(ROTATE !!!!!!!) help plssss i’ll give a lot of points for being quick

An additional information that must be known to prove the triangles are similar by SAS include the following: C. ∠G ≅ ∠R.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆DFG is congruent to ∆PQR when the angles G (∠G) and (∠R) are congruent.

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The correct option is D i.e. the average cost of performance per customer is $ 29.5

Consider the provided information.

E(X) = [tex]\sum X_i[/tex] × [tex]P(X_i)[/tex]

Where The total number of tickets a customer purchases is [tex]X_i[/tex] .

And [tex]P(X_i)[/tex] is the relative frequency distribution.

E(X) = 1 × 0.20 + 2 × 0.45 + 3 × 0.10 + 4 × 0.20 + 5 × 0.05

E(X) = 0.20 + 0.90 + 0.30 + 0.80 + 0.25

E(X) = 2.45

The average cost of performance per customer is,

2.45 × 12 = $ 29.5

Therefore, the average cost of performance per customer is $ 29.5

Hence, the correct option is D) $29.4

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Given question is incomplete, the complete question is below

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Number of tickets purchased Relative frequency 0.20 0.45 0.10 0.20 0.05 Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is mean cost per customer for the performance? (A) $2.45 1 ) $2.75 (C) $24.50 (D) $29.40 (E) $36.00

Non-rivalry and non-excludability apply to public goods. Public goods are goods or services that are non-excludable,

meaning that it is impossible or impractical to exclude people from using them, and non-rivalrous, meaning that consumption of the good by one individual does not diminish its availability to others.

Examples of public goods include national defense, clean air and water, and scientific research. Because of their non-excludable and non-rivalrous nature, public goods often suffer from under-provision in a market economy.

Private goods, on the other hand, are both rivalrous and excludable. This means that only one person can consume the good at a time, and individuals can be prevented from consuming the good if they do not pay for it.

Goods produced by monopolies and natural resources can be either private or public goods depending on their excludability and rivalrousness.

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The chain rule states that if a function is composed of two functions, say f(x) and g(x), then its derivative can be computed as f′(g(x))g′(x). Using this rule and the given information, we can find f′(5) as follows.

First, we know that f(5) = f(g(5)) by definition. Since g(5) = −4, we can write this as f(5) = f(−4). Taking the derivative of both sides with respect to x, we get f′(5) = f′(−4)g′(5). We know f′(−4) = 3 and g′(5) = 4 from the given information, so we can substitute these values into the equation to obtain f′(5) = 3(4) = 12. Therefore, the derivative of the function f(x) at x = 5, denoted by f′(5), is equal to 12. This means that the slope of the tangent line to the graph of f(x) at x = 5 is 12. The chain rule is a powerful tool for computing derivatives of composite functions, and it is widely used in calculus and its applications.

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Answer:

B

Step-by-step explanation:

given

tanΘ = [tex]\frac{3\sqrt{5} }{2}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

this ratio relates to a right triangle, with hypotenuse h and

legs 3[tex]\sqrt{5}[/tex] and 2

using Pythagoras' identity in the right triangle

h² = (3[tex]\sqrt{5}[/tex] )² + 2² = 45 + 4 = 49 ( take square root of both sides )

h = [tex]\sqrt{49}[/tex] = 7

then

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2}{7}[/tex]

The explanatory variable, also known as the independent variable, is the factor that is being manipulated to observe its effects on the outcome.

A variable used in statistical analysis to explain or forecast the outcome of a dependent variable is referred to as an explanatory variable. It is also known as an independent variable or predictor. It stands for an element or circumstance that could affect the dependent variable. Explanatory variables assist researchers comprehend the causes or drivers behind a specific occurrence by providing information about the link between various components. Researchers can examine the effects of modifying or detecting changes in the explanatory variables on the dependent variable. By enabling the discovery of patterns, trends, and correlations, this study offers insightful information regarding the variables that influence the observed results. Explanatory factors are important in many disciplines, including the social sciences, economics, psychology, and medical research.

In this study, the researcher is interested in determining the relationship between the amount of time spent studying and the score on a statistics exam. The explanatory variable, also known as the independent variable, is the factor that is being manipulated to observe its effects on the outcome. In this case, the explanatory variable is the "amount of time spent studying" for the exam.

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The monthly rate of increase was about 2.06 percent.

If participation in the program increased exponentially by 25 percent, this means that the number of participants in the program at the end of the year was 1.25 times the number of participants at the beginning of the year.

To find the monthly rate of increase, we can use the formula for exponential growth:

N = N0 x e^(rt)

where N is the final number of participants, N0 is the initial number of participants, e is the mathematical constant approximately equal to 2.71828, r is the monthly rate of increase (expressed as a decimal), and t is the time in months.

If we assume that the program started at the beginning of the year and ended at the end of the year, then t = 12 (12 months in a year). We also know that N = 1.25N0 (25% increase).

