A doctor wanted to study the effect of four different treatments on mental health. A group of 100 adults experiencing depression volunteered for the study. The doctor randomly assigned one-fourth of them to each of four groups. Group 1 followed a specific exercise plan, group 2 followed a specific diet plan, group 3 followed an exercise and diet plan, and group 4 did not follow any plan. After 4 weeks, the doctor contacted each participant and asked them if they felt any better. The results are displayed in the table.



The doctor would like to know if these data provide convincing evidence that the distribution of responses differs across the treatment groups in the population of all patients like these. What is the appropriate inference procedure?

chi-square test for goodness of fit because the data come from one random sample
chi-square test for homogeneity because the data come from independent treatment groups
chi-square test for association/independence because the data come from one random sample
chi-square test for association/independence because the data come from independent treatment groups

Answer:

333.333...

Step-by-step explanation:

50kg = 50,000 g

so, 50,000/150 = 333.333...

Answer:

x = 2 or x = -2

Step-by-step explanation:

5x² - 15 = 5​

⇌

5x² = 15 + 5

⇌

5x² = 20

⇌

x² = 20/5 = 4

⇌

x² = 2²

⇌

x² - 2² = 0

⇌

(x - 2)(x + 2) = 0

⇌   we use the zero product property

x - 2 = 0 or x + 2 = 0

⇌

x = 2 or x = -2

The probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let A, B, and C represent the events that components A, B, and C work, respectively. Then, the probability that a component works is given as P(A) = P(B) = P(C) = p.

The probability that the entire system works is the probability that either A and B work and C does not, or A and C work and B does not. This can be expressed as:

P(system works) = P((A and B and C') or (A and B' and C))

Using the distributive property of probability, we can rewrite this as:

P(system works) = P(A and B and C') + P(A and B' and C)

Since the components work independently, we can apply the product rule of probability to each term:

P(system works) = P(A) * P(B) * (1 - P(C)) + P(A) * (1 - P(B)) * P(C)

Substituting P(A) = P(B) = P(C) = p, we get:

P(system works) = p² * (1 - p) + p * (1 - p)²

Simplifying this expression, we get:

P(system works) = p * (2p - 3p² + 1)

Substituting the given value of p, we get:

P(system works) = 0.8 * (20.8 - 30.8² + 1) ≈ 0.52

Therefore, the probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

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Answer:

³√6

Step-by-step

³√6

Answer:

she never brought her cost up when they got another cup cake it should

x  y

1  3.50

2  7

3  10.50

4  14

i ant really graph them

Step-by-step explanation:

The domain of f/g(x) is given by B. {x ∈ ℝ | x ≠ -2, -3, 3}The correct option is B. {x ∈ ℝ | x ≠ -2, -3, 3}, which represents the real numbers excluding -2, -3, and 3.

To find the domain of f/g(x), we need to consider the values of x for which the denominator g(x) is non-zero. Division by zero is undefined in mathematics, so we exclude any values of x that make the denominator zero.

The denominator g(x) = x^3 + 2x^2 - 9x - 18 can be factored as follows:

g(x) = (x - 3)(x + 2)(x + 3)

To determine the values of x that make the denominator zero, we set each factor equal to zero and solve for x:

x - 3 = 0 => x = 3

x + 2 = 0 => x = -2

x + 3 = 0 => x = -3

Therefore, the values x = -2, x = -3, and x = 3 make the denominator zero.

To find the domain of f/g(x), we exclude these values from the domain of f(x). Hence, the domain of f/g(x) is given by:

{x ∈ ℝ | x ≠ -2, -3, 3}

Therefore, the correct option is B. {x ∈ ℝ | x ≠ -2, -3, 3}, which represents the real numbers excluding -2, -3, and 3.

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So, y = (1/2)(x + 8) is the equation of the linear function.

To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

This is the equation of the linear function.

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y - y1 = m(x - x1)

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

Answer:

Step-by-step explanation:

-7

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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For a sample of born babies' weight in a large hospital, probability that the mean weight of the sample babies would differ from the population mean by greater than 43 grams is equals to 0.5390.

We have a sample of born babies' weight in a large hospital.

