Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1

an = n​

Answer: 12.54 square yards.

Step by Step Explanation:

The area of a circle is the space occupied by the circle in a two-dimensional plane. The formula for the area of a circle is A = πr^2, where r is the radius of the circle12. The radius is half of the diameter, so r = d/2.

To find the area of the floor of the round hut, you need to use the given circumference of 12.56 yards and find the radius first. The circumference of a circle is C = 2πr, so you can solve for r by dividing both sides by 2π:

r = C / 2π

r = 12.56 / (2 * 3.14)

r = 1.998 yards

Then you can use the formula for the area of a circle and substitute r with 1.998:

A = πr^2

A = 3.14 * (1.998)^2

A = 12.54 square yards

If necessary, you can round your answer to the nearest hundredth, which is 12.54 square yards.

The winner received 168 votes in the eighth-grade class election for president.

To answer this question, we need to find out how many votes the winner received in the eighth-grade class election for president, given that 480 students voted and the results are shown in a pie chart.

1. Examine the pie chart to find the percentage of votes the winner received.

2. Calculate the number of votes the winner received by multiplying the percentage by the total number of votes (480 students).

For example, if the pie chart shows the winner received 60% of the votes:

1. The winner received 60% of the votes.

2. Calculate the number of votes: 60% * 480 = 0.6 * 480 = 288 votes.

Here,

percent of votes received by Melissa = 35%

percent of votes received by Heather= 33%

Total percent of votes received by Melissa and

Heather 35+ 33 68% percent of votes received by Paul 100-68= 32%

So Melissa was the winner.

Total number of votes cast = 480

Total no of votes received by Melissa

(35/100)x(480) = 168

So, the winner received 168 votes in the eighth-grade class election for president.

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False. When a highly accurate estimate of the population is needed, the sampling method needs to be a probability method, not a nonprobability method.

Probability sampling is a sampling method that uses random criteria to select a sample from the population, ensuring that every member of the population has an equal chance of being included. Probability sampling allows researchers to make statistical inferences about the population based on the sample.

Nonprobability sampling is a sampling method that uses non-random criteria to select a sample from the population, such as convenience, availability, or expert judgment. Nonprobability sampling does not allow researchers to make statistical inferences about the population based on the sample.

False. When a highly accurate estimate of the population is needed, the sampling method needs to be a probability method. Probability sampling methods ensure that every member of the population has an equal chance of being selected, which helps to minimize bias and increase the representativeness of the sample.

False. When a highly accurate estimate of the population is needed, the sampling method needs to be a probability method. Probability sampling methods ensure that every member of the population has an equal chance of being selected, which helps to minimize bias and increase the representativeness of the sample.

Nonprobability sampling methods, on the other hand, do not guarantee equal representation and are more likely to introduce bias into the sample. However, nonprobability sampling methods can still be useful in certain situations where probability sampling is not feasible or appropriate, such as when studying hard-to-reach populations or when conducting exploratory research. Ultimately, the choice of sampling method depends on the research question, the characteristics of the population being studied, and the resources available for sampling.
False. When a highly accurate estimate of the population is needed, it is recommended to use a probability sampling method rather than a nonprobability method. Probability sampling methods, such as simple random sampling, systematic sampling, stratified sampling, and cluster sampling, involve the selection of participants based on a known probability. This ensures that each individual in the population has a known and nonzero chance of being included in the sample.
In contrast, nonprobability sampling methods, such as convenience sampling, quota sampling, and snowball sampling, do not provide every individual in the population an equal chance of being selected. These methods are more prone to biases and may not be representative of the overall population, making it difficult to generalize the findings and obtain an accurate estimate.
Probability sampling methods are preferred when aiming for a high level of accuracy and representativeness, as they allow for the calculation of sampling error and the estimation of confidence intervals. These techniques help in understanding the reliability of the results and enable researchers to make valid inferences about the entire population.

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The equation for the least-squares regression line for the given data and the average chance of admission for a student who scores a 305 on the GRE are options b) 51% (or 0.51).

To find the equation for the least-squares regression line, we need to first calculate the slope and y-intercept. Let x be the predictor variable (GRE score) and y be the response variable (admission chance). Then, we have:

n = 10 (number of data points)

Σx = 3100

Σy = 52.1

Σxy = 161750

Σx^2 = 96100

Σy^2 = 24.71

The slope, b, can be calculated as:

b = (nΣxy - ΣxΣy) / (nΣx^2 - Σx^2)

= (10(161750) - (3100)(52.1)) / (10(96100) - 3100^2)

= 0.0644

The y-intercept, a, can be calculated as:

a = (Σy - bΣx) / n

= (52.1 - (0.0644)(3100)) / 10

= 0.336

Therefore, the equation for the least-squares regression line is:

y = 0.0644x + 0.336

To find the average chance of admission for a student who scores a 305 on the GRE, we simply substitute x = 305 into the equation and solve for y:

y = 0.0644(305) + 0.336

= 0.5136

So the average chance of admission for a student who scores a 305 on the GRE is b) 51% (or 0.51).

