Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) -5, 10/3, -20/9, 40/27, -80/81,…

A. Using the given information, we can standardize the value 203.4 using the formula \(z = (X - μ) / σ\), where X is the value of interest, μ is the mean, and σ is the standard deviation.

Thus, we get: \(z = (203.4 - 208.5) / 35.4 = -0.14407\)

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected value is greater than \(203.4\):

\(P(X > 203.4)\) = \(P(Z > -0.14407)\) = \(0.5563\) (rounded to 4 decimal places)

To find the probability that the sample mean is greater than 203.4, we need to use the central limit theorem, which states that the sample mean of a large enough sample size (n >= 30) from a population with any distribution has a normal distribution with mean μ and standard deviation σ / sqrt(n). Thus, we get:

\(z = (203.4 - 208.5) / (35.4 / sqrt(236))\)\(= -1.3573\)

Using a standard normal distribution table or calculator, we can find the probability that the sample mean is greater than 203.4:

\(P(X¯¯¯ > 203.4) = P(Z > -1.3573)\)= \(0.0867\) (rounded to 4 decimal places)

B. Using the given information, we can standardize the values \(217.5\) and \(234.6\) using the same formula as before. Thus, we get:

\(z1 = (217.5 - 223.7) / 56.9\) \(= -0.10915\)

\(z2 = (234.6 - 223.7) / 56.9 = 0.19235\)

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected value is between 217.5 and 234.6:

\(P(217.5 < X < 234.6) = P(-0.10915 < Z < 0.19235) = 0.2397\) (rounded to 4 decimal places)

To find the probability that the sample mean is between 217.5 and 234.6, we can use the same formula as before, but with the sample size and population parameters given in part B. Thus, we get:

\(z1 = (217.5 - 223.7) / (56.9 / sqrt(244)) = -1.0784\)

\(z2 = (234.6 - 223.7) / (56.9 / sqrt(244)) = 1.7256\)

Using a standard normal distribution table or calculator, we can find the probability that the sample mean is between 217.5 and 234.6:

\(P(217.5 < X¯¯¯ < 234.6) = P(-1.0784 < Z < 1.7256)\)= \(0.8414\)(rounded to 4 decimal places)

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∠1 + ∠2 = 180

Substituting the given expressions for ∠1 and ∠2:

8x + (2x - 3) = 180

Simplifying and solving for x:

10x - 3 = 180

10x = 183

x = 18.3

Now we can substitute x back into the expression for ∠1 to find its measure:

∠1 = 8x = 8(18.3) = 146.4 degrees.

Therefore, if ∠1 and ∠2 add up to 180 degrees and ∠1 is given as 8x° and ∠2 is given as (2x - 3)°, then ∠1 measures 146.4 degrees

Answer:

<1=146.4

<2=34.6

Step-by-step explanation:

<1+<2=180 degrees

So,

8x+(2x-3)=180

10x-3=180

10x=183

X=18.3

subsitute:

<1=8x

<1=8(18.3)

<1=146.4

<2=2x-3

<2=2(18.3)-3

<2=34.6

Answer:

12

Step-by-step explanation:

4 • 1/3 = 4/3

9 • 4/3 = 36/3

36/3 simplified is 12

If we use pi equal to 3, the volume of the sphere is 5,324 cubic inches.

For a sphere of radius R, the volume is given by:

V = (4/3)πR³

Here we can see that π = 3, and the diameter of the sphere is 22 inches, the radius is half the diameter, then:

R = 22in/2 = 11in

REplacing all that in the volume formula we will get:

V = V = (4/3)3(11in)³ = 4(11in)³ = 5,324 in³

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Answer:

60°

Step-by-step explanation:

2x and x are linear pair,

=> 2x + x = 180

=> 3x  = 180

=> x = 180/3

=> x = 60°

=>2x =120°

Answer:

x = 60

Step-by-step explanation:

x + 2x =  180   {linear pair}

Combine like terms

3x  = 180

Divide both sides by 3

x = 180/3

x = 60

Answer:

6.

Step-by-step explanation:

Answer:

The answer is "Option A".

Step-by-step explanation:

In this, the question is missing so, we assuming the missing question is this question, which is add in attach file. please find it.

Formula for line:

\(\to \bold{y= mx+ c}\)

\(\to m= slope \\\\\to c= y-intercept\)

In the question the slope "m= 3 and y= -2" so, the line is \(y= 3x+ (-2)\).

