ow that we have defined hypotheses and a test statistic, we are ready to conduct a hypothesis test. we'll start by defining a function to simulate the test statistic under the null hypothesis, and then use that function 1000 times to understand the distribution under the null hypothesis. question 4: write a function to simulate the test statistic under the null hypothesis. the simulate framingham null function should simulate the null hypothesis once (not 1000 times) and return the value of the test statistic for that simulated sample.

The total number of possible combinations will be 10.

Given that:

Total photo, n = 5

Selection of photo, r = 3

The total number of possible combinations will be calculated as,

⁵C₃ = 5! / [(5 - 3)! - 3!]

⁵C₃ = (5 x 4 x 3 x 2!) / (2! x 3 x 2 x 1)

⁵C₃ = 10

The total number of possible combinations will be 10.

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I'll show you how to do the first one so that you can do the rest yourself

Answer:

7, 10, 13, 19, 24

Step-by-step explanation:

First, re-write the numbers in numerical order;

7  8  10  10  13  16  19  23  24

(If there's a double number, add it twice)

Then, find the following values easily

The Minimum is the lowest value, 7

The Median is the middle value, 13

The Maximum is the highest value, 24

Here's where it gets tricky...You split the first half (7-13) and the second half (13-24). You then find the median of both halves to find Q1 and Q3

Simply follow those steps to find the other solutions

The length of the major arc DFE is given as follows:

L = 5.11π

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius in this problem is of 4 ft, hence the length of the whole circumference is of:

C = 8π.

The entire circumference is of 360º, with a minor arc of 130º, hence the length of the major arc is given as follows:

360 - 130 = 230º.

Meaning that the length of the major arc is given as follows:

L = 230/360 x 8π

L = 5.11π

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Making L dependent variable = [tex]\sqrt{\frac{R^{2}T^{2}-E^{2} }{T^{2}W^{2} } }[/tex]

Dependent Variable is a variable that represents a quantity that changes based on other quantities being manipulated in an experiment.

How to determine this

When T = E/√[tex]R^{2}[/tex]-[tex]W^{2}[/tex][tex]L^{2}[/tex]

To make L a dependent variable

By Cross multiplying

T√[tex]R^{2}[/tex]-[tex]W^{2} L^{2}[/tex] = E

Divides through by T

T√[tex]R^{2}[/tex]-[tex]W^{2} L^{2}[/tex] /T = E/T

√[tex]R^{2}[/tex]-[tex]W^{2} L^{2}[/tex] = E/T

By squaring both sides

[tex]R^{2}[/tex]-[tex]W^{2} L^{2}[/tex] = [tex]E^{2} /T^{2}[/tex]

Cross multiply

[tex]T^{2} R^{2}[/tex] - [tex]T^{2} W^{2} L^{2}[/tex] = [tex]E^{2}[/tex]

Collect like terms

[tex]T^{2} R^{2} - E^{2} = T^{2} W^{2} L^{2}[/tex]

By dividing through by [tex]T^{2} W^{2}[/tex] to make L a dependent variable

[tex]T^{2} R^{2} -E^{2}[/tex]/[tex]T^{2} W^{2}[/tex] = [tex]L^{2}[/tex]

By squaring both sides

L = [tex]\sqrt \frac{T^{2}R^{2} -E^{2} }{T^{2} W^{2} }[/tex]

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Considering the definition of an equation and the way to solve it, Amanda wants to rent a boat and spend less than $92, she can rent the boar for less than 12 hours.

An equation is the equality existing between two algebraic expressions connected through the equals sign.

The members of an equation are each of the expressions that appear on both sides of the equal sign. The terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it and the equality must be true. To solve an equation, keep in mind:

Being "t" the numbers of hours Amanda could rent the boat, and knowing that:

the equation in this case is:

8t - 4< 92

Solving:

8t <92 +4

8t <96

t <96 ÷ 8

t <12

Finally, Amanda can rent the boar for less than 12 hours.

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The area to the left of z=1.07 is approximately 0.8577 (rounded to four decimal place. To find the area under the standard normal curve to the left of z = 1.07 using a TI-84 calculator.

