Celiac disease is a digestive disease that damages the small intestine and affects the absorption of food. People who have this disease cannot tolerate gluten, which is a protein found in many grain products such as wheat, barley, and rye. In recent years, the incidence of diagnosed cases of this disease has risen dramatically. The following data has been collected on the incidence of celiac disease since 1950. Years Since 1950 0 8 16 24 32 40 48 52 56 60 Diagnosed Cases of 10 11 14 13 11 9 12 18 31 Celiac x 1000 a. Create a scatter plot of this data. Answer: b. What regression model would best fit this model? Answer: c. Find an appropriate equation for the curve of best fit. Answer: d. Using your model, how many cases of celiac disease may be diagnosed in 2020?

American jurists (fill in the names) defined law as predictions of how a court will decide specific legal questions, based on a functional perspective.

American jurists Oliver Wendell Holmes Jr. and Benjamin Cardozo are known for their functionalist approach to defining law. They viewed law not merely as a set of abstract principles or rules, but as a prediction of how courts will decide specific legal questions in practice. According to their perspective, the law should be seen as a dynamic and evolving system that adapts to societal changes and reflects the judgments and decisions of the judiciary. By emphasizing the functional aspect of law, Holmes and Cardozo recognized the importance of considering how legal principles are actually applied and interpreted in real-world scenarios. Their approach acknowledges that the interpretation and application of law by judges can vary and evolve over time, depending on factors such as legal precedent, social context, and the specific facts of the cases before them.

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Within-groups design compares the same subjects across time. In this design, participants are measured or observed on multiple occasions, such as before and after an intervention or at different time points.

The purpose of the within-groups design is to examine changes within individuals over time, allowing researchers to assess the impact of an intervention or the natural progression of a phenomenon within the same group of subjects.

By comparing the same subjects across time, within-groups designs help to control for individual differences and increase the internal validity of the study.

This design allows researchers to evaluate the effectiveness of an intervention by assessing changes within individuals and determining if those changes are statistically significant.

It also allows for a more precise assessment of the impact of an intervention or the stability of a phenomenon over time.

Within-groups designs are commonly used in fields such as psychology, education, and medicine to study changes in behavior, cognition, or health outcomes.

They provide valuable insights into individual responses to interventions or the natural course of development or disease progression within a specific group of subjects.

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The number that is not equal to the others is d.

a. 0.84% is equal to 0.0084 in decimal form.

b. (0.21)(0.04) is equal to 0.0084.

c. 8.4 * \(10^-^2\) is equal to 0.084. This is the same as 8.4 divided by 100, which is 0.084.

d. This is the number that is not equal to the others. We don't have the value of d.

e. 21/25 * \(10^-^2\) is equal to 0.0084. When we divide 21 by 25 and multiply the result by \(10^-^2\), we get 0.0084.

To summarize, all of the given numbers (a, b, c, and e) are equal to 0.0084 except for d, which doesn't have a specified value. Therefore, d is the number that is not equal to the others.

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A rectangle and another rectangle can occasionally be mapped onto one another using solely stiff transformations and dilations.

By altering the initial shape, shapes can be mapped to other comparable shapes.

The following needs to be accurate for a shape to change.

The respective side lengths of the rectangles must have an equivalent ratio in order for one rectangle to be transferred to another.

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Building linear equations for f and g, it is found that the y-intercept of (f - g)(x) is of y = 8.

------------

A linear function has the following format:

\(y = mx + b\)

In which:

\(m = \frac{14 - 20}{-4 - (-6)} = -\frac{6}{2} = -3\)

Then

\(f(x) = -3x + b\)

Point (-6, 20) means that when \(x = -6, y = 20\), and this is used to find b.

\(20 = -3(-6) + b\)

\(18 + b = 20\)

\(b = 2\)

Thus

\(f(x) = -3x + 2\)

\(m = \frac{-26 - (-36)}{-4 - (-6)} = \frac{10}{2} = 5\)

Then

\(g(x) = 5x + b\)

Applying point (-6, -36):

\(-36 = 5(-6) + b\)

\(b = -6\)

Then

\(g(x) = 5x - 6\)

The subtraction (f - g)(x) is:

\((f - g)(x) = f(x) - g(x) = -3x + 2 - 5x + 6 = -8x + 8\)

Thus the y-intercept is y = 8.

