you do not need to know the rules of probability and the laws of expected value and variance to derive the sampling distribution true false

There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.

We have,

a college board sample estimated the standard deviation of 2016 SAT scores to be 194 points.

We used the formula,

= x ± Z (α/2) × σ/√n

Here, α = 1 - 98% = 0.02

Z (α/2) = Z (0.02/2) = 2.326

Hence, We get;

Z (α/2) × σ/√n = 50

2.326 x 194 /√n = 50

√n = 2.326 x 194 / 50

n = 82

Therefore, There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.

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The polygons are similar with similarity ratio of 1.5, respectively

To check if the polygons are similar, we divide corresponding sides and check if the ratios are equal

So, we have

Rectangle

So, the similarity ratio is 1.5

Triangle

So, the similarity ratio is 1.5

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The two given figures are neither similar nor congruent

Congruent figures are geometric figures that have the same shape and size. That is, if you can transform one figure into another figure by a sequence of translations , rotations , and/or reflections , then the two figures are congruent.

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Therefore, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, it is clear that both shapes are not congruent because the lengths are not congruent.

Similarly, the ratio of the two corresponding sides are not the same. Thus:

We can say neither of both are similar or congruent.

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The length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.

A central angle is an angle with its vertex at the center of a circle and its rays extending out to the edge of the circle, creating an intercepted arc.

The length of the arc intercepted by a central angle of 1.1 radians can be found by using the formula:

Length of arc = (central angle / 2π) × 2πr

where r is the radius of the circle.

Plugging in the given values, we get:

Length of arc = (1.1 / 2π) × 2π(6)

Length of arc = 1.1 × 6

Length of arc = 6.6 cm

Therefore, the length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.

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The amount of money he will have in the account is $922.46

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

Principal, P = 594

Rate , r = 4.5%

TIme = 10 years

Teh amount of money is calcilated s

Amount =  P * (1 + r)^t

substitute the known values in the above equation, so, we have the following representation

Amount = 594 * (1 + 4.5%)^10

Evaluate

Amount = 922.46

Hence, the amount is $922.46

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Based on the information, we can infer that the relationship between the duration of a film and the number of actors is positive, that is, the more actors, the more time. On the other hand, the relationship between hours of practice and errors is inverse.

Based on the information, we can infer that the relationship between these factors would be the following:

Case A

For the length of a movie and the number of actors in the movie, I would expect to see a positive association. Typically, movies with larger ensemble casts will require a longer runtime to properly develop each character and storyline.

Case B.

For the number of hours a musician spends practicing and the number of mistakes the musician makes in a performance, I would expect to see a negative association. The more time a musician spends practicing, the better prepared they will be for their performance.

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The integer 6 represents the mean change in points per minute.

We have,

Video played for 13 min.

points loose= 78

So, the mean change in points per minute is

=  ( total loss of points / total minutes of playing the game )

= 78/ 13

= 6 points per minute.

Thus, the mean change in points per minute is 6.

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The data collected from the survey was then used to inform decision-making and planning in relation to college programs and services.

In February and March 2007, an online survey was conducted to collect data from college parents. The survey was sent via email to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. The goal was to invite parents to participate in the survey and provide their feedback.

Out of the 41,000 parents who were invited, 1727 completed the online survey. The survey was designed to protect the anonymity of the participants, meaning their identities were not disclosed, and their responses were kept confidential.

However, the survey did not allow more than one response from an individual IP address. This means that if multiple responses were received from the same IP address, only the first response would be counted.

Overall, this online survey was conducted to gather information from college parents, and the results were based on the responses received from the 1727 parents who completed the survey. The data collected from the survey was then used to inform decision-making and planning in relation to college programs and services.

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The two positive integers that satisfy the conditions and minimize the sum of their squares are 4 and 4.

We can use the method of Lagrange multipliers to solve this problem. Let x and y be the two positive integers we want to find, then we want to minimize the function [tex]f(x,y) = x^2 + y^2[/tex] subject to the constraint g(x,y) = x + y - 16 = 0.

The Lagrange function is L(x,y,λ) = f(x,y) - λg(x,y) =[tex]x^2 + y^2[/tex] - λ(x + y - 16).