Follow these steps:

1. Press the "2nd" button, then press "Vars" to access the "DISTR" menu.
2. Scroll down to "normalcdf(" and press "Enter".
3. Enter -99999 (or -E99) as the lower limit, since we want to find the area to the left of z = 1.07, which is very close to negative infinity.
4. Enter 1.07 as the upper limit, since we want to find the area to the left of this value.
5. Enter 0 as the mean, since we're working with the standard normal distribution.
6. Enter 1 as the standard deviation, since we're working with the standard normal distribution.
7. Press "Enter" to calculate the area.

The answer should be approximately 0.8577 when rounded to four decimal places.

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The missing length in the triangle is 56 cm.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Let us form a proportional equation to find the value of missing length

p/21 = 24/9

Apply cross multiplication

9p=21×24

9p=504

Divide both sides by 9

p=56

Hence, the missing length in the triangle is 56 cm.

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The regular nonagon has an area of 471.69.

In this problem we find the representation of a regular nonagon, that is, a regular polygon of nine sides of equal length. The area of a regular polygon is determined by following formulas:

a = s / [2 · tan (π / n)]

A = (n · s · a) / 2

Where:

If we know that a = 12 and n = 9, then the area of the polygon:

s = 2 · a · tan (π / n)

s = 24 · tan (π / 9)

s = 8.735

A = (9 · 8.735 · 12) / 2

A = 471.69

The area of the regular nonagon is equal to 471.69.

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The equation when solved for b gives b = y - 1/5x

The subject of formula in an equation is defined as the variable or element that is allowed to stand on its own on one end of the equality sign.

It is also described as the variable that is solved or sort for in an equation.

Examples of subject of formula are;

y = mx + b, here the variable 'y' is the subject of formula.

x = 1 + y, here the variable 'x' is the subject of formula.

From the information given, we have that;

Given the formula;

y= 1/5x+b

To make 'b' the subject, move the other variable to the other side

b = y - 1/5x

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The two numbers are -5 and 7

Algebraic expressions are defined as those expressions that are identified with the presence of variables, terms, coefficients, constants and factors.

These expressions are also identified with arithmetic operations, such as;

From the information given, we have;

Let the numbers be x and y

This is expressed as;

xy = -35

x + y = -2

Make 'x' the subject from 2

x = -2 - y

Substitute the values

(2-y)(y) = -35

2y - y² = -35

-y² + 2y + 35

-y² + 7y - 5y + 35

-y(y + 7)- 5(y + 7)

-y - 5 = 0

y = -5

y = 7

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Answer: A, B, C

Step-by-step explanation:

Congruence of any shape by definition means that the two shapes have the same shape and size. This applies even if the shapes are in different orientations, or if the two shapes are reflected versions of each other, as long as the points are named the same respective to their different orientations. If the two triangles are congruent, their corresponding sides and angles are also congruent, because they are the same shapes, they have the same corresponding sides and angles. If any of these are not true, this means that the shapes are not congruent.

The graph that will most represent this information will display rate of decrease in the number of road accidents per year. The Option D is correct.

This would be rate of decrease in the number of road accidents per year that will display impact of the new rule on reducing the number of road accidents over time.

By graphing this measure, it would allow for a visual representation of the trend in the number of accidents which could help evaluate the success of the new rule. It may need to be combined with other measures like number of tickets issued for violating the rule or the number of vehicles checked for compliance etc.

Full question "The state highway patrol wants to evaluate a new rule for vehicles that was put into place to prevent road accidents across all large cities. Which measure would be displayed in a graph most appropriately representing this information? A. the rate of decrease in the number of vehicles purchased per year B. the total number of road accidents per year C. the total number of vehicles per person D. the rate of decrease in the number of road accidents per year"

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Answer:students develop good habits when they are in elementary school.