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Answer:

1/4

Step-by-step explanation:

The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:

D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.

The mean of the sampling distribution of p is of:

0.388.

The standard deviation of the sampling distribution of p is of:

0.0184.

The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:

As long as these two conditions are respected:

The values of the parameters in this context are given as follows:

N = 30000, n = 700, p = 0.388.

Hence the conditions are:

Then the shape is approximately normal and option D is correct.

The mean of the distribution is of:

\(\mu = p = 0.388\)

The standard error of the distribution is of:

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184\)

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Answer:

A≈19.31

Step-by-step explanation:

Formula to find area of Octagon: A=2(1+√2)a^2

Divide 16/8 since there are 8 sides.

Answer:

19.31

Step-by-step explanation:

Formula:

\(A=2(1+\sqrt{x} 2)a^2\)

Hope this helps :)

Pls Brainliest...

Answer: 499

Step-by-step explanation: You have to add up how many sweets Adam ate, this is the equation:

4+156+1+338

So, if you are wanting to use your calculator, you can, because adding them up will give you 499.

So, your answer is:

Adam has 499 sweets.

Hope this helped!

Answer:

Step-by-step explanation:

Based on ur graph, in a class of 90 students (20 rock, 40 hip hop, and 30 country...added = 90) , 30 chose country....30/90 reduces to 1/3.....so 1/3 chose country.

In a class of 450 students......1/3 * 450 = 450/3 = 150 chose country

Answer:

The total percentages do not equal 100%, they equal 102%. If all friends answered, his total should equal 100%

Step-by-step explanation:

0.42 is 42%, 22% is 22%, and 2/5 is 0.4 which is 40%. Together that is 102%. If all friends answered, his total should equal 100%

Answer:

HUH?

Step-by-step explanation:

(-1/2 2).

A is your answer...

I HOPE IT WILL HELP YOU A LOT.

I hope your day goes great.

In x axis y become minus .

In y axis x become minus .

Your answer i s

A' (1 ,-2 )

B' (3,-5)

C' (2,-1 )

Friend: Hey! Have you heard about the upcoming Sports Day/Week in our school?

You: Yes, I'm really excited about it! Do you know when and where it's going to take place?

Friend: Absolutely! It's scheduled to be held next month on the 15th and 16th of July, and the venue will be the school's sports field.

You: That's great! I'm looking forward to seeing all the events. Speaking of events, do you know what types of sports activities or competitions will be organized?

Friend: Definitely! There will be a variety of events, including track and field races such as sprints, relays, long jump, and shot put.

They are also planning team sports like basketball, football, and volleyball.

You: Awesome! I'm planning to participate in the 100-meter race and maybe even the football match. Are all students allowed to participate?

Friend: Yes, all students from different grades and age groups can participate in various events according to their interests and abilities.

You: That's inclusive and fair. I hope there will be prize distribution for the winners.

Friend: Absolutely! Trophies and certificates will be awarded to the winners and runners-up in each event, and there will be an overall prize for the best-performing house/team.

You: It sounds like a fantastic Sports Day/Week! I can't wait to cheer for our classmates and enjoy the competitive spirit.

Friend: Same here! Let's make sure to gather our friends and show our support during the event. It's going to be a memorable time for all of us.

You: Definitely! I'll mark the dates on my calendar and encourage everyone to participate. It's going to be a fun-filled sports extravaganza!

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Mu X is a statistical concept used to measure the difference between two means.

It is calculated by subtracting the mean of one group from the mean of another group. Mu X is often used to compare the means of two or more groups, or to compare the means of two subgroups within a group. It can also be used to measure the relative size of a group's mean compared to the grand mean or the size of a group's mean compared to the mean of another group. Mu X is a useful tool for distinguishing between true and false differences between two means. It is also useful for understanding the relative importance of different factors in a study. Mu X is sometimes referred to as the difference in means or the mean difference, and it is an important concept in inferential statistics.