Taking partial derivatives of L with respect to x, y, and λ, we get:

dL/dx = 2x - λ = 0

dL/dy = 2y - λ = 0

dL/dλ = x + y - 16 = 0

Solving for λ in the first two equations, we get λ = 2x = 2y. Substituting this into the third equation, we get 4x = 16, or x = 4. Then y = 4 as well, since λ = 2x = 2y.

Therefore, the two positive integers that satisfy the conditions and minimize the sum of their squares are 4 and 4.

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True. Seasonality refers to a regular, repeating pattern in the data that takes longer than one year to complete. It can occur in various forms such as monthly, quarterly, or even weekly patterns.

These patterns are usually associated with external factors such as weather, holidays, or other events that influence consumer behavior. By identifying seasonality in the data, businesses can use it to predict future trends and adjust their strategies accordingly. This information can be valuable in a range of industries such as retail, tourism, and agriculture.

Overall, understanding the repeating patterns in data is essential for making informed decisions and staying ahead of the competition.

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To solve the problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

where A is the final amount, P is the principal (initial deposit), r is the interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time (in years).

In this case, P = $8,100, r = 0.05, n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:

A = $8,100(1 + 0.05/1)^(1*4)

A = $8,100(1.05)^4

A = $10,563.23

Therefore, Priscilla will earn $10,563.23 - $8,100 = $2,463.23 in interest over the next 4 years.

a. The coefficient of determination, r squared, is 0.669. Interpretation: The value of r squared indicates that 66.9% of the variation in box office gross can be explained by the variation in online trailer views.

b. The standard error of the estimate is 16.74.

c. The regression model is somewhat useful for predicting opening weekend box office gross because the coefficient of determination is closer to 1 than it is to 0.

d. Other variables that might explain the variation in opening weekend box office gross include: the amount spent on advertising, the timing of the release of the movie, and the type of movie.
a. To find the coefficient of determination (r^2), you will need to perform a linear regression analysis on the given data. Since we don't have the actual data values, we cannot calculate r^2 directly. However, once you calculate r^2 using the data, you can interpret its meaning as follows:

The value of r^2 indicates that ___% of the variation in box office gross can be explained by the variation in online trailer views. (Fill in the blank with the calculated r^2 value, rounded to one decimal place.)

b. Similarly, without the actual data values, we cannot calculate the standard error of the estimate (Syx). Once you have the data, you can calculate Syx using regression analysis.

c. The usefulness of the regression model depends on the calculated r^2 value. Choose the most appropriate answer based on the calculated r^2:

A. It is not useful for predicting box office gross because the coefficient of determination is close to 0.
B. It is not useful for predicting box office gross because the coefficient of determination is close to 1.
C. It is very useful for predicting box office gross because the coefficient of determination is very close to 1.
D. It is somewhat useful for predicting box office gross because the coefficient of determination is closer to 1 than it is to 0.

d. Other variables that might explain the variation in opening weekend box office gross are:

A. The amount spent on advertising might explain the variation in opening weekend box office gross because viewers are probably more likely to watch a movie that has been advertised heavily.
B. The timing of the release of the movie might explain the variation in opening weekend box office gross because a movie released at the same time as multiple other major movies may get crowded out.
C. The type of movie might explain the variation in opening weekend box office gross since some genres are more heavily attended than others.

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To find the length of the curve r(t) = (5t, 3 cos t, 3 sin t), -4 ≤ t ≤ 4, we can use the formula for arc length: L = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt
Applying this formula to r(t),

we get: L = ∫_(-4)^(4) √(25 + 9sin^2t + 9cos^2t) dt Simplifying the expression under the square root, we get: L = ∫_(-4)^(4) √34 dt
Evaluating the integral, we get: L = 8√34

Therefore, the length of the curve is 8√34, To find the length of the curve √2ti + e^tj + e^-tk, 0 ≤ t ≤ 2, we can use the same formula: L = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.