Mean of weight = 4090 grams

Variance of weight = 31300

Standard deviations = 560

Sample size or included babies = 64

standard error = \(\frac{560}{\sqrt(64)}\) = 70

We have to determine probability that the mean weight of the sample babies would differ from the population mean by greater than 43 grams. Let the population mean would be \(\mu\). Now, the probability, \(P ( \bar X - \mu > 43 ) \). Using Z-score formula, \(Z = \frac{X -\mu}{\frac{\sigma}{\sqrt(n)}} \)

Substitute all known values then, z= ± 43/70, z= ± 0.614

P(z<-0.614 or z>0.614) = P(z<-0.614)+ P(z>0.614)

=2 × 0.2695

=0.5390

Hence, required value is 0.5390.

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Answer:

financial Institution

Step-by-step explanation:

ysbdndkkdkdks

Answer:

x                   y

-2                   1

-1                   -2

0                   -5

1                    -8

Step-by-step explanation:

The elements of a treaty includes, satisfaction of both sides, a proper set of rules and obligation towards the actions.

By the definition are Treaty is a diplomatic agreement between two countries on global issues.

According to the constitution of The United States of America the president of the state can make the treaty with other countries with the support of the two third of the sinters present in the house as per the section 2 of Article II.

An agreement can only be called a Treaty if the agreement is agreed upon by both the sides and the Treaty has a proper set of rules define for both the countries and both the countries give their consent towards their actions which comes under the treaty.

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Laticia completed the exam first

As

Laticia completed first

The required method typically employed is C) Experimental design.

The probability value is utilized as a measure of the merit of the parameter selection, and the parameter set with the highest likelihood is the best option given the available data.

Experimental design is typically employed when a researcher needs to estimate the likelihood of a certain outcome.

In an experimental design, the researcher manipulates one or more independent variables to determine the effect on a dependent variable, which is the outcome being studied.

The researcher can then use this information to make an estimate of the likelihood of the outcome under different conditions. This is the most commonly used method in the natural and social sciences to determine cause-and-effect relationships and make predictions about future outcomes.

Thus, Suitable option is C)Experimental design.

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The smallest fraction among A = 4/11, B = 5/7, and C = -2/3 is C = -2/3.

To determine the smallest fraction, we compare the fractions by finding a common denominator and evaluating the numerators.

In this case, the fractions have different denominators.

First, we can convert all fractions to have a common denominator of 21 by multiplying the denominators accordingly. A = (4/11) * (21/21) = 84/231, B = (5/7) * (3/3) = 15/21, and C remains as -2/3.

Now, comparing the numerators, we find that A has the smallest numerator of 84, followed by B with 15, and C with -2. Therefore, the smallest fraction among the given options is C = -2/3.

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Given :-

To Find :-

Solution :-

Cost of the boat is 7200 and tax on it is 504. We can find the tax% as ,

→ Tax% = Tax/Cost *100

→ Tax % = 504/7200*100% = 7%

Hence the tax on boat costing 8000 will be ,

→ Tax = 7% of 8000

→ Tax = 7/100*8000 = 560

Hence the tax on the boat costing 8000 is 560.

Answer: 182.9

Step-by-step explanation: if the next digit after the tenths place is 5 or higher, you round it up to the next number.

a) There is not enough evidence to conclude that cars get significantly better fuel economy with premium gasoline.

In order to test the belief that premium gasoline provides better fuel economy, a study was conducted using 10 cars from a company fleet. Each car was randomly assigned either regular or premium gasoline, and the mileage for each tankful was recorded. The data was analyzed to determine if there is a significant difference in fuel economy between the two types of gasoline.

To evaluate this, a paired t-test can be used since the same cars were tested with both types of gasoline. The null hypothesis would be that there is no difference in fuel economy between regular and premium gasoline, while the alternative hypothesis would be that there is a significant difference.

The results of the study would be analyzed using the appropriate statistical test, such as a paired t-test, to determine the p-value. If the p-value is less than the chosen significance level (e.g., 0.05), then there would be evidence to reject the null hypothesis and conclude that there is a significant difference in fuel economy.

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The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.

given

A polygon's internal angle measurements are equal to (n-2) * 180, where n is the number of sides.

Therefore, 4 * 180 = 720 is the total of the internal angles of this 6-sided object.

The remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201 .

The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

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A type of plot shows the median and the data spread about the median is called a boxplot.

