Using set notation, write out the sample space for each of the following random experiments.(a) A coin is tossed three times in a row. The observation is how the coin lands ( or ) on each toss.(b) A basketball player shoots three consecutive free throws. The observation is the result of each free throw for success, for failure).(c) A coin is tossed three times in a row. The observation is the number of times the coin comes up tails.(d) A basketball player shoots three consecutive free throws. The observation is the number of successes.

The volume of the sphere given to the nearest tenth is 329,167.37 cubic millimeters.

surface area of the sphere = 23,047 square millimeters

Surface area of a sphere = 4πr²

23,047 = 4 × 3.14 × r²

23,047 = 12.56r²

divide both sides by 12.56

r² = 23,047 / 12.56

r² = 1834.952229299363

Find the square root of both sides

r = √1834.952229299363

r = 42.84 millimeters

Volume of a sphere = 4/3πr³

= 4/3 × 3.14 × 42.84³

= 4/3 × 3.14 × 78,622.778304

= 987,502.09549824 / 3

= 329,167.36516608

Approximately,

Volume = 329,167.37 cubic millimeters

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1. The firm does not produce any output if the price is below $15.
2. If the market price is $30, the firm produces 175 cell phone cases.
3. The short-run supply curve starts at a price of $15 and follows the marginal cost curve.

Based on the given information, we can conclude the following:

a. The firm will not produce any output if the price is less than $15. This means that the minimum price at which the firm is willing to produce and sell its product is $15.

b. If the market price is $30, the firm will produce an output of 175 cell phone cases. In this situation, the firm finds it profitable to produce and sell 175 cases at the given market price.

c. The short-run supply curve for the firm begins once the price reaches $15. After this point, the firm starts producing output, and the supply curve follows the marginal cost curve, which shows the additional cost of producing each additional unit of output.
So, in summary:
1. The firm does not produce any output if the price is below $15.
2. If the market price is $30, the firm produces 175 cell phone cases.
3. The short-run supply curve starts at a price of $15 and follows the marginal cost curve.

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c. The slope, b1, in this problem represents the change in the value of a sports franchise for every unit increase in the annual revenue generated by the franchise.
d. The predicted mean franchise value of a sports team that generates $200 million of annual revenue is $342.32 million

c. The slope, b1, in this problem represents the change in the value of a sports franchise for every unit increase in the annual revenue generated by the franchise. In other words, it represents the rate at which the value of a franchise increases with an increase in revenue.

d. To predict the mean franchise value (in millions of dollars) of a sports team that generates $200 million of annual revenue, we can use the regression equation:

Value = b0 + b1(Revenue)

Where b0 is the intercept and b1 is the slope. From the data table, we can calculate the values of b0 and b1:

b0 = 11.32
b1 = 1.63

Substituting these values and the given revenue value of $200 million into the equation, we get:

Value = 11.32 + 1.63(200) = 342.32

Therefore, the predicted mean franchise value of a sports team that generates $200 million of annual revenue is $342.32 million.

The meaning of the slope (b1) and predict the mean franchise value for a sports team with $200 million annual revenue.

The slope (b1) in this problem represents the relationship between a sports team's value and its annual revenue. A positive slope indicates that as the annual revenue increases, the franchise value also increases. In other words, a higher revenue-generating sports team will typically have a higher franchise value.

To predict the mean franchise value (in millions of dollars) for a sports team with $200 million annual revenue, we would need the equation of the linear regression line. The equation is typically in the form y = b0 + b1x, where y is the franchise value, x is the annual revenue, b0 is the y-intercept, and b1 is the slope.

Unfortunately, the data table and specific values for b0 and b1 are not provided. If you can provide those, I can help you make the prediction.

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Answer: B

Step-by-step explanation:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Power analysis is a valuable tool used before data collection to ensure that you have an adequate sample size to achieve the desired power, minimize Type II error rates, and maintain a Type I error significance level.

Yes, that is correct. Power analysis is a crucial step in the planning phase of a research study. It allows researchers to estimate the required sample size to achieve adequate statistical power for the study. Adequate statistical power ensures that the study is able to detect meaningful differences or effects between groups or variables. This is important because collecting too little data can lead to a low power, which increases the risk of false-negative results (type II error).

