Use the long division method to find the result when x^3+9x² +21x +9 is divided
by x+3

We can conclude after answering the provided question that  If the data expression points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

This graph appears to be a scatter plot of data points based on the visual representation you provided. The values of an independent variable are represented by the horizontal axis (x-axis), while the values of a dependent variable are represented by the vertical axis (y-axis).

Without any additional information, determining the specific function represented by this graph is difficult. The shape and pattern of the scatter plot, on the other hand, can provide some insight into the relationship between the two variables. If the data points are arranged in a linear pattern, for example, the function could be a linear equation. If the data points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

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Answer:

\(6\frac{2}{5}\)

Step-by-step explanation:

\(2\frac{2}{3} *2\frac{2}{5}\)

First make the above fractions as improper fractions.

\(\frac{8}{3}*\frac{12}{5}\)

Let us solve now.

\(\frac{8*12}{3*5}\)

\(\frac{96}{15}\)

Now let us make the above fraction in it's simplest form.

For that divide both sides by 3.

\(\frac{32}{5}\)

Now let's make it as a mixed number.

\(6\frac{2}{5}\)

Hope this helps you:-)

Let me know if you have any other questions :-)

Answer:

B). 16 x 26

Step-by-step explanation:

Product is defined as the result of multiplication, or an expression that identifies factors to be multiplied.

Answer:

The answer is B - 16•26

Hope this helps

The term "average" in statistics refers to a measure that summarizes the central tendency of a data set. Another term that could be used in place of "average" is "mean.  Average plays a crucial role in statistics as it provides a summary measure of central tendency.

The term "average" in statistics refers to a measure that represents the central tendency of a data set. It is commonly used to summarize and describe the typical value or typical level of a particular variable within a population or sample.

The role of the term "average" is to provide a single value that represents the collective information of the data set. It helps in simplifying and summarizing complex data by providing a measure that is representative of the entire distribution. It allows for comparisons, analysis, and inference based on a single value rather than considering each individual data point.

However, it's important to note that depending on the context and the nature of the data, alternative measures of central tendency may be more appropriate than the "average." For example, if the data set contains outliers or is heavily skewed, the median or mode might be better indicators of the typical value.

In summary, the term "average" plays a crucial role in statistics as it provides a summary measure of central tendency. However, it is important to consider the specific characteristics of the data set and potentially use alternative measures when necessary.

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We can write the integral of f(x) as the sum of the integral of the even component, e(x), and the integral of the odd component, o(x). This gives us the following equation:  ∫f(x)dx = ∫e(x)dx + ∫o(x)dx

Integrals can be written as the sum of the integral of an odd function and the integral of an even function. This is because any function can be broken down into its even and odd components. Even functions are those that remain unchanged when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the same as the result for its negative. Odd functions are those that change sign when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the negative of the result for its negative.

The integral of an even function is the same regardless of whether it is written as the sum of the integral of an odd function and the integral of an even function, or if it is written just as an integral of the even function. The integral of an odd function is the negative of the integral of the even function when written as the sum of the two integrals.

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The bonus question asks for the application of the integral test to determine the convergence of the series given by 2n*e^(-a).

The integral test is a method used to determine the convergence or divergence of a series by comparing it to the integral of a related function. In this case, we are given the series 2n*e^(-a), and we can use the integral test because the terms of the series involve the variable 'n', and the function e^(-a) can be integrated.

To apply the integral test, we consider the integral of the function corresponding to the series. In this case, we integrate the function f(x) = 2x*e^(-a) from 1 to infinity. If this integral converges, then the series is also convergent. Conversely, if the integral diverges, then the series is divergent.

By evaluating the integral of f(x) and analyzing its convergence or divergence, we can determine whether the given series 2n*e^(-a) converges or diverges. Showing all the steps in evaluating the integral and discussing the convergence properties of the resulting integral will be necessary to receive full credit for this question.

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The radius οf the circle is apprοximately 1.2 units.

A circle is a twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a fixed pοint called the center. The distance frοm the centre tο any pοint οn the circle is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.

The circumference οf a circle is the distance arοund its οuter edge, and it is equal tο the prοduct οf the diameter and pi (π), a mathematical cοnstant apprοximately equal tο 3.14159. Circles have many prοperties that make them useful in geοmetry and οther areas οf mathematics.

In this prοblem, we are given the angle and the length οf the intercepted arc. Let's call the radius οf the circle "r". Then we can write:

11.8 = r * 9.7

Tο sοlve fοr "r", we can divide bοth sides by 9.7:

r = 11.8 / 9.7

r ≈ 1.2165

Rοunding tο the nearest tenth, we get:

r ≈ 1.2

Therefοre, the radius οf the circle is apprοximately 1.2 units.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

375

Step-by-step explanation:

Answer:

270 → 72%

x ← 100%

x =375

Step-by-step explanation:

x=(270*100)\72

x=375

This expression will give you the probability that it takes a student more than 4.4 years to graduate.

To calculate the probability that it takes a student more than 4.4 years to graduate, we can use the exponential distribution.