\(\to y= 3x-2\)

Answer:

16.92

Step-by-step explanation:

5.64 x 3 = 16.92

Hope that helps!

Answer:

There are 3 feet in one yard, so each foot is 1/3 of a yard/

To find the percentage of each foot, divide 1 by 3

One foot is 33 1/3 percent of a yard.

Twelve inches is 33.33 percent of a yard.

Percentage is defined as a number that can be expressed as a fraction of 100.

The statement is

Twelve inches is what percent of a yard

12 inches in terms of % yard

1 inch = 0.0277778 yard

12 inches = 0.333336 yard

In percentage = 33.33 % yard

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The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer:

Family 1: 2x + 3y = 30

Family 2: 3x + 4y = 40

Answer:

I think it is

24.6

Answer:

Step-by-step explanation:

\(x\times(x+ 28) = 20\times (20+32)\\\\x^2+28x-1040=0\\\\\ x=\dfrac{-28\pm\sqrt{28^2-4\cdot1\cdot(-1040)}}{2\cdot1}= \dfrac{-28\pm\sqrt{4944}}{2}\\\\x\approx21.2\quad or\quad x\approx-49.2\)

x has to be >0 so the answer is 21.2

Answer: slope -1/4 y intercept -8

Step-by-step explanation:

In the form y = mx+b, m is the slope and b is the y-intercept. So let’s get it into this form, by getting y by itself.

4y = -x - 32

divide by 4 on every term

y = -1/4x - 8

therefore the slope is -1/4 and y intercept is -8

Answer:

B

Step-by-step explanation:

This is because all of the other sequences are geometric. They all were being divided by 2 besides letter B.

The population growth of Farmville was approximately 100-141%

For the population growth of Farmville, we need to calculate the percentage increase from 1950 to 2000.

First, We find the absolute increase in population:

25,370 - 10,520 = 14,850

Next, the percentage increase:

(14,850 / 10,520) x 100 = 141%

So, the population of Farmville grew by approximately 141% from 1950 to 2000.

Alternatively, we can also use the rule of 70 to estimate the population growth.

The rule of 70 states that if a quantity grows at a constant rate, it will double in size approximately every 70 divided by the growth rate.

In this case, the population growth rate can be calculated as:

ln(25,370/10,520)/50 = 0.025

So the population of Farmville grew at a rate of approximately 2.5% per year. Using the rule of 70, we can estimate the number of years it took for the population to double:

70 / 2.5 = 28

So the population of Farmville doubled approximately every 28 years. This means that the population would have doubled once between 1950 and 2000, resulting in a growth rate of around 100%.

Therefore, both methods suggest that the population growth of Farmville was , 100-141%

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According to the moral choices textbook, ethics and morality are distinct but interconnected concepts. Ethics refers to the actual content of what is considered right and wrong within a particular moral framework or system. It deals with the principles, values, and standards that guide human behavior and decision-making.

Ethics provides a set of norms or rules that help individuals evaluate actions and determine their moral worth.

On the other hand, morality refers to the process of determining right and wrong. It encompasses the various factors, such as cultural, societal, and personal influences, that shape an individual's moral beliefs and judgments.

Morality is a dynamic and complex phenomenon that evolves over time and differs across cultures and individuals. It involves the consideration of various perspectives, reasoning, and critical thinking to arrive at moral conclusions.

While ethics focuses on the principles and rules that define right and wrong, morality encompasses the broader context in which ethical decisions are made.

It involves the examination of motives, intentions, consequences, and the moral responsibility of individuals. In essence, ethics provides the foundation for morality, and morality applies ethical principles in the real-world decision-making process.

It is important to understand the distinction between ethics and morality to engage in meaningful discussions and analyses of moral choices and ethical dilemmas.

By recognizing the content and process aspects of ethics and morality, individuals can better navigate complex moral landscapes and make informed decisions aligned with their values and principles.

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Answer:

300

Step-by-step explanation:

Answer:

X^13Y^12Z^17

Step-by-step explanation:

Answer:

x^13y^12z^17

Step-by-step explanation:

-(-xy^2z^3)^5(x^4yz)^2

-(-x)^5 x y^10z^15 x^8y^2z^2

calculate the product

-(-x)^5 x x^8y^12z^17

a negative base raised to an odd power equals a negative

x^5 x x^8 y^12 z^17

x^13 y^12 z^17

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

3/36 simplified is 1/12

Hope this helps!