Step-by-step explanation:

iready, I got it right away

The ordered pair that is a solution to the system is (A) (−1, −1)

From the question, we have the the system of linear equations to be

x + 3y = −4

y = −3x − 4

By substitution, we have

x + 3(−3x − 4) = −4

Open the brackets

This gives

x - 9x - 12 = -4

Evaluate the like terms

-8x = 8

So, we have

x = -1

Recall that

y = −3x − 4

So, we have

y = −3(-1) − 4

Evaluate

y = -1

Hence, the solution is (A) (−1, −1)

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Answer:

Answer and Explanation: The side length of the equilateral triangle is 8√3 . Therefore, the area of the equilateral triangle is 48√3 square units 48 3 square units .

Step-by-step explanation:

Mark brainliest, pls

The number of different-appearing ways to arrange three identical marbles in the holes shown, with no three marbles in three adjacent holes, is:  20 - 6 = 14.

To answer your question, we need to first determine how many ways there are to place three identical marbles into the six holes shown. This can be calculated using the combination formula:

C(6,3) = 6! / (3! * (6-3)!) = 20

So there are 20 different ways to place three identical marbles into the holes.

However, we need to exclude any arrangements where three marbles are in three adjacent holes. To do this, we can count the number of arrangements where this occurs and subtract from the total.

There are three ways this can happen: the marbles can be in holes 1, 2, and 3; or in holes 2, 3, and 4; or in holes 3, 4, and 5.

In each case, we can treat the three adjacent holes as a single "super hole" and place the marbles in the remaining three holes. This can be done in 2 ways, since the marbles are identical and can be placed in any order.

So the number of arrangements with three marbles in three adjacent holes is 3 x 2 = 6.

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The area of each of the circles are:

Area of Circle A = 64π

Area of Circle B = 121π

Area of circle C = 225π

Area of circle D = 169π

The formula for the area of a circle is:

A = πr²

where:

A is Area

r is radius

Thus:

Area of Circle A = π * 8²

Area of Circle A = 64π

Radius of circle B is 3 mm greater than that of circle A. Thus:

Radius of circle B = 3 + 8 = 11 mm

Area of Circle B = π * 11²

Area of Circle B = 121π

The radius of Circle C is 4 mm greater than the radius of Circle B.

Radius of circle C = 4 + 11 = 15 mm

Area of circle C = π * 15²

Area of circle C = 225π

The radius of Circle D is 2 mm less than the radius of Circle C. Thus:

Radius of circle D = 15 - 2 = 13 mm

Area of circle D = π * 13²

Area of circle D = 169π

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The reason scientists use the parameter "b" instead of "c" when obtaining the general solution to the logistic differential equation is because the logistic equation typically contains two important parameters: the growth rate "r" and the carrying capacity "K."

The parameter "b" is introduced as a constant in the logistic equation to ensure that the solution remains mathematically correct and easy to interpret.

The logistic differential equation is written as:

[tex]dP/dt = r * P * (1 - P/K)[/tex]

Here, "P" represents the population size, "r" is the growth rate, "t" is time, and "K" is the carrying capacity. To obtain the general solution to this equation, the parameter "b" is used as follows:

b = K - P

This parameter "b" helps express the relationship between the current population "P" and the carrying capacity "K," allowing for a clear understanding of the population dynamics in relation to the environment's resources. By using "b" instead of "c" in this context, it creates consistency and ease of interpretation in the mathematical solutions to the logistic differential equation.

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The sign of m^13 ⋅ n^5 depends on the signs of the variables m and n.

If both m and n are positive, then m^13 is positive, n^5 is positive, and their product is positive.

If both m and n are negative, then m^13 is negative (an odd power of a negative number is negative), n^5 is negative (an odd power of a negative number is negative), and their product is positive (a negative multiplied by a negative is positive).

If one of m or n is negative and the other is positive, then m^13 is negative (an odd power of a negative number is negative), n^5 is positive (an odd power of a positive number is positive), and their product is negative (a negative multiplied by a positive is negative).

Therefore, we cannot determine the sign of m^13 ⋅ n^5 without additional information about the signs of m and n.

The correct statement regarding the law of conservation of energy is given as follows:

C. Energy is neither destroyed nor created during energy transformations.

The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another.

One example is that the kinetic energy may be transformed to potential energy in a system, but the total energy of the system will remain constant.

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The equivalent expression is 20(r + 3t).