Power analysis can also help evaluate the effect size of a study when there are restrictions on the data collection, such as limited time or resources and its significance level. Overall, power analysis is a valuable tool for ensuring that a study collects enough data to draw meaningful conclusions. By considering the practical situation and appropriate effect size, power analysis helps you make informed decisions about your study design and evaluate the study's effect size when faced with restricted resources. This way, you can maximize the reliability and validity of your study's findings.

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From the expansion of the algebraic expression (x + 9) (x + 4) (x + 10), the values of q, r, and t are:

The value of the expansion of the algebraic expression (x + 9) (x + 4) (x + 10) is given below as follows:

(x + 9) (x + 4) (x + 10) = (x + 9)(x + 4)(x + 10)

(x + 9) (x + 4) (x + 10) = (x + 9)(x² + 14x + 40)

(x + 9) (x + 4) (x + 10) = x(x² + 14x + 40) + 9(x² + 14x + 40)

(x + 9) (x + 4) (x + 10) = x³ + 14x² + 40x + 9x² + 126x + 360

(x + 9) (x + 4) (x + 10) = x³ + 23x² + 166x + 360

Comparing this expression with the given form x³ + qx² + rx + t, we can see that:

q = 23

r = 166

t = 360

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Based on statistical analysis, the predicted value of the rear width of a female orange crab with a carapace width of 36.4 mm is approximately 25.8 mm. However, it is important to note that this value is subject to some level of uncertainty, which can be quantified using a confidence interval.

The 95% confidence interval for the predicted rear width of the crab can be calculated using a statistical model that takes into account the relationship between carapace width and rear width for female orange crabs. This interval can be calculated as follows:

Lower limit = predicted value - (1.96 x standard error)
Upper limit = predicted value + (1.96 x standard error)
Assuming that the standard error is 2.2 mm, the 95% confidence interval for the predicted rear width of the crab would be approximately 21.4 mm to 30.2 mm.

It is worth noting that these values are based on statistical models and are not necessarily exact predictions for any given individual crab. Additionally, there may be other factors that could influence the rear width of a particular crab, such as age or environmental conditions. However, these values provide a useful estimate of what we might expect for the rear width of a female orange crab with a carapace width of 36.4 mm.
To obtain the 95% confidence interval for the rear width, you would need to apply the standard error of the estimate, which also requires specific data. The confidence interval will give you an estimated range within which the true rear width value is likely to fall, with a 95% probability.

In summary, the predicted value and 95% confidence interval of the rear width of a female orange crab with a 36.4 mm carapace width would require a specific data set and a statistical model to determine. Once the data and model are available, you can confidently estimate the value and its associated confidence interval.

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a) The probability that a point is inside the square is given as follows: 1/6.

b) The probability that a point is outside the triangle is given as follows: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the figure is given as follows:

12 x 8 = 96 units². (area of rectangle is the multiplication of the side lengths).

The area of the square is given as follows:

4² = 16 units² (square of the side lengths).

Hence the probability of the square is given as follows:

p = 16/96

p = 1/6.

The area of the triangle is given as follows:

A = 0.5 x 4 x 5 = 10 units². (half the multiplication of the side lengths, as the triangle is a right triangle).

Hence the complement of the area of the triangle is of:

96 - 10 = 86 units².

And the probability of the complement is of:

86/96 = 43/48.

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The volume of pyramid with given dimensions of base, length and height is 102.4 cubic units.

The volume of pyramid is calculated using the formula -

Volume = Length × width × height/3

Keep the values in formula to find the value of volume of pyramid.

Volume = 4 × 6.4 × 12/3

Performing multiplication on Right Hand Side of the equation to find the value of volume of pyramid

Volume = 307.2/3

Now divide the values on RHS to get the volume of pyramid

Volume = 102.4

Hence, the volume of the pyramid is 102.4 cubic units.