The exponential distribution is characterized by a rate parameter, λ, which is the reciprocal of the mean (λ = 1/mean). In this case, the mean is 5.2 years, so the rate parameter λ is 1/5.2.

The probability density function (PDF) of the exponential distribution is given by f(x) = λ * e^(-λx), where x is the time taken to graduate.

To find the probability that it takes a student more than 4.4 years to graduate, we need to calculate the integral of the PDF from 4.4 years to infinity.

P(X > 4.4) = ∫[4.4, ∞] λ * e^(-λx) dx

To calculate this integral, we can use the complementary cumulative distribution function (CCDF) of the exponential distribution, which is equal to 1 minus the cumulative distribution function (CDF).

P(X > 4.4) = 1 - CDF(4.4)

The CDF of the exponential distribution is given by CDF(x) = 1 - e^(-λx).

P(X > 4.4) = 1 - CDF(4.4) = 1 - (1 - e^(-λ * 4.4))

Now, substitute the value of λ:

λ = 1/5.2

P(X > 4.4) = 1 - (1 - e^(-(1/5.2) * 4.4))

Calculating this expression will give you the probability that it takes a student more than 4.4 years to graduate.

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Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

Answer:

Por tanto, la raíz cuadrada de 100 es 10. 2. Elementos de la raíz. El número 36 es el cuadrado de 6.

Step-by-step explanation:

The probability of a standard normal variable falling between -2.51 and 1.35 is calculated using the standard normal distribution.

The standard normal distribution, also known as the Z-distribution, has a mean of 0 and a standard deviation of 1. To find the probability of a standard normal variable falling within a specific range, we use the Z-table or a statistical calculator. In this case, we need to calculate the probability of the variable falling between -2.51 and 1.35. By looking up these values in the Z-table or using a calculator, we can find the corresponding probabilities. This probability represents the area under the curve of the standard normal distribution between -2.51 and 1.35.

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Answer:

-4

Step-by-step explanation:

The y-intercept is at -4 meaning y is negative four.

Answer:

Step-by-step explanation:

\(P = l + l + b + b\)

\(P = 2(2a + 3) + 2(8a - 12)\)

\(\boxed{\sf{P=20a-18}}\)

\(P = 20(3) - 18\)

\(P = 60 - 18\)

\(\boxed{\sf{P = 42 cm}}\)

\(P = (3b + 7) + (7b - 2) + (7b - 2)\)\(\boxed{\sf{P = 17b+3}}\)

\(P = 17(6) + 3\)

\(P = 102 + 3\)

\(\boxed{\sf{P = 105 \: m}}\)

After 7 weeks, the plant's approximate height is 8.7 cm.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

You are given a a graph titled Plant Height that shows Number of Weeks on x axis and Height of Plant in cm on y axis. Plotting this and you will get an equation of y = 1.2792x - 0.1665 (I used excel using the given points from the above problem).

y = 1.2792x - 0.1665

y = 1.2792 (7) - 0.1665

y = 8.78 centimeters.

The most likely approximate height of the plant after 7 weeks is 8.7 centimeters.

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The sample space for the experiment of tossing a pair of dice consists of all possible outcomes of the two dice rolls. Using a rule method, we can represent the sample space as S = {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}.

(a) The event A corresponds to the sum of the outcomes being greater than 8. The elements of event A are (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(b) The event B corresponds to a 2 occurring on either die. The elements of event B are (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2).
(c) The event C corresponds to a number greater than 4 appearing on the green die. The elements of event C are (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
(d) The event A∩C corresponds to the outcomes where both the sum is greater than 8 and a number greater than 4 appears on the green die. The elements of event A∩C are (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(e) The event A∩B corresponds to the outcomes where both the sum is greater than 8 and a 2 occurs on either die. There are no elements in this event.
(f) The event B∩C corresponds to the outcomes where both a 2 occurs on either die and a number greater than 4 appears on the green die. The elements of event B∩C are (5,2), (6,2).
(g) The Venn diagram illustrating the intersections and unions of the events A, B, and C would have three overlapping circles representing each event. The area where all three circles intersect represents the event A∩B∩C, which is empty in this case. The area where circles A and C intersect represents the event A∩C, and the area where circles B and C intersect represents the event B∩C. The unions of the events can also be represented by the combinations of overlapping areas.

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2.4

(a) Sample space S: {(1, 1), (1, 2), ... (6, 5), (6, 6)}

(b) Rule method: S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) A: {(3, 6), (4, 5), ... (6, 6)}

(b) B: {(1, 2), (2, 1), (2, 2)}

(c) C: {(5, 1), (5, 2), ... (6, 6)}

(d) A∩C: {(5, 4), ... (6, 6)}

(e) A∩B: {}

(f) B∩C: {}

2.4

(a) Sample space S by listing the elements (x, y):

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Sample space S using the rule method:

S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) Elements corresponding to event A (the sum is greater than 8):

A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Elements corresponding to event B (a 2 occurs on either die):

B = {(1, 2), (2, 1), (2, 2)}

(c) Elements corresponding to event C (a number greater than 4 on the green die):

C = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(d) Elements corresponding to event A∩C:

A∩C = {(5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(e) Elements corresponding to event A∩B:

A∩B = {} (No common elements between A and B)

(f) Elements corresponding to event B∩C:

B∩C = {} (No common elements between B and C)

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The population in the year 2020 is 4628

The given parameters are:

Initial, a = 12910

Rate, r = 5%

Since the population decreases, then we make use of an exponential decay function.