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Answer:

The quotient is 4x+5  and  the remainder is -13

Step-by-step explanation:

Using synthetic division

-5        4      25   12

Bringing down the 4 and multiplying

-5        4      25   12

        ↓       -20 -25

    ----------------------

         4        5    -13

The quotient is 4x+5  and  the remainder is -13

Answer:

  4x   +5    \(\frac{-13}{x+5}\)

Step-by-step explanation:

          .           4x   +5    \(\frac{-13}{x+5}\)

x + 5 | 4x^2 + 25x + 12

        - 4x^2 + 20x

                         5x + 12

                         5x + 25

                               -13

The equation of best fit is y = (-22/5)x + 10.

What is an equation of a line?

The equation of a line is given by:

y = mx + c where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The following coordinates are given:

Pick two coordinates.

(0, 10) and (25, -100)

The equation of best fit.

y = mx + c

Now,

m = (-100 - 10) / (25 - 0)

m = -110 / 25

m = -22/5

Now,

(0, 10) = (x, y)

10 = (-22/5) x 0 + c

c = 10

Now,

y = mx + c

y = (-22/5)x + 10

Thus,

Using the coordinates the equation of best fit is y = (-22/5)x + 10.

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Answer:

162 Cans more to reach goal of 550 cans.

Step-by-step explanation:

See attached image for the calculations

The statistic that indicates how much scores differ from each other is Standard deviation.

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

To calculate the standard deviation, you must first calculate the mean of the data set. This is done by adding up all the values in the data set and dividing by the number of values. Once you have the mean, you must subtract it from each value in the data set and square the result.

Then, you must add up all of the squared values, divide by the total number of values, and take the square root of that number. The result is the standard deviation.

Standard deviation is important because it can be used to compare the data to its mean and can help determine the amount of risk associated with a particular data set. Standard deviation is a measure of how spread out a data set is from its mean or average. It is used to measure the amount of variability or dispersion for a given data set.

Thus, The statistic that indicates how much scores differ from each other is Standard deviation.

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Answer: C

Step-by-step explanation:

The standard deviation measures the amount of variation or dispersion of a set of scores from the mean. Therefore, the correct answer is C.

The values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

The limit is a concept in mathematics that describes the behavior of a function near a particular value, called the limit point. The limit of a function gives the value that the function approaches as the input (variable) approaches the limit point.

For f(x) to be continuous everywhere, the function must have the same value and the same limit as x approaches 2 from the left and the right. In other words, f(2-) = f(2+) and the limit of f(x) as x approaches 2 from the left and the right must be equal.

Let's start by finding f(2-), which is the value of f(x) as x approaches 2 from the left. In this case, f(x) = (x2 - 4)/(x - 2) for x < 2, so as x approaches 2 from the left, f(x) approaches (2^2 - 4)/(2 - 2) = 0.

Next, let's find f(2+), which is the value of f(x) as x approaches 2 from the right. In this case, f(x) = ax^2 - bx + 3 for 2 <= x < 3, so as x approaches 2 from the right, f(x) approaches a(2^2) - b(2) + 3 = 4a - 2b + 3.

Since f(x) must be continuous at x = 2, we need to have f(2-) = f(2+), so we can set f(2-) = f(2+) and solve for a and b:

0 = 4a - 2b + 3

2b = 4a - 3

b = 2a - 3/2

Now that we have an expression for b in terms of a, we can substitute b = 2a - 3/2 into the expression for f(x) for x >= 3 to find the value of a that makes f(x) continuous everywhere:

f(x) = 2x - a + b for x >= 3

f(x) = 2x - a + (2a - 3/2) for x >= 3

f(x) = 2x + 3/2 - a for x >= 3

Since f(x) must be continuous at x = 2, we need to have f(2+) = f(2+), so we can set f(2+) = f(2+) and solve for a:

4a - 2b + 3 = 2x + 3/2 - a for x >= 3

4a - 2(2a - 3/2) + 3 = 2x + 3/2 - a

4a - 4a + 3 + 3/2 = 2x + 3/2 - a

3/2 = 2x + 3/2 - a

a = 2x

So, the values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

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Using Percentage formula , The change in the price of a jar of peanut butter is 15.02%.

Percentage : It is defined as a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.

First of we need to calculate difference between initial price and final price to

get the change in price.

Initial Price of jar of peanut butter = $ 5.99

Final price of jar of peanut butter = $ 6.89

Change in price of a jar of peanut butter = final price of jar of peanuts butter - initial price of jar of peanuts butter

= $ 6.89 - $ 5.99 = $ 0.9.