Applying this formula to the given curve, we get:
L = ∫_0^(2) √(2^2 + e^(2t) + e^(-2t)) dt, Simplifying the expression under the square root, we get: L = ∫_0^(2) √(e^(2t) + 2 + e^(-2t)) dt
Making a substitution u = e^t + e^(-t),

we get: L = 1/2 ∫_2^(e^2 + e^(-2)) √(u^2 - 4) du Making another substitution v = u/2, we get:
L = ∫_√2^(√(e^2 + e^(-2))/2) √(v^2 - 1) dv
Using a trigonometric substitution v = sec θ, we get:
L = ∫_(π/4)^(π/2) sec θ dθ
Evaluating the integral, we get:
L = ln(1 + √2) + ln(√(e^2 + e^(-2)) + 1)
Therefore, the length of the curve is ln(1 + √2) + ln(√(e^2 + e^(-2)) + 1).

To reparametrize the curve r(t) = 3ti + (6 - 4t)j + (8 + 2t)k with respect to arc length measured from the point where t = 0 in the direction of increasing t, we can use the formula for arc length:
s = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.

We first find the arc length of the curve from t = 0 to some arbitrary value t: s = ∫_0^t √(9 + 16 + 4) dt
Simplifying, we get:
s = 3√29 t
Solving for t in terms of s, we get:
t = s/(3√29)
Substituting this expression into the given curve, we get:
r(s) = 3(s/(3√29))i + (6 - 4(s/(3√29)))j + (8 + 2(s/(3√29)))k
Simplifying,

we get: r(s) = si/√29 + (6 - 4s/(3√29))j + (8 + 2s/(3√29))k
Therefore, the reparametrized curve is r(s) = si/√29 + (6 - 4s/(3√29))j + (8 + 2s/(3√29))k.

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Using the Pythagorean's theorem we can see that length of the segment AB =is6.4 units

We can see that this is a right triangle, notice that we know two sides, these are

AC = 4

CB = 5

(to know that just count the number of squares between the given vertices)

Using Pythagorean's theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) we can write an equation that allows us to find the length of AB, the hypotenuse of the right triangle:

AB² = 4² + 5²

AB = √(16 + 25)

AB = 6.4 units.

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This statistics is an example of the "interference theory" in motor learning.

Interference theory suggests that when individuals learn multiple skills or movements in a random order, they perform better in retention and transfer tests compared to those who learn the same skills or movements in a blocked or constant order. The random practice group in this scenario was able to better transfer their knot-tying skills to new situations because they learned the knots in a more varied and unpredictable way, which helped them develop more adaptable and flexible motor patterns.

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The point estimate of the difference between the two population means is -51.975.

The point estimate of the difference between the two population means can be calculated by finding the difference between the sample means. From the given samples, the sample mean for the first sample is (-20 + 30 + (-223))/3 = -71, and the sample mean for the second sample is (-20.1 -24 + 5 - 40)/4 = -19.025.

It is important to note that this is only an estimate and may not perfectly represent the true difference between the two population means.

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The probability is approximately 0.9429. Rounded to four decimal places, the probability is 0.9429. Therefore, the probability that the sample mean would be less than 107.81 liters is about 0.9429 or 94.29%.

To solve this problem, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean:

standard error = standard deviation / square root of sample size
standard error = 26 / sqrt(220)
standard error ≈ 1.756

Next, we can standardize the sample mean using the formula for z-scores:

z = (sample mean - population mean) / standard error
z = (107.81 - 105) / 1.756
z ≈ 1.574

Finally, we can use a standard normal distribution table or calculator to find the probability of getting a z-score less than 1.574.

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The values of the variables x and y are 12 and 3 respectively, while the measure of angles m∠A and m∠B are 36° and 126° respectively

1). m∠A and m∠D are complementary angles so their sum is equal to 90°

3x + (4x + 6)° = 90°

7x = 90° - 6°

x = 84/7

x = 12

2). m∠A = 3(12) = 36°

3). m∠B and m∠C are on a straight line and their sum is equal to 180° {also called supplementary angles}.

18y + 42y = 180°

60y = 180°

y = 180°/60°

y = 3

4). m∠C = 42(3) = 126°

In conclusion, the values of the variables x and y are 12 and 3 respectively, while the measure of angles m∠A and m∠B are 36° and 126° respectively

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Probabilistic data refers to data that involves uncertain or random events.

it is typically analyzed using probability theory or statistical methods. Examples of probabilistic data include the outcomes of a coin toss, the probability of a person having a certain genetic trait, or the likelihood of an event occurring given certain conditions. The formula P(A) x P(B) = P(A and B) is a probability formula that applies to probability theory and statistics, which deal with random events and their likelihoods. Therefore, it is related to probabilistic data

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The given equation in standard form can be written as (x - 1)² + (y + 3)² = 5².