The factor 20r+60t can be factored further by finding the greatest common factor of the terms 20r and 60t, which is 20:

20r + 60t = 20(1r + 3t)

Therefore, an equivalent expression for 20r+60t is 20(1r+3t).

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Answer:

{1/2}{1/2}=1/4

Step-by-step explanation:

The probability of rolling a 1 then a prime number when rolling a fair number cube twice is 1/12.

To find the probability of rolling a 1 then a prime number when rolling a fair number cube twice, we need to determine the possible outcomes. When rolling a number cube, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. The probability of rolling a 1 is 1/6. Now, when rolling the cube a second time, the possible outcomes remain the same. However, only the numbers 2, 3, 5, have prime values. So the probability of rolling a prime number is 3/6.

To find the probability of both events happening together, we multiply the probabilities. Therefore, the probability of rolling a 1 then a prime number is (1/6) * (3/6) = 1/12. This means that there is a 1 in 12 chance of rolling a 1 and then rolling a prime number when rolling a fair number cube twice.

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Under normal circumstances and assuming no interfering factors. This suggests a unidirectional relationship between the variables, with a being the independent variable and b being the dependent variable.

If a and b are highly correlated, and b changes when you manipulate a but a does not change when you manipulate b, then it is most likely that b is the dependent variable and a is the independent variable. if a and b are highly correlated and b changes when you manipulate a, but a does not change when you manipulate b, the most likely scenario is that a has a causal influence on b, but b does not have a causal influence on a.

This suggests that changes in a are causing changes in b, and not the other way around. However, it is important to note that this conclusion assumes normal circumstances and no interfering factors, which may impact the relationship between a and b.

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To multiply the polynomials 2x+y and 5x-y+3 using a table, we can follow these steps:

   Write the two polynomials side by side, with the terms arranged in descending order of degree:

     2x + y

   x | 5x - y + 3

   Multiply each term in the first polynomial by each term in the second polynomial, and write the products in the table:

     2x   y

   x | 5x² -xy 3x

   -y y² -3y

     5x² -xy +3x

     -y² +3y

   Simplify the products by combining like terms:

     5x² -xy +3x -y² +3y

Therefore, the product of the polynomials 2x+y and 5x-y+3 is 5x² -xy +3x -y² +3y.

Based on the information provided and the mention of a "national polling scenario," the most appropriate statistical procedure to use would be a two-sample z-test for proportions.

Based on the given research question in the national polling scenario, the appropriate statistical procedure that should be used is regression analysis. Regression analysis helps to examine the relationship between two variables, which in this case would be the dependent variable (the poll results) and the independent variable (the factors that may influence the poll results). This would allow researchers to determine which variables are significantly related to the poll results and to predict the future trends of the poll results. Therefore, the answer is "a t-test for the slope of a regression line".
This test compares the proportions between two independent groups, which is commonly used in polling and survey analysis to determine if there is a significant difference between the groups.

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The slope of a line parallel to the line whose equation is 2x - 5y = 30 is equal to 2/5.

In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

Slope, m₁ = Slope, m₂

Based on the information provided about this line, we have the following equation in standard form;

2x - 5y = 30.

By making y the subject of formula, we have:

5y = 2x - 30

y = 2x/5 - 6

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The difference in the amount of interest is $847.36. The Option B is correct.

For the 3-year loan at 6.00% interest. We need to first find the amount with the formula A = P(1 + r/n)^(nt).

Plugging in the values, we get:

A = $5,000(1 + 0.06/1)^(1*3)

A = $5,000(1.191016)

A = $5,955.08

The total interest paid is:

I = A - P

I = $5,955.08 - $5,000

I = $955.08

For the 4-year loan at 8.00% interest:

A = $5,000(1 + 0.08/1)^(1*4)

A = $5,000(1.36048896)

A = $6,802.44

The total interest paid is:

I = A - P

I = $6,802.44 - $5,000

I = $1,802.44

Difference in amount of interest for these two loans is:

= $1,802.44 - $955.08

= $847.36

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Answer: To find the reconciled balance, you need to adjust the checkbook balance for any items that have not yet cleared the bank and add or subtract any other items that have not been recorded in the checkbook.

