A chi-square goodness-of-fit test was conducted to determine whether the data provide convincing evidence that the distribution has changed. the test statistic was 10.13 with a p-value of 0.0175. What is true?

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Aut(G) is a subgroup of S_G. To prove that automorphisms by Aut(G) is a subgroup of S_G, we need to show that it satisfies the three conditions of a subgroup: closure, identity, and inverses.

Closure: Let f, g be two automorphisms in Aut(G). We need to show that their composition, f∘g, is also an automorphism. Since f and g are automorphisms, they preserve the group operation.

Therefore, for any elements a, b in G, we have (f∘g)(ab) = f(g(ab)) = f(g(a)g(b)) = f(g(a))f(g(b)). This shows that f∘g is a well-defined function. Moreover, f∘g is also bijective since f and g are both bijective. Hence, f∘g is an automorphism, and closure is satisfied.

Identity: The identity element of S_G is the identity function, denoted as id. We need to show that id is an automorphism. Since id(g) = g for all g in G, it preserves the group operation and is bijective. Therefore, id is an automorphism, and it serves as the identity element of Aut(G).

Inverses: Let f be an automorphism in Aut(G). We need to show that f^(-1) is also an automorphism. Since f is bijective and preserves the group operation, its inverse, f^(-1), is also bijective and preserves the group operation. Therefore, f^(-1) is an automorphism, and inverses are satisfied.

Since Aut(G) satisfies closure, identity, and inverses, it is a subgroup of S_G.

Aut(Z) is the set of automorphisms of the group of integers under addition. Any automorphism of Z must preserve the group operation and the identity element, 0.

It can be shown that there are two types of automorphisms: the identity automorphism, which maps every integer to itself, and the negation automorphism, which maps every integer to its additive inverse.Therefore, Aut(Z) is isomorphic to the cyclic group Z_2, where Z_2 = {0, 1} with addition modulo 2.

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

The equation of the line is y = 1/2x - 2

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

y= 1/2x +1

Point = (8, 2)

Parallel lines have equal slopes

This means that the slope of the line is 1/2

So, the eqiuation is calculated as

y = m(x - x1) + y1

substitute the known values in the above equation, so, we have the following representation

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

Evaluate

y = 1/2x - 2

Hence, the equation is y = 1/2x - 2

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Answer:

4x-10

Step-by-step explanation:

Combine like terms :)

Both equations are same ?

Take 2 out

Table

\(\overset{\sf Here\:we\:go\downarrow}{\boxed{\begin{array}{c|c}\underline{\bf x}&\underline{\bf y}\\ \rm 0&\rm 2\\ \rm -2&\rm 0 \\ \rm 1&\rm 3\end{array}}}\)

Forty-seven and seven tenths minus twenty-three and nineteen-hundredths is equal to twenty-four and fifty-one hundredths, or 24.51 as a decimal.

To find the difference between forty-seven and seven tenths (47.7) and twenty-three and nineteen hundredths (23.19), we can simply subtract the two numbers using the standard subtraction method for decimals. Here are the steps:
1. Line up the decimals:
47.70
-23.19
2. Subtract the hundredths place: 0 - 9 = -9. Since we can't have a negative number in the hundredth place, we need to borrow 1 from the tenths place. So, 10 - 9 = 1.
3. Subtract the tenths place: 6 (after borrowing) - 1 = 5.
4. Subtract the ones place: 7 - 3 = 4.
5. Subtract the tens place: 4 - 2 = 2.
So, the final answer is 24.51.

Therefore, forty-seven and seven tenths minus twenty-three and nineteen-hundredths is equal to twenty-four and fifty-one hundredths, or 24.51 as a decimal.

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The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A jumper is at a height of - 18 feet comparative with ocean level. The jumper plunges to an undersea cavern that is 4 times as distant from the surface

The elevation of the cave is given as,

Elevation = - 18 x 4

Elevation = - 72 feet

The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.

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Answer:

the angle that has the same measure as /2 is A

Answer:

54

Step-by-step explanation:

6*5=30

4*6=24

24+30=54

Answer: 3 boxes every 4 minutes, and 0.75 boxed every minute. And  0.75 boxes are filled per minute.