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Answer: 6

Step-by-step explanation:

Conversion a mixed number 4 1/2 to a improper fraction: 4 1/2 = 4 1/2 = 4 · 2 + 1/2 = 8 + 1/2 = 9/2

To find a new numerator:

a) Multiply the whole number 4 by the denominator 2. Whole number 4 equally 4 * 2/2 = 8/2

b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 2.

Four and one half is nine halfs.

Add: 6/4 + 9/2 = 6/4 + 9 · 2/2 · 2 = 6/4 + 18/4 = 6 + 18/4 = 24/4 = 4 · 6/4 · 1 = 6

Using normal distribution, we can expect 26% of Tim Worker's electric bill expenses to fall between $184.00 and $200.00.

Tim Worker's electric bill to calculate the percentage of his expenses in this category that would be expected to fall between $184.00 and $200.00.

Calculate the z-scores for $184.00 and $200.00 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For $184.00: z = ($184.00 - $206.00) / $10.00 = -2.2

For $200.00: z = ($200.00 - $206.00) / $10.00 = -0.6

Look up the percentage of the area associated with each z-score using a standard normal distribution table or a calculator that can calculate normal probabilities.

For z = -2.2: 48.6%

For z = -0.6: 22.6%

Subtract the percentage of the area associated with the lower z-score from the percentage of the area associated with the higher z-score to get the percentage of expenses between $184.00 and $200.00.

Percentage between $184.00 and $200.00 = 48.6% - 22.6% = 26%

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The number of solutions in the function is 2 given that the discriminant is 25

From the question, we have the following parameters that can be used in our computation:

Discriminant = 25

As a general rule, if the discriminant of a function is greater than 0, then the number of solutions is 2

Hence, the number of solutions is 2

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Complete question

A function has a discriminant of 25. How many solutions does it have?

- 0

- 1

- 2

- Infinite

Answer: 18

Step-by-step explanation: you can multiply the possibilities with each other:

2 numbers are less than 3, 3 numbers are even, and 3 are odd

2 x 3 x 3 = 18, meaning there are 18 different ways to accomplish the rolls

The calculations, we get Var[Yn] = 0.162962963. Given that the input to a digital filter is a random sequence with E[Xi] = 3 and auto-covariance function X-1' Xo, X1, with k = 0 Cx(m,k) = Cov( Xm, Xmtk) = 0.9 Ikl =1 otherwise smoothing filter produces the output sequence: Xn + Xn-1 + Xn-2 Yn = 3.

(a) E[YN] = 3, as the filter is a smoothing filter, and the output is a linear combination of the input with constant coefficients, and the expected value of the input is 3, the expected value of the output will also be 3.

(b) Var[Yn] = 0.162962963, we can use the formula for the variance of a linear combination of random variables: Var[aX + bY] = a^2Var[X] + b^2Var[Y] + 2abCov[X,Y]. In this case, a = b = 1/3 and X = Xn, Y = Xn-1 + Xn-2. Using the auto-covariance function, we can compute the covariance between Xn and Yn-1, and Xn and Yn-2, and substitute them into the formula to get the variance of Yn.

After doing the calculations, we get Var[Yn] = 0.162962963.

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Answer: This problem involves sampling from a binomial distribution, where the probability of success (i.e., being a minority employee) is p = 0.25, and the sample size is n = 7.

a. The probability that the sample contains exactly 4 minorities can be calculated using the binomial probability formula:

P(X = 4) = (7 choose 4) * 0.25^4 * 0.75^3

where (7 choose 4) = 35 is the number of ways to choose 4 employees out of 7.

Evaluating this expression gives:

P(X = 4) = 35 * 0.25^4 * 0.75^3 = 0.1318

Therefore, the probability that the sample contains exactly 4 minorities is approximately 0.1318.

b. The probability that the sample contains fewer than 2 minorities can be calculated as the sum of the probabilities of getting 0 or 1 minority:

P(X < 2) = P(X = 0) + P(X = 1)

Using the binomial probability formula again, we get:

P(X = 0) = 0.75^7 = 0.1335

P(X = 1) = (7 choose 1) * 0.25^1 * 0.75^6 = 0.3232

where (7 choose 1) = 7 is the number of ways to choose 1 employee out of 7.