Here are the steps to reconcile the checkbook balance:

1. Add any deposits in transit to the checkbook balance.

68,599.10 + 2,800.10 = 71,399.20

2. Subtract any outstanding checks from the adjusted checkbook balance.

71,399.20 - 24,741.10 = 46,658.10

3. Add or subtract any other items that have not been recorded in the checkbook.

46,658.10 + 6,000.00 - 50.00 = 52,608.10

Therefore, the reconciled balance is $52,608.10.

Step-by-step explanation:

For simulated data from a right-skewed population, as the sample size increases:
a. The mean will be closer to the true population mean. When the sample size is 1, the mean will be very susceptible to outliers and might not represent the population well.
b. The standard deviation will generally decrease with larger sample sizes.

a. When the sample size is 1, the mean of the simulated data will be the same as the mean of the original population, since there is only one data point in the sample. Therefore, the mean will be the same as the population mean.

b. When the sample size is 10, the mean of the simulated data will still be slightly skewed to the right, but it will be closer to the population mean compared to the sample size of 1. This is because the larger sample size allows for a more representative sample of the population.

c. When the sample size is 30, the mean of the simulated data will be even closer to the population mean, and the skewness will be even less noticeable. This is because with a larger sample size, the random variation in the sample means tends to decrease, resulting in more stable estimates of the population mean.

f. When the sample size is 1, the standard deviation of the simulated data will be equal to the standard deviation of the original population, since there is only one data point in the sample.

g. When the sample size is 10, the standard deviation of the simulated data will be smaller compared to the sample size of 1, due to the larger sample size providing more representative data.

h. When the sample size is 30, the standard deviation of the simulated data will be even smaller compared to the sample size of 10, due to the larger sample size providing even more representative data.

For simulated data from a right-skewed population, as the sample size increases:

a. The mean will be closer to the true population mean. When the sample size is 1, the mean will be very susceptible to outliers and might not represent the population well. As the sample size increases to 10 and 30, the sample mean will more closely approximate the true population mean.

b. The standard deviation will generally decrease with larger sample sizes. This is because larger samples better represent the population, so the variation within the sample tends to decrease. When the sample size is 1, the standard deviation may be quite large. As the sample size increases to 10 and 30, the standard deviation will likely decrease.

Keep in mind that these are general trends and each simulation might produce slightly different outcomes. The overall pattern, however, should remain consistent.

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To find the domain of the function f(x,y) = ln(9 - x^2 - 9y^2), we need to identify any values of x and y that would make the argument of the natural logarithm negative or equal to zero.

Since the natural logarithm of a non-positive number is undefined, we need to ensure that 9 - x^2 - 9y^2 > 0.

Rearranging this inequality, we get x^2 + 9y^2 < 9, which is the equation of an ellipse centered at the origin with semi-axes of length 3 and 1 in the x and y directions, respectively.

Therefore, the domain of the function is the interior of this ellipse, which we can sketch as follows:

(please imagine an ellipse centered at the origin with semi-axes of length 3 and 1 in the x and y directions, respectively, shaded in)
To find and sketch the domain of the function f(x, y) = ln(9 - x² - 9y²), we need to determine the values of x and y for which the function is defined.

Step 1: Identify the restrictions of the function.
For the natural logarithm function, ln(x), it is defined for x > 0. Therefore, the inside of the logarithm, 9 - x² - 9y², must be greater than 0.

Step 2: Solve for the domain.
9 - x² - 9y² > 0

Rearrange the inequality:
x² + 9y² < 9

Divide by 9:
x²/9 + y² < 1

This inequality represents the interior of an ellipse with semi-major axis a = 3 and semi-minor axis b = 1.

Step 3: Sketch the domain.
To sketch the domain, draw an ellipse centered at the origin (0, 0) with horizontal axis length 6 (from -3 to 3) and vertical axis length 2 (from -1 to 1). The domain includes all points inside the ellipse but does not include the boundary (the ellipse itself).

So, the domain of the function f(x, y) = ln(9 - x² - 9y²) is the interior of the ellipse with equation x²/9 + y² < 1.

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