Answer:

A) s and t.

Step-by-step explanation:

just trust me. Plus lines s and t are the only pair of lines that don't touch each other and can go on forever not touching each other.

Answer:

no solution

Step-by-step explanation:

- 2(v - 2) = - 3 - 2v ← distribute left side

- 2v + 4 = - 3 - 2v ( subtract 4 from both sides )

- 2v = - 7 - 2v ( add 2v to both sides )

0 = - 7 ← not possible

Hope this helps

Answer:

0 solutions

Step-by-step explanation:

\(-2\left(v-2\right)\\-2v-\left(-2\right)\cdot \:2\\-2v+2\cdot \:2\\-2v+4\\-2v+4=-3-2v\\-2v+4-4=-3-2v-4\\-2v=-2v-7\\-2v+2v=-2v-7+2v\\0=-7\\\mathrm{a < 0 = a \neq\:or\: not > 0 = No\:Solution}\)

The measure of angle C in radians is 3.6 radians.

The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.

We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr

28π= θ/360×2π×7

4= θ/360×7

θ=1440/7

θ=205.7

θ=3.6 radians

Therefore, the measure of angle C in radians is 3.6 radians.

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There are 210 different samples of 4 apples that can be chosen from the bag.

a. to find the number of different samples of 4 apples that can be chosen from the bag of 10 apples, we use the combination formula:

n choose k = n! / (k!(n-k)!)

where n is the total number of apples (10), and k is the number of apples chosen for the sample (4).

so the number of different samples of 4 apples that can be chosen from the bag of 10 apples is:

10 choose 4 = 10! / (4! * 6!) = 210 b. to find the number of samples that contain all good apples, we need to choose 4 apples from the 7 good apples in the bag. this can be done using the combination formula:

7 choose 4 = 7! / (4! * 3!) = 35

so there are 35 different samples that contain all good apples.

c. to find the number of samples that contain at least 1 rotten apple, we can use the complement rule, which says that the probability of an event happening is 1 minus the probability of the event not happening. in this case, we can find the number of samples that do not contain any rotten apples, and then subtract that from the total number of samples found in part a.

to find the number of samples that do not contain any rotten apples, we need to choose 4 apples from the 7 good apples in the bag. this can be done using the combination formula as in part b:

7 choose 4 = 35

so there are 35 different samples that do not contain any rotten apples.

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Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

So, she charges $10 a window plus a $5 flat supply fee, we are going to add 10 and 5 to find are answer and we are going to use c:

→ w = 10

→ 10w

$5 in the other hand, is independent.

→ + 5

→ c = 10w + 5

Therefore, Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

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Arguments are a key component of political campaigns. They are used to convince voters to support a particular candidate or issue. Political campaigns often make claims, which are statements that assert a fact or belief. These claims are backed up by reasoning, which is the evidence or explanation that supports the claim. The conclusion is the result of the reasoning and supports the overall argument.

For example, a candidate may claim that they have a plan to improve the economy. The reasoning may be that the candidate has experience in business and has implemented successful economic policies in the past. The conclusion is that if the candidate is elected, they will be able to improve the economy.
Political campaigns also use arguments to attack opponents and discredit their claims. They may use reasoning to point out flaws in their opponent's plans or past actions. The conclusion is that the opponent is not fit for office and voters should not support them.

Overall, arguments are a crucial tool in political campaigns. They are used to persuade voters and shape public opinion. Successful candidates and campaigns are often those that can make the most convincing arguments and win over the most supporters.

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Answer:

B

Step-by-step explanation:

Since sin is opposite over hypotenuse, the side opposite of angle T is RS and the hypotenuse is RT.

The probability associated with obtaining a particular value of z is referred to as its statistical probability or simply its probability. It represents the likelihood of observing a specific value of z in a given statistical distribution.

The probability of a specific value of z can be calculated using various statistical methods, depending on the distribution being considered. In statistics, z represents a standard score or a z-score. It is a measure of how many standard deviations a particular value is away from the mean of a distribution. The probability associated with a specific value of z is determined by the characteristics of the distribution, such as its shape, mean, and standard deviation. Different distributions, such as the normal distribution or the t-distribution, have different methods for calculating probabilities associated with specific values of z.

The probability associated with a particular value of z can be useful in hypothesis testing, confidence interval estimation, or determining the likelihood of an event occurring. By understanding the probability distribution of z-values, statisticians can make informed decisions and draw conclusions based on data analysis.

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