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Answer: D. 9(y + 3) and 27 + 9y

Step-by-step explanation:

    We will distribute the left expressions and see which is equal to the right expressions.

A] 3(3y + 3) ➜ 9y + 9 ≠ 6y + 6

B] 3(3y + 3) ➜ 9y + 9 ≠ 9y + 6

C] 9(y + 3) ➜ 9y + 27 ≠ 12 + 9y

D] 9(y + 3) ➜ 9y + 27, 27 + 9y = 27 + 9y

Answer:

D.

Step-by-step explanation:

The answer is D.

these are equivalent for any value of y

Answer: The college will have about 480 students who prefer cookies.

Step-by-step explanation:

Answer:

Step-by-step explanation:

add the number of cookies then subtract  it by the number of students

Answer:

Step-by-step explanation:

To solve the quadratic equation x^2 = x + 3 using the quadratic formula, we first need to write the equation in standard form:

x^2 - x - 3 = 0

Then, we can identify the coefficients a, b, and c as follows:

a = 1, b = -1, c = -3

Now, we can plug these values into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-1) ± √((-1)^2 - 4(1)(-3))) / 2(1)

Simplifying:

x = (1 ± √(1 + 12)) / 2

x = (1 ± √13) / 2

Therefore, the solutions for the quadratic equation x^2 = x + 3 using the quadratic formula are:

x = (1 + √13) / 2 or x = (1 - √13) / 2

The probability of a randomly selected student completing the test in 45 minutes or less is 15.87%.

The probability of a randomly selected student completing the test in 95 minutes or less is 84.13%.

Using the standard normal distribution to standardize the values:

z = (x - μ) / σ

where:

For 45 minutes or less:

z = (45 - 70) / 25

z = -1

Using a calculator, we can find that the probability of a z-score less than or equal to -1 is approximately 0.1587.

For 95 minutes:

z = (95 - 70) / 25

z = 1

Using a calculator, the probability of a z-score less than or equal to 1 is approximately 0.8413.

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Answer:

C. 16x² y + 20xy

Step-by-step explanation:

16x² y + 20xy

Factor out 4xy

4xy(4x + 5)

So, only C is correct answer, the other options are wrong.

The 3 sentences that describe your observations are,

Additionally, the coordinates of the vertices are all integer values.

Finally, it appears that the three triangles are all similar to one another,

meaning that they have the same shape but may be different sizes.

Now, We get;

Upon examining the triangles and their vertices,

I can see that all three triangles have two vertices with the same coordinates.

Additionally, the coordinates of the vertices are all integer values.

Finally, it appears that the three triangles are all similar to one another, meaning that they have the same shape but may be different sizes.

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The most appropriate technique for gathering data on the average class size of "mathematics" classes and "English" classes in a "high-school" would be (d) Observational study.

In an "observational-study", the researcher simply observes and records the data without manipulating any variables.

In this case, the researcher would observe and record the class sizes of mathematics and English classes in the high school. This technique is appropriate because it allows for a comparison between the two types of classes without any interference or manipulation from the researcher.

The Census is used to collect data from an entire population, which may not be feasible or necessary in this case.

The "Sample-Surveys" involve collecting data from a subset of the population, but it may not be representative of the entire population.

The Experiments involve manipulating variables, which is not necessary in this case.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Suppose you wish to compare the average class size of mathematics classes to the average class size of English classes in your high school. Which is the most appropriate technique for gathering the needed data?

(a) Census

(b) Sample survey

(c) Experiment

(d) Observational study.

Step-by-step explanation:

Total yards =    11+11    +   31+31 = 84 yards

84 yd * $9/yd =  $ 756 total

Answer:

Step-by-step explanation:

The area of the shaded segment of the circle is 39.27 square meter.

From the given figure, radius = 8 m.

We know that, the area of the minor segment of the circle is (θ / 360°) × πr²- (1/2) r² sin θ.

Angle of minor arc = 360°-240°

= 120°

Here, area of the segment = (120°/360°) ×3.14×8²-1/2 ×8²×sin 120°

= 1/3 ×3.14×64-1/2×64×√3/2

= 39.27 square meter

Therefore, the area of the shaded segment of the circle is 39.27 square meter.