A box-and-whiskers plot, also referred to as a boxplot, presents a summarized information such as the median, quartiles, minimum, and maximum values.

It indicates the measure of skewness of a distribution data or how the values are spread out.

It is made up of a box, which lies between the first and third quartiles with the whiskers as line segments extending from the ends of the box to the smallest and largest values that are not outliers.

Attached photo is a figure that illustrates a boxplot.

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Answer: 3

Step-by-step explanation: try to solve for a by itself by multiplying it on both sides that give you 3 = 1*a. that simply just means that a is equal to 3, so you substitute three to the a variable that will give 3/3 that's equal to 1.

Answer:

4 gal / day

Step-by-step explanation:

12 gallons / 3 days

12/3 = 4

4 gallons / 1 day

i think its 7

Hope this helps

-scav

Answer: 14%

Step-by-step explanation:

Answer:

well you need to have your friends personal email then login to you email and press new message once your logged in put in you friends email and you are all set

Step-by-step explanation:

The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.

The commutative property of addition states that the order in which numbers are added does not affect the result. In this equation, both sides of the equation involve adding numbers, and the numbers being added are the same: 6, 4, and x.

The equation shows that regardless of whether we add 4 and x first or x and 4 first within the parentheses, the final result will be the same. The commutative property of addition allows us to freely rearrange the order of the terms being added without changing the overall sum.

Therefore, The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.

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Answer:

D

Step-by-step explanation:

The ends of the graph is approaching -∞, which means it is decreasing

These inequalities ensure that Bob buys at least three albums, and no more than 35 individual songs, while staying within his budget of $60.

The system of inequalities that represents the situation is:

x + 10y ≤ 60 (total cost cannot exceed $60)

x ≤ 35 (no more than 35 individual songs)

y ≥ 3 (at least three albums)

Here, x represents the number of individual songs and y represents the number of albums.

The first inequality, x + 10y ≤ 60, ensures that the total cost of Bob's purchases does not exceed $60.

The second inequality, x ≤ 35, ensures that Bob does not buy more than 35 individual songs.

The third inequality, y ≥ 3, ensures that Bob buys at least three albums.

Together, these inequalities ensure that Bob buys at least three albums, and no more than 35 individual songs, while staying within his budget of $60.

Note that this system of inequalities assumes that Bob only buys whole albums, and not individual songs from albums. If he buys individual songs from albums, the system of inequalities would be more complex.

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The solution of the initial value problem remains finite as t approaches infinity if the eigenvalues of the system are negative or have negative real parts.

The eigenvalues of a system determine the stability of the solution. Negative eigenvalues indicate that the solution will approach a steady state as time goes on. Positive eigenvalues indicate that the solution will diverge, or grow without bound, as time goes on. If the real parts of the eigenvalues are negative, the solution will approach a steady state, but if the real parts of the eigenvalues are positive, the solution will diverge as t approaches infinity.

In order to check for finite solution for a given initial value problem, one needs to evaluate the eigenvalues of the system, and check their real parts. If they are negative, the solution will remain finite, otherwise the solution will diverge as t approaches infinity.

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Answer:

6) C

8) A

Step-by-step explanation:

6) A=(base*height)/2 is the formula for a triangle.

8) yes

6. The formula that can be used to find the total amount of paint she will need if the entire space is painted is C) A= (8)(9)/2.

The area of the triangle is given as,

Area = (1/2)*(base)*(height)

Now it is given that,

Base of space = 8 feet

Height of space = 9 feet

Thus,

Area of the space = (1/2)*(base of space)*(height of space)

⇒ Area of the space = (1/2)*(8)*(9)

or, Area of the space =  (8)(9)/2

⇒ Area of the space = 36 square feet

Thus, the formula that can be used to find the total amount of paint she will need if the entire space is painted is C) A= (8)(9)/2.

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8. The properties use to solve the equation 4x + 2 = 18 is C) The inverse property of addition and then the inverse property of multiplication.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

4x + 2 = 18

To solve the equation first using inverse property of addition

4x = 18 - 2

4x = 16

Now using inverse property of multiplication we get,

4x/4 = 16/4

x = 4

this is the required value of x.

Thus, the properties use to solve the equation 4x + 2 = 18 is C) The inverse property of addition and then the inverse property of multiplication.

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