This is represented as:

f(n) = a * (1 - r)^n

So, we have:

f(n) = 12910 * (1 - 5%)^n

Evaluate the difference

f(n) = 12910 * 0.95^n

2020 is 20 years from 2000.

So, we have:

f(20) = 12910 * 0.95^20

Evaluate

f(20) = 4628

Hence, the population in the year 2020 is 4628

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Answer:

Step-by-step explanation:

y= money earned , x is the number of hours

k is the constant=y/x=12

b- if she worked 18 hours:

y=12(18)

c- if she earned 330 dollars:

330=12x

x=330/12

Answer: Andre subtracted 3x from both sides

The expressions are evaluated below

Expression 1: 4 < 7

Multiplying both sides by 3, 2, 4, and 9 respectively:

3 * 2 * 4 * 9 * (4 < 7)

864 < 1515

Expression 2: 11 > -2

Adding 3 to both sides, then adding 3, then adding (-4) respectively:

3 + 3 - 4 + (11 > -2)

13 > 0

Expression 3: -2 = -2

Subtracting 6 from both sides, then adding 8, then adding 2 respectively:

-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2

14 = 14

Expression 4: -4 < 8

Dividing both sides by -4, then by -2 respectively:

-4/(-4 * -2) < 8/(-4 * -2)

-1/2 < 1

The operations performed on the inequalities in each question did not affect the inequality sig.

The truth of the inequality was also not affected by the operations in all cases.

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Leeann provided a clue or hint for her friend to guess the name of her favorite actor.

By giving the first initial of both the first and last name, she offered a partial but crucial piece of information to narrow down the possibilities. This clue could be seen as a form of "initialism" or "initial hint."

Using initials to represent names or words is a common practice to create puzzles, riddles, or guessing games.

In this case, Leeann employed the initial hint strategy to engage her friend in a guessing game, making it more fun and challenging.

By providing the first initials, Leeann ensured that her friend had a starting point and could begin narrowing down the list of potential actors.

By not revealing the full names, Leeann added an element of suspense and intrigue to the conversation.

This approach encouraged her friend to think creatively, consider different options, and ultimately engage in an interactive and entertaining exchange.

The use of a partial clue not only sparked curiosity but also allowed Leeann's friend to actively participate in the guessing process, making it a shared experience between the two friends.

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Step-by-step explanation:

7x - 5 = 8

7x = 8 + 5

7x = 13 (divide both sides by 7 to get x)

7x/7 = 13/7

x = 1.85714285714

Question 4: Laura applies for the position of ambulance medic. To give her a job simulation (behavioral interview) screening test, the interviewer...

This question involves providing a job simulation or behavioral interview, which allows the interviewer to observe how the candidate performs in a simulated work situation. This type of question assesses the candidate's skills, abilities, and behavior in a real or simulated work scenario, providing a more accurate evaluation of their capabilities for the job.

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Answer:

420 69

Step-by-step explanation:

620 +90 = 42069

Answer: C. are perpendicular

Step-by-step explanation:

I took the test and got it right

Answer:

(A)Yes

Step-by-step explanation:

A right triangular prism has five faces.

We are to determine if the pattern is a net for the three-dimensional figure.

Therefore, the pattern is a net for the three-dimensional figure

The cost of one lily is 5 and cost of one ivy is 12.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. Every mathematical equation begins with L.H.S = R.H.S.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

Perry store perry spent $132 on 12 daylilies and 6 post of ivy .

chelsea spent $159 on 3 daylilies and 12 pots of ivy.

let the number of daylilies sold be x.

let the number of ivy sold be y.

So, the equation is

12x+ 6y = 132

2x + y = 22......(1)

3x + 12y = 159

x + 4y = 53....(2)

Now solving (1) and (2)

x= 5

y= 12

hence, cost of one lily is 5 and cost of one ivy is 12.

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The largest number which divides 70 and 125 , leaving remainders of 5 and 8 is 13.

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, we can follow these steps:

Subtract the remainders from their respective numbers:

70 - 5 = 65 and

125 - 8 = 117.

Find the factors of each resulting number:

Factor of 65 = 5 and 13

factor of 117 = 3 and 13

Determine the highest common factor (HCF) of the resulting factors:

The HCF of 5 = 1

the HCF of 13 = 1

the HCF of 3 = 3

the HCF of 13 = 13

Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, is 13.

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Answer:D:1/2

Step-by-step explanation:

Answer:

A. The first option

Step-by-step explanation:

Answer:

Option a

Step-by-step explanation:

If the input value only leads to one output than its a function