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After 8 years, Austin's savings account would have a balance of [tex]$861.39[/tex].

Assuming the interest rate remains constant, the balance of Austin's savings account after 8 years can be calculated using the formula for compound interest: Balance =

[tex]Principal x (1 + (Interest Rate/Number of times compounded per year))^(Number of years x Number of times compounded per year)[/tex]

The principal is [tex]$600.00[/tex], the interest rate is 5%, compounded annually (meaning it's compounded once a year), and the number of years is 8. Plugging in the values, we get:

Balance = [tex]$600.00 x (1 + (0.05/1))^(8 x 1)[/tex]

Balance = [tex]$861.39[/tex]

This means that the initial deposit of [tex]$600.00[/tex] would have earned [tex]$261.39[/tex] in interest over the 8-year period. It's worth noting that the longer the money remains in the account, the more it will earn due to the compounding effect.

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The length of the arc that has a central angle measure of 45 degrees and a circle radius of 12 cm is calculated as: 9.42 cm.

The length of an arc can be calculated by using the formula below:

length of arc = ∅/360 * 2πr, where:

∅ = central angle measure

r = the radius of the circle.

The central angle measure (∅) = 45°

Radius (r) = 12 cm

Plug in the values:

length of arc = 45/360 * 2 * 3.14 * 12

length of arc = 9.42 cm

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The survey mode that is not mentioned in the text is "puter-administered." The correct option is b: puter-administered.

The following is not a survey mode mentioned in the text: a.person-administered. b: puter-administered. c.self-administered. d.mixed-mode.

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we have -4 = -4 on the left-hand side and 3 = 3 on the right-hand side, so the equation is balanced.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

12894 ( 36 ÷ 9 ) − ( 36 ÷ 2 ) = 5 ( × 3 ) − 12

Explanation:

36 ÷ 9 = 4, so we can use the digit 4 from the number 12894.

36 ÷ 2 = 18, so we can use the digit 8 from the number 12894.

Now we have (4 - 8) = -4 on the left-hand side of the equation.

5 × 3 = 15, so we can use the digit 1 from the number 12894.

15 - 12 = 3, so we can use the digit 3 from the number 12894.

Thus, we have -4 = -4 on the left-hand side and 3 = 3 on the right-hand side, so the equation is balanced.

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( 36 ÷ 4 ) − ( 36 ÷ 9) = 5 (8 × 3 ) − 12 = 12

4   9   8   12

Step-by-step explanation:

i did the test

The value of x in the right angled triangle is 11.12.

A right angled triangle is a triangle in which one of the angles is 90°.

To calculate the value of x in the right angled triangle, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Hence, the value of 11.12.

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By looking at the domain of the graphed function we can see that the correct option is D.

f(x) = 5√x - 4

We can see that the function is not defined for x ≤ 0.

Remember that it happens for square roots, then we need to have a function with a square root of x, √x.

Or a square root of a product of x, √(a*x), where a is a real number.

The only option with that is D, which is:

f(x) = 5√x - 4

So that is the correct option.

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The mean and MAD of the two sets are solved

Given data ,

Set A: {1,2,3,4,10}

Mean of Set A: (1 + 2 + 3 + 4 + 10) / 5 = 4

To find the mean absolute deviation (MAD), we first find the absolute difference of each value from the mean:

|1 - 4| = 3

|2 - 4| = 2

|3 - 4| = 1

|4 - 4| = 0

|10 - 4| = 6

Next, we find the average of these absolute differences:

MAD of Set A = (3 + 2 + 1 + 0 + 6) / 5 = 2.4

And ,

Set B: {1, 2, 3, 4, 5}

Mean of Set B: (1 + 2 + 3 + 4 + 5) / 5 = 3

To find the mean absolute deviation (MAD), we first find the absolute difference of each value from the mean:

|1 - 3| = 2

|2 - 3| = 1

|3 - 3| = 0

|4 - 3| = 1

|5 - 3| = 2

Next, we find the average of these absolute differences:

MAD of Set B = ( 2 + 1 + 0 + 1 + 2 ) / 5 = 1.2

Hence , mean absolute deviation of Set A is less than the mean absolute deviation of Set B and mean of Set A is greater than the mean of Set B

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Answer:

1/4 ÷ 6 would be 1/24

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact Form: 1/24

Decimal Form: 0.041¯6

Answer:

The answer is 1/24.

Step-by-step explanation:

1/4 divided by 6

Here , 4 is the denominator in 1/4 and 6 is the numerator in 6/1

So, denominator and numerator will be multiplied .

=1/(4 x6)

=1/24

The relation is not function because for each input there is not exactly one output.

