The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine if health and happiness level are related. Use the a= 0.05 level of significance to test the claim. Health Excellent Good Fair Poor Very Happy 271 261 82 20 Pretty Happy 247 567 231 53 Not Too Happy 33 103 92 36 *Source: General Social Survey 1) Determine the null and alternative hypotheses. Select the correct pair. OH,: Health and happiness have the same distribution Ha Health and happiness follow a different distribution OH,: Health and happiness are independent H: Health and happiness are dependent 2) Determine the test Statistic. Round your answer to two decimals. 3) Determine the p-value. Round your answer to four decimals. p-value=

Answer:

-13

Step-by-step explanation:

Answer:

t = -13

Step-by-step explanation:

2.6 = -0.2t         Equation

2.6 / -0.2 . = -0.2t/-0.2          Divide -0.2 on both sides

t = - 13       Simplify

The graph of the solutions on the number line represents all the values to the left of -2, with an open circle at -2 to indicate that it is not included in the solution.

To graph the solutions of the inequality c < -2 on a number line, we start by plotting a point at -2.

Since the inequality is strict (c < -2), the point at -2 should be an open circle to indicate that it is not included in the solution.

Then, we draw an arrow to the left to represent all the numbers that are less than -2.

On the number line, any number to the left of -2 would satisfy the inequality.

This means that all values from negative infinity up to but not including -2 are solutions to the inequality c < -2.

In interval notation, we can represent this solution set as (-∞, -2).

In words, the solution to the inequality c < -2 can be described as all real numbers less than -2.

This includes any number that is to the left of -2 on the number line, such as -3, -4, -5, and so on.

However, it does not include -2 itself.

Therefore, the graph of the solutions on the number line represents all the values to the left of -2, with an open circle at -2 to indicate that it is not included in the solution.

The interval notation (-∞, -2) summarizes the range of solutions to the inequality.

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The coefficient of variation is usually expressed as a percentage and is not the same as the variance or the square of the standard deviation. It is, however, related to the standard deviation and variance.

The coefficient of variation (CV) is a statistical measure that represents the relative variability or dispersion of a dataset. It is calculated by dividing the standard deviation of the dataset by its mean, and is typically expressed as a percentage.

The CV is used to compare the variability between datasets with different means. A higher CV indicates a higher relative variability, while a lower CV indicates a lower relative variability.

The CV is not the same as the variance or the square of the standard deviation, which are absolute measures of variability. It provides a standardized measure that allows for comparison across datasets.

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Answer:

20 - 20 =0 me trying to get the points lol edit : oh well I couldn't get the points:( lol

Answer:

-13.5v-21.6

Step-by-step explanation:

Distribute Rule: a(b+c) = ab+ac

2.7(-5v-8)

= 2.7*(-5v) + 2.7(-8)

= -13.5v-21.6

Answer:

4) ?

there is something wrong. none of the solution options fit to the original equation. you must have missed something.

maybe it is 7y=... to begin with. or there is a y/7 in the solution options.

Step-by-step explanation:

this is the result, if your original equation is correct :

y = 7x - 7z - 9

y + 7z = 7x - 9

y + 7z + 9 = 7x

x = y/7 + z + 9/7

we always have to apply an operation to both sides of the "=" sign to keep the overall value and validity of the expression unchanged.

so, as mentioned, either we started with 7y, or the answer has to contain y/7.

or something else is wrong here entirely.

Answer:

3) x = (y + 7z + 9)/7

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ y = 7x - 7z - 9

Then the value of x will be,

→ y = 7x - 7z - 9

→ y - 7x = -7z - 9

→ -7x = -y - 7z - 9

→ 7x = y + 7z + 9

→ x = (y + 7z + 9)/7

→ x = (y/7) + (7z/7) + (9/7)

→ x = (y/7) + z + (9/7)

Hence, option (3) is correct.

Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.

For example, if X = 2 and y = -7, then the equation becomes:

2 + (-7) = -5

-5 = -5

Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.

Step-by-step explanation:

The correct value of the given trigonometric function is (B) -½.

So, cos(11π/21)cos(π/7)-sin(11π/21)sin(π/7):

Now, substitute (A = 11π/21) and (B = π/7) in the identity as follows:

Therefore, the correct value of the given trigonometric function is (B) -½.

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In this study, the researchers are assessing the risk factors of diabetes among a small rural community of men. The sample size for the study is 12. One of the risk factors being assessed is overweight.

