be the probability distribution function for X, such that P(X = xi) = pi for all i.

The PDF must be non-negative for all values of the random variable. This means that for any value xi of the random variable, the probability pi must be greater than or equal to zero. That is,

pi ≥ 0 for all i.

This property ensures that probabilities are never negative, which is a necessary condition for a valid probability distribution.

The sum of the probabilities for all possible values of the random variable must be equal to 1. That is,

∑ pi = 1 for all i.

This property ensures that the total probability of all possible outcomes is equal to 1, which is a necessary condition for a valid probability distribution.

Therefore, if the PDF satisfies these two properties, we can conclude that it represents a valid probability distribution for the given discrete random variable.

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Answer:

Step-by-step explanation:

[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]

Answer:

a=18 b=24

Step-by-step explanation:

We know that BC=25 and QR=30, the key term is that they are similar triangles. Therefore, BC: QR=25:30=5:6. Then BA:A=5:6=15:X

x=a=18

20:b=5:6

b=24

At equilibrium we expect [Reactants} < [Products)  from the the profile that has been shown.

An energy profile diagram, also known as an energy diagram or reaction coordinate diagram, is a graphical representation of the energy changes that occur during a chemical reaction or a physical process. It shows the energy levels of the reactants, products, and any intermediate species that may form during the reaction.

The horizontal axis of an energy profile diagram represents the reaction coordinate, which is a measure of the progress of the reaction from the reactants to the products. The vertical axis represents the energy of the system.

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The dimensions of the rectangular frame is found as : 12 and 6 inches.

When a triangle is just a right triangle, the hypotenuse square is equal to the sum of the squares of the triangle's legs.

That's a picture frame, therefore pay attention that it must be rectangular.

Hence, the triangle is really a right triangle, and the Pythagorean theorem will eventually be applied.

You are aware that the square of the hypotenuse is 20 and equals 400.

hence, a²  + b²  = 400 and...

So because length is 4 times more than the breadth, a = b + 4.

This can be resolved if "b + 4" is substituted for "a":

(b + 4)² + b²  = 400,

(b + 4)(b + 4) + b²  = 400,

b² + 8b + 16 + b²  = 400,

2b² + 8b = 384

Further solving;

b² + 4b = 192

b² + 4b - 192 = 0

(b + 16)(b - 12) = 0

Due to the fact that a length cannot be negative, b must therefore be between b - 16 or 12 (negative value not taken)

The second leg is 12 + 4 = 6.

Thus,  the dimensions of the rectangular  frame is found as : 12 and 6 inches.

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The conditions in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal : (C) A random sample of 10 taken from a population distribution that is skewed to the right.

In statistics, the normal or Gaussian distribution is a continuous probability distribution for real-valued random variables.

The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases.

Now,

If we look at the options given below, we see that the random samples in options A and B are normally distributed, so their sample means will be approximately normally distributed.

Similarly, option E indicates that the population is uniform, so the sample mean will also be approximately normal.

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Answer:

Step-by-step explanation:

Для решения задачи мы можем использовать свойства треугольников и окружностей.

Первое, что мы можем заметить, это что треугольник ABD является равносторонним, так как все его стороны имеют одинаковую длину 13. Это означает, что угол ABD также равен 60 градусам.

Также мы можем заметить, что точка O является центром окружности, вписанной в треугольник ABD, так как все ее стороны касаются окружности в точке D. Из свойств вписанных углов, мы знаем, что угол AOD равен половине угла ABD, то есть 30 градусам.

Далее, мы можем заметить, что треугольник AOC является равнобедренным, так как угол ACO равен углу OCA (они оба равны 75 - 30 = 45 градусов), а сторона AC имеет одинаковую длину с стороной AB.

Таким образом, мы можем найти длину стороны AC, используя теорему косинусов для треугольника AOC:

AC^2 = AO^2 + OC^2 - 2 * AO * OC * cos(45)

Заметим, что AO = DO, так как точка O является центром вписанной окружности, а DO является радиусом этой окружности. Из прямоугольного треугольника ADO мы можем выразить DO как DO = AD/2 = 6.5.