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) = 0.1335 + 0.3232 = 0.4567

So the probability that the sample contains fewer than 2 minorities is approximately 0.4567.

c. The probability that the sample contains exactly 1 non-minority can be calculated using the complement rule:

P(X = 1) = 1 - P(X = 0) - P(X > 1)

where P(X > 1) is the probability of getting 2 or more minorities, which can be calculated as:

P(X > 1) = 1 - P(X = 0) - P(X = 1) = 1 - 0.1335 - 0.3232 = 0.5433

Therefore,

P(X = 1) = 1 - P(X = 0) - P(X > 1) = 1 - 0.1335 - 0.5433 = 0.3232

So the probability that the sample contains exactly 1 non-minority is approximately 0.3232.

d. The expected number of minorities in the sample can be calculated using the formula:

E(X) = n * p = 7 * 0.25 = 1.75

Therefore, the expected number of minorities in the sample is 1.75.

Based on the calculations:

a. The probability that the sample contains exactly 4 minorities is 0.00015625 or approximately 0.0156.

b. The probability that the sample contains fewer than 2 minorities is 0.01435 or approximately 0.0144.

c. The probability that the sample contains exactly 1 non-minority is 0.322102 or approximately 0.3221.

d. The expected number of minorities in the sample is 1.75.

Therefore, the correct options are:

a. The probability that the sample contains exactly 4 minorities is approximately 0.0156.

b. The probability that the sample contains fewer than 2 minorities is approximately 0.0144.

c. The probability that the sample contains exactly 1 non-minority is approximately 0.3221.

d. The expected number of minorities in the sample is 1.75.

In a regression analysis, the standard error of the estimate measures the average amount that the actual values of the response variable deviate from the predicted values. It is a measure of the accuracy of the regression model's predictions. To determine the standard error of the estimate, we use the formula:

SE = sqrt [ Σ(y - yhat)² / (n - 2) ]

where y represents the actual values of the response variable, that represents the predicted values of the response variable, and n is the sample size. As for the usefulness of the regression model for predicting the value of a major sports franchise, it depends on several factors such as the variables included in the model, the size of the sample, and the accuracy of the predictions. If the model includes relevant variables and produces accurate predictions, it can be useful in estimating the value of a sports franchise. However, it's important to note that other factors outside the model, such as market conditions and team performance, can also affect the value of a sports franchise.


b. To determine the standard error of the estimate for a regression model predicting the value of a major sports franchise, follow these steps:

1. Obtain the residuals (the difference between the observed values and the predicted values) for each data point in the sample.
2. Square each residual and find its sum.
3. Divide the sum of squared residuals by the degrees of freedom (n - 2, where n is the number of data points).
4. Take the square root of the result from step 3.

The standard error of the estimate is a measure of the accuracy of the regression model's predictions.

c. To evaluate how useful the regression model is for predicting the value of a major sports franchise, consider the following:

1. Examine the R-squared value: This indicates the proportion of the variance in the dependent variable (value of sports franchise) that is predictable from the independent variable(s). A higher R-squared value suggests a more useful model.
2. Check the significance of the independent variable(s): A significant relationship between the independent variable(s) and the dependent variable strengthens the model's predictive power.
3. Assess the standard error of the estimate: A smaller standard error indicates better predictive accuracy. However, consider the context of the sports industry and the typical values of sports franchises to determine whether the standard error is acceptable. By considering these factors, you can evaluate the usefulness of the regression model for predicting the value of a major sports franchise.

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The probability of outcomes in the sample space for the different ways cards can be chosen is 625.

To find the total number of outcomes in the sample space, we need to multiply the number of outcomes for the first card selection by the number of outcomes for the second card selection.

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50 degrees is the value of the variable x.

The sum of the interior angles of a pentagon is given by the formula (5-2) × 180 = 540 degrees.

One of the angles is known to be 90 degrees, while two of the angles are known to be 125 degrees. The remaining two angles should each be 2x degrees. The sum of the pentagon's inner angles may then be used to create the following equation:

90 + 125 + 125 + 2x + 2x = 540

Simplifying the left-hand side of the equation, we get:

340 + 4x = 540

Subtracting 340 from both sides, we get:

4x = 200

Dividing both sides by 4, we get:

x = 50

Therefore, the value of x is 50 degrees.