The given equation is as follows;

x² - 2x + y² + 6y = 15

(x² - 2x) + (y² + 6y) = 15

(x² - 2x + 1 - 1) + (y² + 6y) = 15

The first three terms inside the parentheses can be factored as a perfect square:

(x - 1)² - 1 + (y² + 6y) = 15

(x - 1)² - 1 + (y² + 6y + 9 - 9) = 15

The first three terms inside the second set of parentheses can be factored as a perfect square:

(x - 1)² - 1 + (y + 3)² - 9 = 15

Combining like terms and simplifying, we get:

(x - 1)² + (y + 3)² = 25

So, the equation in standard form is:

(x - 1)² + (y + 3)² = 5²

Therefore, the center of the circle is at (1,-3) and the radius is 5.

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Step-by-step explanation:

Answer:

306cm

Step-by-step explanation:

15x12=180  18+7=126

180+126=306

P.S i'm emo

Answer:Let's call the two numbers we are trying to find "x" and "y".

We know that the sum of these two numbers is 16, so we can write the equation:

x + y = 16

We also know that the difference between these two numbers is 27, so we can write the equation:

x - y = 27

Now we have two equations and two unknowns. We can use substitution or elimination to solve for x and y.

Using the substitution method, we can solve for y in the first equation:

y = 16 - x

Now we can substitute this expression for y into the second equation:

x - (16 - x) = 27

Simplifying this equation, we get:

2x - 16 = 27

Adding 16 to both sides, we get:

2x = 43

Dividing both sides by 2, we get:

x = 21.5

Now we can substitute this value for x into either of the original equations to solve for y:

y = 16 - x = 16 - 21.5 = -5.5

So the two numbers are 21.5 and -5.5.

Step-by-step explanation:

Based on the survey results, it can be concluded with 90% confidence that the proportion of students who prefer exercising outside over-exercising in a gym is between 0.8085 and 0.9296. This interval does not include the previously known proportion of 0.822, which suggests that there may have been a change in student preferences over time.

However, it should be noted that the sample size of 84 is relatively small and there may be some degree of sampling error present. Overall, the SRC should continue to monitor student preferences for exercising and consider offering a variety of options to accommodate different preferences.

In the Student Recreation Center, it was found that 73 out of 84 students preferred exercising outside over exercising in a gym. This gives us a sample proportion of 73/84 = 0.869. This proportion's 90% confidence interval is (0.8085, 0.9296).

Since the past data proportion of 0.822 falls within the 90% confidence interval, we can conclude that there is no significant difference between the past data and the current survey results regarding students' preferences for outdoor exercise over gym exercise.

Based on past data, the Student Recreation Center knew that the proportion of students who prefer exercising outside over-exercising in a gym was 0.822. To update their records, the SRC conducted a survey. Out of 84 students surveyed, 73 indicated that they preferred outdoor exercise over-exercising in a gym. The 90% confidence interval is ( 0.8085, 0.9296 ).

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The statement true about the rectangle and scale factor is

A scale factor of 2.5 was applied to create the enlargement

Given data ,

A rectangle with a long side of 3 and an arrow points to a larger rectangle with a long side of 7.5

Now , the long side of the original rectangle is 3 units, and the long side of the enlarged rectangle is 7.5 units.

And , the ratio of the long sides is 7.5/3 = 2.5, which indicates that the rectangle was enlarged by a factor of 2.5.

Hence , the scale factor of dilation is d = 2.5

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In the context of data patterns and variations in a time series, cyclical patterns are characterized by repeatable periods of ups and downs over short periods of time. The answer is: a. cyclical patterns.

Cyclical patterns refer to fluctuations that occur over an extended period of time, usually several years or more, and are often related to economic or business cycles. These patterns are not as predictable as seasonal patterns, as they may vary in amplitude and duration from cycle to cycle. Cyclical patterns can also be influenced by a variety of factors, including changes in consumer behavior, technological innovations, and geopolitical events.

Irregular variations, on the other hand, refer to unexpected, random fluctuations in the data that cannot be attributed to any known factors. Random variations are also unpredictable, but they are not necessarily cyclical in nature.