Также, мы можем выразить OC, используя равенство углов в треугольнике ACO (ACO и AOD являются вертикальными углами):

ACO = AOD = 30 градусов

Тогда, угол OCA равен 180 - 2 * 45 = 90 градусам, что означает, что треугольник OCA является прямоугольным, и мы можем использовать теорему Пифагора:

OC^2 + AC^2 = OA^2

OC^2 + AC^2 = DO^2

AC^2 = DO^2 - OC^2

Теперь мы можем подставить выражения для DO и OC, и получить:

AC^2 = 6.5^2 - (6.5/sqrt(2))^2

AC^2 = 42.25 - 22.5625

AC^2 = 19.6875

AC = sqrt(19.6875)

AC = 4.43 (с точностью до сотых)

Таким образом, длина стороны AC равна пр

1. The diagonals are equal. Rectangle

2. All sides are equal, and one angle is 60°. Rhombus

3. All sides are equal, and one angle is 90°. Square

4. It has all the properties of parallelogram, rectangle, and rhombus. Square

5. It is an equilateral parallelogram. Rhombus

A rectangle is a four-sided figure with two sets of parallel sides, with each side being a different length. The opposite sides of a rectangle are always equal in length, so the angles of a rectangle are all 90 degrees. A rectangle can also be referred to as a quadrilateral.

A rhombus is a four-sided figure with all sides the same length. The angles of a rhombus are not all 90 degrees, but the opposite sides of a rhombus are equal in length. A rhombus can also be referred to as a diamond.

A square is a four-sided figure with all sides being the same length and all angles being 90 degrees. A square can also be referred to as a regular quadrilateral.

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The complete question is:

Identify whether the following statements describe a rectangle, rhombus or square.

1. The diagonals are equal. ____________

2. All sides are equal, and one angle is 60°. ____________

3. All sides are equal, and one angle is 90°. ____________

4. It has all the properties of parallelogram, rectangle, and rhombus. ____________

5. It is an equilateral parallelogram. ____________

Answer:

The width of the frame is 10 inches.

5x7 = 35

80-35 = 45

45/7 = 6.4

5 + 6.4 = 11.4

11.4 rounded down = 11

11 - 5 = 10

Width of the frame = 10 inches

Jack needed 7 7/8 pounds of flour for his batch of cookies.

Define Pounds

"Pounds" is a unit of measurement for weight, commonly used in the United States and other countries that have adopted the imperial system of measurement. One pound is equal to 16 ounces, and there are 2.20462 pounds in one kilogram.

Mary used 2 1/4 pounds of flour for her batch of cookies.

finding out how much flour Jack needed, we first need to determine how many cookies Jack made.

Since Jack made 3 1/2 times the amount of cookies that Mary made, we can calculate:

Number of cookies Jack made = 3.5 x Number of cookies Mary made

Let's start by finding out how much flour Mary used per cookie:

2 1/4 pounds of flour / Number of cookies Mary made

So, if Mary made X cookies, Jack made 3.5X cookies.

Now we can set up an equation:

2 1/4 pounds of flour / X cookies = Amount of flour per cookie

Amount of flour per cookie x Number of cookies Jack made = Total amount of flour Jack needed

Amount of flour per cookie = 2 1/4 pounds of flour / X cookies

Number of cookies Jack made = 3.5X

Total amount of flour Jack needed = Amount of flour per cookie x Number of cookies Jack made

Total amount of flour Jack needed = (2 1/4 pounds of flour / X cookies) x (3.5X cookies)

Total amount of flour Jack needed = 7 7/8 pounds of flour

Therefore, Jack needed 7 7/8 pounds of flour for his batch of cookies.

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The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.

Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.

Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.

Here we have

y = -5 cοs (π/16 x) - 4    

Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.

The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.

The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.

Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.

Therefοre,

The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

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Angle PLE is measured at 90°. The options supplied do not contain the solution.

The acute angle is defined as being less than 90 degrees. Right angles are 90 degrees in length. Angles that are obtuse have a greater angle than 90 degrees. Discover the various sorts of angles and examples of each.