Percent change in price = ((Change in Price)/(initial price))× 100

percent change = (0.9/5.99)× 100 = 15.02

Hence, 15.02% is the change in price of a jar of peanuts butter.

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The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer: 4 inches by 6 inches or 8 inches by 3 inches.

Step-by-step explanation:

The area of a rectangle is A = W*L

where L is the width and L is the lenght.

Now, the original rectangle has a measure of 8 in by 6 in.

if 8in is the lenght and 6 in is the width.

We want to divide only one of those measures in equal parts, such that when we take the product of the end results is equal to 24 in.

If we divide the lenght by half (so both parts will have the same width as this did not change), we now have that the lenght is 8in/2 = 4in and the width is 6in.

Now the area is 4in*6in = 24in, which is the area that we where looking for.

We also could cut the width in half, and get the dimensions 8 inches by 3 inches.

Answer:A coordinate system is a two-dimensional number line

Step-by-step explanation:

A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes. An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x,y

The difference between an ordered pair and coordinates will be;

''Coordinates are used in geometry, and when there are two coordinates, they are ordered pairs when both component are of the same type.''

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

There are an ordered pair and coordinates.

Now,

The difference between an ordered pair and coordinates will be;

''Coordinates are used in geometry, and when there are two coordinates, they are ordered pairs when both component are of the same type.''

And, An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of

(a, b) and a coordinate system is a two-dimensional number line.

Thus, The difference between an ordered pair and coordinates will be;

''Coordinates are used in geometry, and when there are two coordinates, they are ordered pairs when both component are of the same type.''

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The basis for the null space of the checkerboard matrix A is {[-1, 0, 1, 0], [0, -1, 0, 1]}, where t and s are arbitrary constants.

8.1 The 4x4 checkerboard matrix is:

A = [[1, 0, 1, 0],

    [0, 1, 0, 1],

    [1, 0, 1, 0],

    [0, 1, 0, 1]]

8.2 To find the basis for the null space of the matrix A, we need to find the vectors x such that Ax = 0, where 0 represents the zero vector. In other words, we are looking for vectors that satisfy the equation Ax = 0.

To solve this, we can set up the equation Ax = 0 and find the solutions by performing row reduction on the augmented matrix [A | 0].

[A | 0] = [[1, 0, 1, 0 | 0],

          [0, 1, 0, 1 | 0],

          [1, 0, 1, 0 | 0],

          [0, 1, 0, 1 | 0]]

Performing row operations, we can obtain the row-reduced echelon form:

[RREF | 0] = [[1, 0, 1, 0 | 0],

             [0, 1, 0, 1 | 0],

             [0, 0, 0, 0 | 0],

             [0, 0, 0, 0 | 0]]

From this, we can see that the third and fourth rows are zero rows. The pivot variables are x1 and x2, while x3 and x4 are free variables. Therefore, the basis for the null space consists of vectors of the form:

x = t * [-1, 0, 1, 0] + s * [0, -1, 0, 1], where t and s are arbitrary constants.

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L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Answer: -6 and 5

Step-by-step explanation:

-6 and 5

x+y = -1

xy = -30

x=-1-y

y(-1-y)=-30

-y^2-y=-30

-y^2-y+30=0

(y-5)(5+6)

y=5,-6

Whenever a set X is a subset of set Y, we say the Y is a superset of X and we write, Y ⊇ AX.

Symbol ⊇ is used to denote ‘is a super set of’

Answer:

x=-2 using quadratic formula but factoring it would be -4(x+2)

Step-by-step explanation:

\(\bold{Heya}\) ~

Your answer will be is :

\(\sf{=~-4(x~+~2)}\)

\(\sf{-4x-8}\)

\(\sf{Rewrite~-8~as~4}\) · \(\sf{2}\)

\(\sf{=~4x~-~4~4}\) · \(\sf{2}\)

\(\sf{Factor~out~common~term~-4}\)

\(\sf{=~-4(x~+~2)}\)

Hope It Helps !

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Be safe ~

And, also Happy The New Year !

\(\underline{Answer~:}\)

\(\bold{Dollinxa}\) ~