In a particular chi-square goodness-of-fit test, there are six categories and 325 observations. Use the 0.10 significance level.
How many degrees of freedom are there?
What is the critical value of chi-square? (Round your answer to 3 decimal places.)

Answer:

18

Step-by-step explanation:

That's if the 2 equations are equal

The value of x for the given expressions will be 18.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expressions are 8x - 37 and 5x + 17. The value of x will be calculated as,

8x - 37  = 5x + 17

Arrange the like terms and solve for the value of x,

8x - 5x = 17 + 37

3x = 54

x = 18

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer: about TWO

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

8% of 30 is 2.4. So, 2.4 + 30 is 32.4.

Answer:

Step-by-step explanation:

Hey there mate :)

When a number is multiplied by a fraction equal to 1, the value of the number remains the same.

Using this, we can find the values:-

Image 2 answers :

\( \frac{4}{5} \times \frac{4}{4} = \frac{4}{5} \)

When we cancel the same 4 of LHS remaining we get as 4/5. By doing the same method, we can find the remaining answers.

\(\frac{2}{3} \times \frac{7}{7} = \frac{2}{3} \\ \\ \frac{5}{6} \times \frac{8}{8} = \frac{5}{6} \\ \\ \frac{3}{4} \times \frac{5}{5} \)

Image 1 answers :

\( \frac{2}{3} \times \frac{4}{2} = \frac{4}{3}\)

Here, cancel the common numbers in LHS and write back the remaining uncancelled numbers to get 4/3 in RHS.

Using same method,

\( \frac{3}{4} \times \frac{5}{3} = \frac{5}{4} \)

Next, Now in last two questions, we have to do a little differently. Till this much time we did by cancelling the common numbers. So, multiply the numerator and denominator.

\( \frac{1}{4} \times \frac{3}{2} \\ = > \frac{1 \times 3}{4 \times 2} \\ = > \frac{3}{8} \)

So, above question's answer is 3/8.

Likewise, using the same method, find the next question :-

\( \frac{2}{5} \times \frac{4}{3} \\ = > \frac{2 \times 4}{5 \times 3} \\ = > \frac{8}{15}\)

So, next answer is 8/15.

Hope this Helps...

\(Benjemin360 :)\)

The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.

A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.

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• Solution

To solve for x, we take the logarithm of both sides.

Applying the law of logarithm to the equation above;

Therefore, the approximate value of x is 3.562

The correct option is E.

Answer:

2340 degrees.

Step-by-step explanation:

The sum of the interior angle measures of any polygon can be calculated using the following expression (\(n\) is the number of sides the polygon has):

\(180(n-2)\)

For a 15-sided polygon, plug in 15 for n and simplify:

\(180(15-2)=180(13)\)

Multiply to solve:

\(180(13)=2340\)

For a 15-sided polygon, the sum of the interior angles must be 2340 degrees. You can go a step further and divide 2340 by 15 to figure out the individual measure of each interior angle (156 degrees).

The sum of the interior angles of a fifteen-sided polygon is 2340°.

The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given that, a fifteen-sided polygon.

Now, the sum of the interior angle measures is

(15-2)×180°

= 13×180°

= 2340°

Therefore, the sum of the interior angle measures is 2340°.

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Answer:

42

Step-by-step explanation:

3x + 12 + x = 180

4x  + 12 = 180

4x = 168

x = 42

The probability that x is greater than or equal to 1 is 0.875 or 87.5%

To find the probability that x, the number of heads in three tosses of a fair coin, is greater than or equal to 1, we can use the following steps:

1. Determine the total possible outcomes: There are 2 outcomes for each coin toss (heads or tails), so for 3 tosses, there are 2^3 = 8 possible outcomes.
2. Count the outcomes where x is greater than or equal to 1: We have 7 favorable outcomes (HHH, HHT, HTH, THH, HTT, THT, and TTH). The only outcome not included is TTT (no heads).
3. Calculate the probability: Divide the number of favorable outcomes by the total possible outcomes.

Probability(x ≥ 1) = (favorable outcomes) / (total possible outcomes) = 7 / 8 = 0.875

So, the probability that x is greater than or equal to 1 is 0.875 or 87.5%.

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The patient can consume approximately 2 cans of 12 oz Coca Cola without exceeding the advised sugar limit.

To determine the number of 12 oz cans of Coca Cola the patient can consume, we need to convert the sugar limit provided by the doctor into grams and then calculate the amount of sugar in a 12 oz can of Coca Cola.

Provided:

Sugar limit: 8.5 × 10^(-2) kg

Coca Cola sugar content: 110 g/L

Volume of a 12 oz can: 12 oz (which is approximately 355 mL)

First, let's convert the sugar limit from kilograms to grams:

Sugar limit = 8.5 × 10^(-2) kg = 8.5 × 10^(-2) kg × 1000 g/kg = 85 g

Next, we need to calculate the amount of sugar in a 12 oz can of Coca Cola:

Volume of a 12 oz can = 355 mL = 355/1000 L = 0.355 L

Amount of sugar in a 12 oz can of Coca Cola = 110 g/L × 0.355 L = 39.05 g

Now, we can determine the number of cans the patient can consume by dividing the sugar limit by the amount of sugar in a can:

Number of cans = Sugar limit / Amount of sugar in a can

Number of cans = 85 g / 39.05 g ≈ 2.18

Since the number of cans cannot be fractional, the patient should limit their consumption to 2 cans of Coca Cola.