As complementary angles, ZPLA and ZELA, we can infer that:

ZPLA + ZELA = 90°

Using the following expressions in place of ZPLA and ZELA, we obtain:

5x-2 + x+8 = 90

When we simplify the equation, we obtain:

6x + 6 = 90

6 is subtracted from both sides to yield:

6x = 84

Dividing by 6, we get:

x = 14

With the knowledge of x, we can determine the dimensions of ZPLA and ZELA:

ZPLA = 5x-2 = 5(14)-2 = 68°

ZELA = x+8 = 14+8 = 22°

Therefore, we can find the measure of angle PLE by subtracting the measures of ZPLA and ZELA from 180°:

PLE = 180 - ZPLA - ZELA

PLE = 180 - 68 - 22

PLE = 90

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Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.

Outside the sphere, the potential is given by

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]

where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]

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the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.

One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.

A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.

Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:

[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]

This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).

Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.

To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.

There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.

There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.

There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.

Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:

[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]

[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]

Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

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Answer:

12/2652

Step-by-step explanation:

First, the probability of drawing a king for the first time is 4/52. The chance of drawing another is 3/51. Multiplying, we get the 3rd answer choice, 12/2652

Answer:

Step-by-step explanation:

The given sequence is geometric.

To find the common ratio (r) of the sequence, we need to divide any term by its preceding term. Let's divide the second term (8) by the first term (32):

r = 8/32 = 1/4

Now, we can use the formula for a geometric sequence to find any term:

an = a1 * r^(n-1)

where:

an = nth term of the sequence

a1 = first term of the sequence

r = common ratio

n = position of the term we want to find

Let's use this formula to find the third term:

a3 = 32 * (1/4)^(3-1) = 2

So, the common ratio of the sequence is 1/4, and each term is obtained by multiplying the preceding term by 1/4. The sequence is decreasing rapidly because the ratio is less than 1.

Step-by-step explanation:

it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).

so, it would be helpful, if you could put a message to an answer that was not giving you what you need.

so, here now an answer for an immediate change rate (hopefully that is what you need) :

we have a right-angled triangle.

the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).

the 50 ft and 180 ft are the legs.

Pythagoras gives us the length of the Hypotenuse :

Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900

Hypotenuse = sqrt(34900) = 186.8154169... ft

in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).

x² + y² = z²

now, the first derivative of distance is the change of distance = speed.

then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.

now, we take the derivative of our equation

x² + y² = z² with respect to time, variable by variable :

d(x² + y² = z²)/dt =

dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt

that gives us the equation

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

x(dx/dt) + y(dy/dt) = z(dz/dt)

from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.

and we get

50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s

we solve for y' (the speed of the car on the road)

y' = sqrt(34900)×85/180 = 88.21839132... ft/s

≈ 88.22 ft/s

and now here the difference for an average change rate over the unrevealed of 1 second :

the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.

so, 1 second ago, the distance was

186.8154169... + 85 = 271.8154169... ft

the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)

271.8154169...² = 50² + leg²

leg² = 271.8154169...² - 50² = 71,383.62088...

leg = 267.1771339... ft

so, the red car traveled

267.1771339... - 180 = 87.1771339... ft/s

as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.

The probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is 0.000055

The multiplication rule of probability can be used to determine the likelihood of drawing three kings consecutively from a standard deck of cards when the drawn card is not put back into the deck each time.

Since there are four kings in a deck of 52 cards, the likelihood of drawing a king from a standard 52-card deck is 4/52 or 1/13.

There are still 51 cards in the deck after the first king is drawn, and three of them are kings. Therefore, there is a 3/51 chance of drawing another king.

There are 50 cards left in the deck after drawing the second king, and two of them are kings. The likelihood of drawing a third king is therefore 2/50 or 1/25.

Therefore, the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is:

(1/13) x (3/51) x (1/25) = 3/54,600 or approximately 0.000055.

Hence, 0.000055 is the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time.