To understand the prevalence of overweight among all men, we need to look at the proportion of overweight individuals in parts (a) and (b) of the study.
Since the study is conducted on a small rural community of men, the proportion of overweight in part (a) and part (b) represents the prevalence of overweight among all men.
However, since you have not mentioned what parts (a) and (b) refer to in the study, I cannot provide a more detailed answer. Please provide more information or clarify the question if you would like a more specific response.

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Answer:

a

Step-by-step explanation:

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

Equation

1.95+1.6m ≤ 22

If solved

m ≤ 12.53

Step-by-step explanation:

SO we know the initial fee is 1.95

and for every mile driven, its $1.6

And we know that Shelly can spend less then or exactly the price of 22.

We know that m is miles driven

So we can make an equation

1.95+1.6m ≤ 22

1.95 can’t change since initial fee

1.6*m becuase its 1.6 for every mile driven and since “m” miles were driven, we multiply that by 1.6

Now it can’t go over 22 but it could be less than 22.

So this equation makes sense

If we solve it, it would be about  m ≤ 12.53 miles

Answer:

48 items

Step-by-step explanation:

6 packs of cupcakes with 4 in them, is 24 items. and 3 packs of candy with 8 pieces in them is also 24. 24+24=48. so (6×4)+(8×3)=48

Answer:

48

Step-by-step explanation:

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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The approximate measure of angle z in triangle XYZ is 78.5°.

To determine the measure of angle z, we can use the properties of triangles. One way to find this angle is by using the slope formula to calculate the slopes of the lines formed by the given points. Then, we can use the inverse tangent function to find the angle.

First, let's calculate the slopes of the lines XY and YZ using the formula:

m = (y2 - y1) / (x2 - x1)

For line XY:

mXY = (1 - (-1)) / (-2 - (-1)) = 2 / (-1) = -2

For line YZ:

mYZ = (2 - 1) / (1 - (-2)) = 1 / 3

Next, we can calculate the angle using the inverse tangent function:

angle z = arctan(mYZ - mXY) = arctan(1/3 - (-2)) = arctan(1/3 + 2) = arctan(7/3)

Using a calculator, we find that arctan(7/3) is approximately 78.5°.

Therefore, the approximate measure of angle z in triangle XYZ is 78.5°.

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Answer:

54

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

Angles in a triangle adds up to 180 degrees

so 105 + (6x+20) + (7x-10) = 180

simplify

115+13x=180

subtract 115 to each side

13x=65

divide by 13

x=5

check work

105 + (6(5) + 20) + (7(5) -10)

105 + (30 +20) +(35 - 10)

105 + 50 + 25 = 180

Answer:

None of these

Step-by-step explanation:

The lines aren't parallels so none of these property's can be applied

Answer:

It increases 3cm each minute.

Step-by-step explanation:

The function \($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

\($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

\(\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}\) f(x)

\(\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\\)

= 1 - 1

= 0

\(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\\)

= ln 1

= 0

Therefore  \(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0\).

Hence f(x) is continuous on (-∞, ∞)

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The area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

To find the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ), we need to determine the limits of integration for θ.

First, let's find the values of θ where the circle and the vertical line intersect:

r = 4cos(θ)

sec(θ) = 4cos(θ)

To simplify the equation, let's convert sec(θ) to its reciprocal form:

1/cos(θ) = 4cos(θ)

Multiplying both sides by cos(θ), we get:

1 = 4\(cos^2\)(θ)

Rearranging the equation, we have:

4\(cos^2\)(θ) - 1 = 0

Using the identity \(cos^2\)(θ) - \(sin^2\)(θ) = 1, we can rewrite the equation as:

\(cos^2\)(θ) - \(sin^2\)(θ) = 1/4

Applying the double-angle formula for cosine, we get:

cos(2θ) = 1/4

Taking the inverse cosine of both sides, we have:

2θ = ± \(\cos^{-1}\left(\frac{1}{4}\right)\)

Solving for θ, we get two values:

θ = ± (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Since we are interested in the region to the right of the vertical line, we'll consider the positive value of θ:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Now, we can find the area by evaluating the integral:

A = ∫[θ, π/2] 1/2 (\(r^2\)) dθ

Substituting the equations for r, we have:

\(A = \int_{\theta}^{\frac{\pi}{2}} \frac{1}{2} (4\cos^2(\theta)) \, d\theta\)

Simplifying further:

\(A = \int_{\theta}^{\frac{\pi}{2}} 8\cos^2(\theta) \, d\theta\)

Using the double-angle formula for cosine, we have:

A = ∫[θ, π/2] 4(1 + cos(2θ)) dθ

Integrating term by term, we get:

A = [4θ + 2sin(2θ)] evaluated from θ to π/2

Now, Substituting the limits of integration, we get:

A = [4(π/2) + 2sin(2(π/2))] - [4θ + 2sin(2θ)] evaluated from θ to π/2

Simplifying:

A = 2π + 2sin(π) - (4θ + 2sin(2θ))

Since sin(π) = 0, we can simplify further:

A = 2π - (4θ + 2sin(2θ))

Now, we need to substitute the value of θ, which we found earlier:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Substituting this value, we have:

A = 2π - (4(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(2(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)))

Simplifying:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(\(\cos^{-1}\left(\frac{1}{4}\right)\)))

Since cos(\(\cos^{-1}\left(x\right)\)) = x, we have:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(1 - (1/4)^2)))

Simplifying further:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(15/16)))

A = 2π - 2 \(\cos^{-1}\left(\frac{1}{4}\right)\) - √15

So, the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

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The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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Answer:

24x+18

Step-by-step explanation:

distributive property

6(4x+3)

24x+18

Hope this helps :)

The probability of selecting a score greater than X = 50 from a normal population with μ = 60 and σ = 20 is approximately 0.3085, which corresponds to answer choice b).

To determine the probability of selecting a score greater than X = 50 from a normal population with μ = 60 and σ = 20, we need to calculate the z-score and find the corresponding probability using the standard normal distribution table or a statistical calculator.

The z-score can be calculated using the formula:

z = (X - μ) / σ

Substituting the values:

z = (50 - 60) / 20

z = -0.5

Using the standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of -0.5.

The correct answer is b) 0.3085, as it corresponds to the probability of selecting a score greater than X = 50 from the given normal distribution.

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Answer:

it is the 3rd one.

Step-by-step explanation:

brainliest?

Answer:

a

Step-by-step explanation:

i think its a or d

32+(2x-12)=90

32+2x-12=90

2x+20=90

2x=70

x=35

Answer:

A x=35

Step-by-step explanation:

(2x-12)+32=90

2x-12=90-32

2x-12=58

2x=12+58

2x=70

x=70/2=35

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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The number of observations in a complete data set with 10 elements and 5 variables is a. data.

In the context of data analysis, a complete data set refers to a collection of data that includes all the required observations or cases. In this scenario, the data set consists of 10 elements, which represent the individual observations or data points. Each element is associated with 5 variables, which are the characteristics or attributes being measured or observed.

Therefore, the number of observations in this data set is determined by the number of elements, which is 10. The term "observations" refers to the individual data points or cases in the data set. The other options, such as "variables" and "elements," do not accurately represent the count of observations in this context.

Hence, the correct answer is a. data, indicating that the number of observations in the complete data set is determined by the number of elements, which in this case is 10

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The value of the chi-square test statistic is χ2 = 2.87, and the P-value is between 0.025 and 0.05.

Let's assume the observed counts are as follows:

Erica: 75

Jen: 5

Heather: 12

Tonya: 8

Now, we can calculate the chi-square test statistic:

χ2 = Σ((O - E)^2 / E)

where O is the observed count and E is the expected count for each category.

Calculating the chi-square test statistic:

χ2 = ((75 - 70)^2 / 70) + ((5 - 10)^2 / 10) + ((12 - 10)^2 / 10) + ((8 - 10)^2 / 10)

= 1.07 + 1 + 0.4 + 0.4

≈ 2.87

Referring to the chi-square distribution table, the P-value for a chi-square test statistic of 2.87 and 3 degrees of freedom is approximately between 0.025 and 0.05.

Therefore, the value of the chi-square test statistic is χ2 = 2.87, and the P-value is between 0.025 and 0.05.

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Answer:

Angle zxy = 55 degrees, x = 12

Step-by-step explanation:

Since the angle WXY is labeled as a right angle from the square in the angle, and angle WXZ is 35 degrees, we know that angle ZXY must be 55 degrees, because 55+35 = 90. Then to solve for x, we use the measure of angle ZXY to construct the equation 4x+7 = 55. subtract 7 from both sides to get 4x = 48, then divide both sides by 4 to arrive at the answer of x = 12.