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heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyhhhhhhhhhhhhhhhhhhhhhoooooooooooooooowwwwwwwwwwaaaaaaaaaaaaaaaaaarrrrrrrrrrrrrrrrrrrreeeeeeeeeeeeeeeeeeyyyyyyyyyyyyooooooooooouuuuuuuuuuuudddddddddoooooooiiiiiiinnnnnnng

The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

The value of the expression is 1/(9x)^2

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

(-9x)^-2

We can write the expression without negative exponents by using a fraction with a positive exponent:

(-9x)^-2 = 1/(-9x)^2

And without parentheses, this expression becomes:

1/(9x)^2

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Lurking variables, such as experience with exercise or past practice of meditation, should be approximately equal for the two groups if random assignment is used. Option D

Randomization ensures that the groups being compared are comparable in terms of any potential confounding factors or hidden variables that can affect the study's conclusion. The researchers can evenly divide these characteristics throughout the groups by randomly allocating people to the programs, which lessens the possibility of skewed outcomes.

As a result, it is possible to compare the benefits of exercise and meditation on stress reduction with more accuracy because any differences between the groups may be more reliably assigned to the intervention itself rather than to unrelated factors.

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Answer:

Erin

Step-by-step explanation:

I believe Erin is right in this case.

SOLUTION

The triangle in the picture has two sides to be equal. This means that the triangle is an isosceles triangle.

The base angles of an isosceles triangle are equal.

This implies that angle C = B = 49 degrees

So both angles B and C are 49 degrees each.

Now let's find angle A

A + B + C = 180 degrees (sum of angles in a triangle)

Then

The line bisects angle A into two equal triangles, that is angle y and the angle at the other side

This means that

Now let's find x.

Angles x, y, and B make up a triangle. This means that

Therefore, x = 90, and y = 41

Answer:

Solution for If f(x) = 2x – 6 and g(x) = x – 2x2, find each value. f(2)

The required value of each function is

f(h + 9) = 2(h + 6)

g(h + 9) = -(2h + 19)(h - 9)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Now the given functions are,

f(x) = 2x – 6

g(x) = x – 2x²

Now putting x = h + 9 in f(x) and g(x)we get,

f(h + 9) = 2(h + 9) – 6

⇒ f(h + 9) = 2h + 18 – 6

⇒ f(h + 9) = 2h + 12

⇒ f(h + 9) = 2(h + 6)

and

g(h + 9) = (h + 9) – 2(h + 9)²

⇒ g(h + 9) = h + 9 – 2(h² + 81 + 18h)

⇒ g(h + 9) = h + 9 – 2h² + 162 + 36h

⇒ g(h + 9) = -2h² + 37h + 171

⇒ g(h + 9) = -(2h + 19)(h - 9)

Thus, the required value of each function is

f(h + 9) = 2(h + 6)

g(h + 9) = -(2h + 19)(h - 9)

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Answer:

S=540

140+33+x+75+x+2x=540

173+x+75+x+2x=540

x+75+x+2x=367

x+x+2x=292

4x=292

x=73

2x=146

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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The interest earned at 1.6% for 20 years will be $960.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given that a new bank customer with ​$3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.6​%.

The interest after 20 years will be calculated as,

SI = ( P x R X T ) / 100

SI = ( 3000 x 1.6 x 20 ) / 100

SI = $960

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EXPLANATION

We can affirm that the length of the adjacent leg is 5 units and the length of the hypotenuse is 8 units.

As given, the length of the third side is 6.245 units.

Now, computing sin A give us the following expression:

The solution is 1249/1600

Answer:

it looks like it would be 69% like the one below it

Step-by-step explanation:

To randomly select a sample of students from the population enrolled in the Probability and Statistics course, we will use a random number table. Starting with the second row, the first 6 students listed in the table will be chosen for the random sample.

To ensure the sample selection is random and unbiased, a random number table can be used. The random number table consists of a grid of numbers that are considered equally likely to occur. Each number in the table corresponds to a specific student in the population.

In this case, the population consists of 98 students, each assigned a number from 01 to 98. We want to select a sample of 6 students from this population. Starting with the second row of the random number table, we can use the numbers listed to determine the students for our sample.

By matching the random numbers from the table with the corresponding student numbers in the population, we can select the first 6 students listed. These students will form our random sample.

It is important to use a random sampling method to ensure the sample represents the larger population and reduces the potential for bias or non-representativeness.

By following the instructions and using the random number table, we can achieve a random and unbiased sample for further analysis or study in the Probability and Statistics course.

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Answer: 4/1

Step-by-step explanation:

Rise over run. Starting at 1 on the y axis this line moves up 4 and over (right) 1 before it hits 1 on the x axis.

Answer:

0.0007264

Step-by-step explanation:

I think it is right but if not I am so sorry! Hope this helps!

In a right-angle triangle, a sine function of an angle θ is equal to the opposite side to θ divided by hypotenuse.

Sin θ = Opposite side/Hypotenuse

y = f(x) → x in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say θ is the angle, then:

sin θ = (Opposite side to θ/Hypotenuse)

Or θ = Sin-1 (Opposite side to θ/Hypotenuse)

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