Step-by-step explanation: Hope This Helps!

The number that could not be a value of y if y = 4x² - 6 is -12.

The value of y for which a function f(x) = y = 4x² - 6 can be determined by knowing the smallest value of y for which x is equal to zero.

So, from the equation y = 4x² - 6, we will replace the value of x with zero to determine the smallest value of y.

i.e.

y = 4(0) - 6

y = 0 - 6

y = -6

Thus, any number smaller than -6 could not be a value of y for the equation y = 4x² - 6.

Therefore, we can conclude that the number that could not be a value of y if y = 4x² - 6 is -12.

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Answer:

-12 is the answer.

The slope of the line, based on the information given in the table is: the cost of purchasing one pencil.

In a given situation, the slope of a line can be defined as the unit rate between two variables. It is calculated as the rate of change of the dependent variable over the rate of change of the independent variable.

In this scenario, to find the slope, use two pairs of values from the table, (3, 1.05) and (7, 2.45):

Slope in this case = cost of purchasing one pencil (unit rate) = 2.45 - 1.05 / 7 - 3

Slope = $0.35 per pencil.

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To determine the amount of variation in the sample values of total points earned that the model explains, you can use the coefficient of determination, also known as R-squared. R-squared represents the proportion of the dependent variable's variation that can be explained by the independent variables in the model.

To calculate R-squared, you need to compare the sum of squares of the model's predicted values (SSR) to the total sum of squares (SST). The formula for R-squared is:

R-squared = SSR / SST

Now, in order to calculate SSR and SST, you will need the sums of squares for residuals (SSE) as well. SSE is the sum of the squared differences between the actual values and the predicted values. The formula is:

SSE = Σ(y - ŷ)^2

Once you have SSE, SSR, and SST, you can calculate R-squared as follows:

R-squared = 1 - (SSE / SST)

In your case, you need to use the model estimated in part (b) to calculate R-squared. Once you have the value of R-squared, you can interpret it as the proportion of the variation in the sample values of total points earned explained by the model. Round your answer to two decimal places if necessary.
R-squared is a statistical measure that indicates the goodness of fit of a regression model. It ranges from 0 to 1, where a value of 0 implies that the model explains none of the variation in the dependent variable, and a value of 1 implies that the model explains all of the variation.

To determine the amount of variation explained by the model you estimated in part (b), calculate the R-squared value.

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Answer:

(1, 3)

Step-by-step explanation:

The solution to any system is where the two lines meet. It would be no solution if the lines were parallel. An ordered pair is written out in the format (x, y).

Answer:

-21

Step-by-step explanation:

comments

Answer: (-3.5 + (-1.5))

Step-by-step explanation:

Given the expression :

The temperature in the morning was -3.5 °F. By noon, the temperature had dropped by 1.5 °F. Write an addition expression to represent this scenario.

Morning temperature : - 3.5°F

By Noon : change (drop) in temperature

Addition expression to represent the scenario :

A drop in temperature means a further reduction in the initial temperature level :

Addition expression :

(Morning temperature + ( - drop in temperature))

(-3.5 + (-1.5))

=====================================================

Explanation:

Check out the diagrams below.

We'll start with the left diagram (marked "before") which is a right triangle with the horizontal leg of 25 feet and hypotenuse 65 feet.

Use the pythagorean theorem to find the vertical side x.

a^2 + b^2 = c^2

25^2 + x^2 = 65^2

625 + x^2 = 4225

x^2 = 4225 - 625

x^2 = 3600

x = sqrt(3600)

x = 60

The top of the ladder is 60 feet high when placed against the wall in this configuration.

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

If the upper end is moved down 8 feet, then x-8 = 60-8 = 52 feet is the new height of the ladder. Refer to the "after" in the diagram below.

Like earlier, we'll use the pythagorean theorem to find the missing side.

a^2 + b^2 = c^2

y^2 + 52^2 = 65^2

y^2 + 2704 = 4225

y^2 = 4225 - 2704

y^2 = 1521

y = sqrt(1521)

y = 39

The horizontal distance from the ladder base to the wall is now 39 feet.

Earlier it was 25 feet, so it has increased by 39-25 = 14 feet.

Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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Answer:

It is 1/5

Step-by-step explanation:

rise/run and it rises by one and runs by 5.

Answer:

6

Step-by-step explanation:

The graph of the absolute value function is an inverted "V" such that the vertex is at (-4, -5) and opens downwards.

How to calculate the modular function?

Among modular functions, f(x) = |x| has its domain given by the real numbers and its range given by the positive real numbers. This is because the modular function will make |-y| = -(-y) = y given every negative y-value.

Given modular function is :

y = -|x + 4| - 5.

Hence, to plot the graph of a modular function, we need to determine some values for x and then apply them to the function f(x) = | x |.

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The equivalent integral is ∫ba∫0g(x)∫0k(x,z)f(x,y,z)h(x,z)dydzdx.

To obtain the equivalent integral, we need to rewrite the original integral limits and order of integration.

Starting from the innermost integral, we have ∫x=0^(z) f(x,y,z)dy, where y varies from 0 to z.

Moving to the second integral, we now have ∫z=1^(0) ∫x=0^(z) f(x,y,z)dydx, where z varies from 1 to 0 and x varies from 0 to z.

Finally, for the outermost integral, we have ∫z=1^(0) ∫x=0^(z) ∫y=0^(z) f(x,y,z)dydxdz, where z varies from 1 to 0, x varies from 0 to z, and y varies from 0 to z.

To obtain the equivalent integral in the desired order, we can change the limits of integration and rewrite the integrand as follows:

∫z=0^(b) ∫x=0^(g(z)) ∫y=0^(k(x,z)) h(x,z)f(x,y,z)dydzdx.

Finally, we can rearrange the order of integration to obtain the equivalent integral:

∫ba∫0g(x)∫0k(x,z)f(x,y,z)h(x,z)dydzdx.

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The x = 30°, the simplified value of 4cos(3x - 45°) is 2√2.

To simplify the expression 4cos(3x - 45°) when x = 30°, we substitute the given value of x into the expression:

4cos(3(30°) - 45°)

First, we simplify the inside of the cosine function:

3(30°) - 45° = 90° - 45° = 45°

Substituting this back into the expression:

4cos(45°)

Next, we evaluate the cosine of 45 degrees:

cos(45°) = √2/2

Finally, we substitute this value back into the expression:

4 * (√2/2) = 2√2

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Answer:

How to write numbers in standard form:

Write the first number 8.

Add a decimal point after it: 8.

Now count the number of digits after 8. There are 13 digits.

So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³

Step-by-step explanation:

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Answer:

The interval over  which the cost is constant is from >0 to 15,000 gallons

The interval for which the the cost is increasing is from above 15,000 gallons

Step-by-step explanation:

For 15,000 gal or less the cost of the monthly water bill = $15.50

For over 15,000 gal, the cost of the monthly water bill = $15.50 plus $1 for each 1000 gal over 15,000 with any fraction of $1,000 charged at a fraction of $1

The interval for which the cost is constant is from 0 ≤ x ≤ 15,000 gal

The interval over which the const is increasing per 1000 gal over 15,000 gallons is from x > 15,000 gal.

Answer:

The interval in which the cost is constant is

[0,15000]

Step-by-step explanation:

The interval is increasing by [1500,∞]

Answer:

pi ≈ 3,141593

Step-by-step explanation:

I think this is the right answer

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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Answer:

  both interpretations make sense

Step-by-step explanation:

Reginald says (2650 L)/(49 1/10 bags) will give the volume of each bag; Peni says (2650 L)/(49 1/10 containers) will give the volume of each container. You want to know which intepretation makes sense.

The result of Reginald's calculation is ...

  \((2650\text{ L})\div(49\dfrac{1}{10}\text{ bags})=\dfrac{2650}{49.1}\text{ L/bag}\)

The result has units of volume per bag, which is exactly what Reginald says it is.

The result of Peni's calculation is ...

  \((2650\text{ L})\div(49\dfrac{1}{10}\text{ containers})=\dfrac{2650}{49.1}\text{ L/container}\)

The result has units of volume per container, which is exactly what Peni says it is.

Both interpretations make sense.

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Answer:

both

Step-by-step explanation:

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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