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The value of length of side g using the  similar triangles is found as 20 ft.

In the given figures:

DC || EA

So,

∠D = ∠A

∠C = ∠E

By Angle -Angle similarity both triangles are similar.

Thus,

Taking the ratios of their side, it will be also equal.

EA / DC = EB / BC

5 / 10 = g / 10

g = 10*10 / 5

g = 100 / 5

g = 20

Thus, the value of length of side g using the  similar triangles is found as 20 ft.

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Answer:

The critique of the sample method and survey used by the guild is as follows:

In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.

The number of times larger Cell S is compared to Cell W is 4 x 10²,

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

When the power of the scientific notation is negative, it means that the number is less than 1. 0.01 would be written as 1 x [tex]10^{-2}[/tex]. Cell S is larger than Cell W.

(7.2 x [tex]10^{-5}[/tex]) ÷ (1.8 x [tex]10^{-7}[/tex])

(7.2 / 1.8) x [tex]10^{-5--7}[/tex]

4 x 10²

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Option C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.

Relative frequency is a measure of the proportion or percentage of times an event occurs in a given sample. It is calculated by dividing the frequency of an event by the total number of events in the sample. The formula for relative frequency is given as follows:

Relative frequency = Frequency of an event / Total number of events in the sample

For the joint relative frequency of 10th grade students in geometry, the parameters are given as follows:

Hence the joint relative frequency is obtained as follows:

20.7/100 x 100%= 20.7%.

Hence option C is correct.

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The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

Trigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.

Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.

We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.

Then, tan(5°) = οppοsite/adjacent = 139/x

Sοlving fοr x, we get:

x = 139/tan(5°) ≈ 1592.53 feet

Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

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Explanation: The evolution of numbers developed differently with disparate versions, which include the Egyptian, Babylonians, Hindu-Arabic, Mayans, Romans, and the modern American number systems.

The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.

A cash discount refers to a reduction in the price of an item due to payment within the discount period.

A cash discount incentivizes the customer to make prompt payments.

The list price of the equipment = $6,300

Sales terms: 3/10, n/30 FOB

Prepaid freight = $40

Cash discount = $189 ($6,300 x 3%)

Payment after the discount = $6,111 ($6,300 - $189)

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Answer: Let's denote the two unknown angles as x and y.

We know that the sum of the angles in any quadrilateral is 360°, so we can set up an equation using this fact:

235° + 40° + x + y = 360°

Simplifying this equation, we get:

x + y = 85° (equation 1)

We also know that the other two angles are in a ratio of 5:12. This means that:

x/y = 5/12

Multiplying both sides by y, we get:

x = (5/12)y (equation 2)

Now we can substitute equation 2 into equation 1 and solve for y:

(5/12)y + y = 85°

(17/12)y = 85°

y = (12/17) * 85°

y = 60°

Substituting y = 60° into equation 2, we can solve for x:

x = (5/12) * 60°

x = 25°

Therefore, the two angles that are in a ratio of 5:12 measure 25° and 60°, respectively.

Step-by-step explanation:

Answer:

Step-by-step explanation:

yr face add more points NOW

[tex]T(11) = -1[/tex] represents the initial negative term inside the series.

A phrase that acknowledges a characteristic or trait in anything is said to be positive. Negative terms are those that downplay some aspect or characteristic of something. The positive or negativizes of a phrase is termed its quality.

Positive simply denotes excellent or the polar opposite of negative. For instance, you're less likely to receive favorable feedback on your scorecard if you've a good mindset toward your assignments. It might be difficult to keep track of all the different definitions of the word positive.

T(n) is negative when [tex]32 - 3n < 0[/tex], which can be rearranged as:

[tex]3n > 32[/tex]

[tex]n > 32/3[/tex]

Since [tex]n[/tex] is an integer, the smallest value of n that satisfies this inequality is [tex]n = 11[/tex].

Therefore, the [tex]11th[/tex] term of the sequence is:

[tex]T(11) = 32 - 3(11) = -1[/tex]

So the first negative term in the sequence is [tex]T(11) = -1.[/tex]

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