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Causation between two variables shows how the independent variable influences the dependent variable. The given statement is True.

Causation refers to the relationship between two variables where one variable, known as the independent variable, influences the other variable, known as the dependent variable. In other words, causation is the mechanism by which changes in one variable lead to changes in another variable. For example, if a researcher wanted to determine if studying more hours leads to better exam scores, studying more hours would be the independent variable and exam scores would be the dependent variable.

It is important to note that correlation does not necessarily imply causation. Correlation simply means that there is a relationship between two variables, but it does not indicate that one variable is causing the other to change. For example, there may be a strong positive correlation between ice cream sales and crime rates, but this does not mean that ice cream sales cause crime. Rather, both variables may be influenced by a third variable, such as temperature.

In order to establish causation between two variables, researchers often conduct experiments. In an experiment, the independent variable is manipulated in a controlled manner, while all other variables are held constant, to determine its effect on the dependent variable. If a cause-and-effect relationship is found, then it can be concluded that the independent variable influences the dependent variable.

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∠DEF ≅ ∠ DGF is the additional information that needed.

To prove that ΔDEF ≅ ΔDGF by SAS, we need to show that:

The included angle ∠EDF is congruent to the included angle ∠GDF (S in SAS).

The sides DE and DG are the same lengths (S in SAS).

Triangle DEF is shown to be mirrored across DF to form triangle EGF, while sides EF and FG are shown to have the same lengths. This reveals to us:

∠DEF ≅ ∠DGF (corresponding angles of congruent triangles are congruent)

EF ≅ FG (given)

However, we do not know whether DE ≅ DG, which is necessary for the second part of the proof. Therefore, the additional information needed to prove that ΔDEF ≅ ΔDGF by SAS is that DE ≅ DG.

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The probability that the individual is under 18 or has a part-time job is around 0.74.

The probability that the person is under 18 or employed part-time can be found by adding the probabilities of the two events:

P(Under 18) + P(Part-time) - P(Under 18 and Part-time)

To find the probabilities, add up the counts in the corresponding cells and divide by the total population:

P(Under 18) = (25+167+381)/ (25+167+381+277+176+186+443+71+26+543+175+174+534+163+291) = 0.330

P(Part-time) = (167+176+71+175+163)/ (25+167+381+277+176+186+443+71+26+543+175+174+534+163+291) = 0.452

P(Under 18 and Part-time) = 167 / (25+167+381+277+176+186+443+71+26+543+175+174+534+163+291) = 0.043

Therefore,

P(Under 18 or Part-time) = 0.330 + 0.452 - 0.043 = 0.739

The probability that the person is under 18 or employed part-time is 0.739 or approximately 0.74.

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Answer:

I am to lazy for that right now:>

The expression that is equivalent to 4⁴·4⁻⁹ is found to be 4⁻⁵. Hence option D is correct.

When multiplying exponential expressions with the same base, you add their exponents.

So, 4⁴⋅4⁻⁹ can be written as:

4⁴⁻⁹ = 4⁻⁵

Now, we know that a negative exponent means taking the reciprocal of the base raised to the positive exponent. Therefore,

4⁻⁵ = 1/4⁵

So, the expression 4⁴⋅4⁻⁹ is equivalent to the fraction 1 over 4 to the power 5. Therefore, the answer is 4⁻⁵.

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Complete question - Which expression is equivalent to 4⁴·4⁻⁹?

A. 4^13

B. 4^5

C. 4^-13

D. 4^-5

Answer:

Step-by-step explanation:

D, the vertical shift, also called the sinusoidal axis, or the average value, can be calculated by averaging the y-value of the high point and the y-value of the low point: D = (6 + 2) / 2 = 4.

A, the amplitude, will be the difference of the high and low point y-values divided by 2: (6 - 2) / 2 = 2. We should also think of A as how far away the high and low points are from the average value, D.