Seasonal patterns refer to regular, predictable fluctuations in the data that occur within a single year. These patterns are often related to seasonal changes in weather, holidays, or other seasonal factors that affect consumer behavior.

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The statements that must be true based on the histogram are as follows:

A. The range of the data set is 50 min.

C. The most common amount of exercise is 0 to 9 min.

E. The distribution is skewed right.

You can say that the distribution of a histogram is skewed right if the highest point in the distribution lies towards the left-hand side of the graph.

The graph above is an example of a distribution that is skewed right. Also, the range of the dataset is between 0 to 50 and the most common amount of exercise engaged in by the students is 0 to 9 min.

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The probability that the coin lands heads up and the cube lands on a composite number is 1/3 or approximately 0.333.

To find the probability that the coin lands heads up and the cube lands on a composite number, we need to first determine the number of outcomes in the sample space that satisfy these conditions, and then divide that by the total number of possible outcomes.

There are two possible outcomes for the coin flip: heads or tails. There are six possible outcomes for rolling the number cube: 1, 2, 3, 4, 5, or 6. To determine the number of outcomes in the sample space that satisfy the given conditions, we need to identify the composite numbers among the possible outcomes for rolling the number cube.

The composite numbers are 4, 6, and they occur two times each. Therefore, there are four outcomes that satisfy the given conditions: (heads, 4), (heads, 6), (tails, 4), and (tails, 6).

The total number of possible outcomes is the product of the number of outcomes for the coin flip and the number of outcomes for rolling the number cube, which is:

2 x 6 = 12

So the probability of the coin landing heads up and the cube landing on a composite number is:

4 / 12 = 1/3

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Answer:

To solve the quadratic equation x^2 + 9x +25 = 5 by factoring, we first rearrange the equation to get:

x^2 + 9x +20 = 0

Next, we need to find two numbers that multiply by 20 and add to 9, the coefficient of x. The two numbers are 4 and 5.

So, we can factor the quadratic as:

(x + 4)(x + 5) = 0

Setting each factor to zero and solving for x, we get:

x + 4 = 0 or x + 5 = 0

Solving for x in each equation, we get:

x = -4 or x = -5

Therefore, the solutions to the quadratic equation x^2 + 9x +25 = 5 are x = -4 and x = -5.

Yes, the function C is a piecewise function.

The domain of C is the set of non-negative integers (0, 1, 2, 3, ...),

The range of C is the set of non-negative real numbers

(0, 8, 16, 24, ..., 40),

We have,

The function C is a piecewise function.

When a passholder watches between 1 and 5 movies, the cost is $8 per movie, so the total cost C is:

C(n) = 8n

When a passholder watches more than 5 movies, but not more than 15 movies, the cost is a fixed price of $40 for the first 5 movies plus additional movies watched for free.

Therefore, the total cost C is:

C(n) = 40, for 5 < n ≤ 15

When a passholder watches more than 15 movies, the cost is undefined since the maximum number of movies allowed is 15.

The domain of C is the set of non-negative integers (0, 1, 2, 3, ...), since you cannot watch a negative or fractional number of movies.

However, since the maximum number of movies allowed is 15, the domain is restricted to integers between 0 and 15, inclusive.

The range of C is the set of non-negative real numbers (0, 8, 16, 24, ..., 40), since the cost per movie is $8 and the cost for watching between 6 and 15 movies is a fixed price of $40.

The minimum cost is 0 (if no movies are watched) and the maximum cost is 40 (if 15 or more movies are watched).

Thus,

The domain of C is the set of non-negative integers (0, 1, 2, 3, ...),

The range of C is the set of non-negative real numbers

(0, 8, 16, 24, ..., 40),

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The probability of Event 1 is 5/36 and the probability of Event 2 is 1/2.

Comparing the results of the roll of two fair die yields the probability of each of the following events:

There are 6 × 6 = 36 outcomes that could occur.

Event 1: The total exceeds eight.

There are five outcomes where the total exceeds eight.

P(Event 1)=5/36

Event 2: The sum can be divided by two.

Where the total is divisible by 2, there are 18 possible results.

The likelihood of this occurrence is:

P(Event 2) =18/36

P(Event 2) equals 1/2

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