We know that a function is said to be relation if each input value have distinct output.

Also, No two same input value have different output value0

Here, for x = 0,

there are two values of y, -4 and -2

This, shows that given relation is not a function.

Hence, it is not a function.

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The point estimate for the population mean number of weeks it takes a worker aged 55 plus to find a job is 22.9 weeks, with a margin of error of approximately 4.18 weeks and a 95% confidence interval of (18.72, 27.08) weeks. The data is skewed to the right, and collecting data from a larger sample and accounting for other factors could improve the study.

The point estimate for the population mean number of weeks it takes a worker aged 55 plus to find a job can be found by calculating the sample mean. Adding up all the values in the data and dividing by the sample size of 39 gives a point estimate of 22.9 weeks.

To find the margin of error at 95% confidence, we need to first calculate the sample standard deviation. The sample standard deviation is 12.9 weeks. Using the formula for the margin of error at 95% confidence level, we get:

Margin of error = 1.96 * (12.9 / √(39)) ≈ 4.18 weeks

The 95% confidence interval estimate of the mean is given by

(22.9 - 4.18, 22.9 + 4.18) = (18.72, 27.08)

Therefore, we are 95% confident that the true population mean number of weeks it takes a worker aged 55 plus to find a job lies between 18.72 and 27.08 weeks.

To determine the degree of skewness in the sample data, From the data provided, the distribution appears to be skewed to the right, as there are a few very large values that pull the mean to the right of the median.

For a repeat of this study, it would be useful to collect data from a larger sample size to improve the precision of the estimates. Additionally, it may be useful to collect data on other factors that may affect job search time, such as education level, prior work experience, and industry.

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--The given question is incomplete, the complete question is given

" Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings (AARP Bulletin, April 2008). a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job. b) At 95% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the mean? d) Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study? Job Search Time (Weeks) 21 14 51 16 17 14 16 12 48 0 27 17 32 24 12 10 52 21 26 14 13 24 19 28 26 26 10 21 44 36 22 39 17 17 10 19 16 22 5 22"--

Answer: 26 [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

4 2/5 * 6                    convert mixed to improper

22/5 * 6

132/5                      convert back

26 2/5

Answer:

Step-by-step explanation:

The maximum height reached from the ground is 242.75 m

Here, we have,

The horizontal speed of a projectile is regular, and there's a vertical acceleration because of gravity; its cost is 9.8 m/s/s, down, The vertical speed of a projectile changes via nine.8 m/s every second, The horizontal motion of a projectile is impartial to its vertical movement.

we know that,

Projectile motion is a form of motion experienced with the aid of an object or particle that is projected in a gravitational field, such as from Earth's floor, and movements alongside a curved route below the action of gravity best.

Projectile motion is the movement of an object thrown (projected) into the air. After the initial force that launches the item, it most effectively reports the pressure of gravity. The object is known as a projectile, and its route is called its trajectory.

Calculation:-

vertical velocity = 70 cos 35° = 57.34 m/s.

height = 64 m tall

time = ?

S = ut +1/2 at²

75 =  57.34t + 1/2×9.8 t²

4.9t² + 57.34t - 75 = 0

t = 1.50035 Sec

V² = U² - 2aS

0 =  U² - 2aS

U² = 2aS

S = U² /2a

  =  (57.34)²/2× 9.8

  = 167.75

Total height = 75 + 167.75

                    = 242.75 m

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complete question:

A man fired a bullet from the top of a tree whick is 64m tall. The bullet is fired with а velocity of 70ms-1 and angle of 35° to the horizontal line from the eye view of the man. If Sitting position the man is 0.8m Tall. Find the maximum height reached from the ground.

​

Answer:

The correct answer is 5 and 8. A right triangle has two sides whose lengths are the square root of two consecutive integers and one side whose length is the difference between those two integers. In this case, the two consecutive integers are 34 and 35. This means that the side lengths of the right triangle would be √34 and √35, or 5 and 8.

The answer of the given question based on the ticks are in an OCTILLA is , an OCTILLA contains 4,096 sticks.

In general, a bundle is a collection of similar objects that are tied or wrapped together in some way for ease of handling, transport, or storage. The term "bundle" can be used to refer to different types of collections of objects depending on the context in which it is used. "bundle" refers to a specific quantity of a certain object.

According to the given information:

1 OC = 8 sticks

1 OCTA = 8 OC = 8 x 8 sticks = 64 sticks

1 OCTIL = 8 OCTA = 8 x 64 sticks = 512 sticks

1 OCTILLA = 8 OCTIL = 8 x 512 sticks = 4,096 sticks

Therefore, an OCTILLA contains 4,096 sticks.

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