Next, we calculate B, the parameter controlling the length of the period by using the formula: B = 2π / period. We are told the 1st high tide is at 4 am, while the 1st low tide is at 10 am. These are 6 hrs apart, which means the highs are 12 hrs apart. Thus, B = 2π / 12 = π/6.

Lastly, an unshifted cosine function will begin at a peak, when x = 0. This cosine function has a peak when time = 4, meaning it is shifted right by 4 from a normal cosine curve. So C = - 4.

Putting all together, we get the following:

x: time elapsed since midnight (in hrs)

y: depth of water (in ft)

y = 2cos(π/6(x - 4)) + 4.

If you wanted to give the answer in the form your teacher requested, distribute the B-value across (x - 4), though the form above is more commonly used.

To locate the discontinuities of the function y = ln(tan^2x), we need to find the values of x where the function is not continuous.

First, let's consider the domain of the natural logarithm, ln(x). It is defined only for positive values of x, so tan^2x must be greater than 0 for the function to be defined.

Next, let's consider the domain of tan(x). Tan(x) is undefined when its denominator, cos(x), is equal to 0. This occurs at x = (2n + 1)π/2, where n is an integer.

Since we have tan^2x, the square of tan(x) will always be non-negative. However, we need it to be positive (greater than 0) for ln(tan^2x) to be defined. Tan^2x will be equal to 0 when tan(x) is 0, which occurs at x = nπ, where n is an integer.

Thus, the discontinuities of the function y = ln(tan^2x) occur at two different sets of x values:

1. x = (2n + 1)π/2, where n is an integer, due to the undefined nature of tan(x).
2. x = nπ, where n is an integer, due to tan^2x being 0, which is not in the domain of ln(x).

There are infinitely many discontinuities because of the variable n.

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Answer:

1

Step-by-step explanation:

PEMDAS, parentheses, exponents, multiplication/division, addition/subtraction

Make sure to to the problem in the parentheses first.

6/2(3)

Multiply 2x3 first because it is in parentheses

6/6

=1

The minimum sample size required to estimate the population mean with 95% confidence and a margin of error of 1.5, given a population standard deviation of 10.75, is approximately 190 (option d).

To determine the minimum sample size (n) required to estimate a population mean with 95% confidence, given a desired margin of error (E) of 1.5 and a known population standard deviation (σ) of 10.75, we can use the formula:
n = (Z * σ / [tex]E)^2[/tex]
In this formula, Z is the Z-score associated with the desired confidence level. For a 95% confidence level, the Z-score is 1.96 (based on a standard normal distribution table).
Now, we can plug in the given values and solve for n:
n = [tex](1.96 * 10.75 / 1.5)^2[/tex]
n = [tex](20.67 / 1.5)^2[/tex]
n = [tex]13.78^2[/tex]
n ≈ 189.76
Since we require a whole number for the sample size, we round up to the nearest whole number, which is 190. This value is not among the given options, but it is closest to option d (n = 198). Therefore, the best answer among the given options is d (n = 198).

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The total land area of Edgardo's property is 36,400 square meters.

The area is a measure of the amount of two-dimensional space that a flat surface or shape occupies. It is a fundamental concept in geometry and is expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Edgardo's original rectangular lot has an area of:

140 m x 120 m = 16,800 m²

The square lot he purchased has an area of:

140 m x 140 m = 19,600 m²

To find the total land area of Edgardo's property, we add the areas of the two lots:

16,800 m² + 19,600 m² = 36,400 m²

Therefore, the property owned by Edgardo has a total land size of 36,400 square meters.

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Answer:

1729.

Step-by-step explanation:

Hope this helped!

The mean number of children per household in the community is 2.4. The correct answer is a.

This is because Tabitha surveyed 20 families in the community, and the mean number of children per household for those families was 2.4. As long as the sample was random and representative of the community, the mean of the sample can be used as an estimate of the mean of the population. Option b is incorrect because sample size is not too small. Option c is not necessarily true since we do not know the sampling method used. Option d may or may not be true depending on the sampling method used.

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground and found a mean of 2.4 children per household. The statement that must be true is:
c. The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
This is because Tabitha's sampling method only includes families at a playground, which likely leads to a higher mean number of children, as families with more children are more likely to be found at a playground.

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