Substituting these values into the formula, we get:

1.25N0 = N0 x e^(r x 12)

Simplifying, we get:

1.25 = e^(12r)

Taking the natural logarithm of both sides, we get:

ln(1.25) = 12r

Solving for r, we get:

r = ln(1.25)/12

r ≈ 0.0206

Therefore, the monthly rate of increase, expressed as a percent, is

approximately:

r x 100% ≈ 2.06%

So the monthly rate of increase was about 2.06 percent.

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1) The polygons are not similar.

2) They polygons are similar.

3)  They polygons are similar.

Two polygons are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.

Using the above concept, we can equate the ratio of the corresponding sides to see if the polygons are similar. That is:

No. 1

10/5 = 2

12/6 = 2

8/4.5 = 1.77

The ratios of the corresponding sides are equal. Thus, they are not similar.

No. 2

24/12 = 2

13.2/6.6 = 2

The ratios of the corresponding sides are equal. Thus, they are similar.

No. 3

22/5.5 = 4

26/6.5 = 4

12/3 = 4

The ratios of the corresponding sides are equal. Thus, they are similar.

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a. residual is much larger than the rest of the residual values.

In regression analysis, an outlier refers to an observation that significantly deviates from the expected pattern or trend of the data. Specifically, it is an observation whose residual (the difference between the observed value and the predicted value) is much larger than the residuals of the other observations.

Outliers can have a considerable impact on the regression model, affecting the estimated coefficients and overall model fit. It is important to identify and assess outliers to determine if they are influential or if they should be treated or removed to ensure the reliability and validity of the regression analysis.

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The best way to display this data would be in a contingency table or a cross-tabulation table.

What is the frequency?

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

The birth order would be shown in one column with three categories (oldest, in-between, youngest), and the IQ test scores would be shown in another column with different categories or ranges of scores.

The table would show the frequency or percentage of individuals in each cell of the table, which would help to determine if there is a relationship between birth order and IQ scores.

A graphical display, such as a stacked bar chart or a mosaic plot, could also be used to visualize the relationship.

Hence, The best way to display this data would be in a contingency table or a cross-tabulation table.

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The Taylor rule predicted the federal funds rate (in the text) was derived from the equation:  t 2 = 1% + 1.5π t + 0.5 Y ˉ t

This is a long answer because it provides a detailed explanation of the specific equation used in the Taylor rule to predict the federal funds rate.
The Taylor rule predicted the federal funds rate was derived from the following equation:
t = 1% + 1.5π + 0.5Y

Where:
- t represents the federal funds rate
- π represents the inflation rate
- Y represents the output gap (the difference between actual output and potential output)

This equation is known as the Taylor rule and is used to determine the appropriate federal funds rate to achieve macroeconomic stability.

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The length of the missing side of the right triangle is given as follows:

x = 5.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The sides for this problem are given as follows:

3 and 4.

Hence the hypotenuse is given as follows:

x² = 3² + 4²

x² = 25.

x = 5.

The missing side is the hypotenuse.

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The dimension of the null space of a is 5.

If t(x) = ax is onto, it means that every element in the codomain of t has at least one preimage in the domain of t. In other words, for any b in R^7, there exists an x in R^12 such that ax = b. Since a has 7 rows and x has 12 columns, it follows that there are 12 unknowns and 7 equations. Therefore, the number of free variables is 12-7 = 5. The null space of a consists of all solutions to the homogeneous equation ax = 0. Since the number of free variables is 5, the dimension of the null space of a is 5.

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Answer:

5 in.

Step-by-step explanation:

For a square:

perimeter = 4 × side

20 in. = 4 × side

side = 20 in. / 4

side = 5 in.

the question is that as we increase the sample size in a one sample test for the population mean, the size of the rejection region decreases. This means that the probability of rejecting the null hypothesis when it is actually true, also known as a Type I error, decreases.

The t critical value is a constant value determined by the sample size and the significance level. It is the point at which we decide to reject or fail to reject the null hypothesis. As we increase the sample size, the t critical value moves closer to zero, but this does not have a direct impact on the probability of a Type I error.

The size of the rejection region, on the other hand, is determined by the t critical value and the variability of the sample. As the sample size increases, the variability decreases, leading to a smaller rejection region. This means that it is less likely to reject the null hypothesis when it is actually true, resulting in a lower probability of a Type I error.

Therefore, we can conclude that increasing the sample size in a one sample test for the population mean decreases the size of the rejection region and the probability of a Type I error.

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The correct answer is 1. I and II only. Interest rates to decrease. when the Federal Reserve increases the money supply, it can lead to a decrease in interest rates and an increase in consumption and investment.

When the Federal Reserve increases the money supply, it injects more money into the economy. This can lead to a decrease in interest rates, as there is more money available for borrowing and lending. This is because an increase in the money supply can lead to a decrease in the demand for money, which in turn causes the interest rates to fall.

A decrease in interest rates can lead to an increase in consumption and investment. Lower interest rates make it cheaper for consumers to borrow money to buy goods and services, and for businesses to borrow money to invest in new projects. As a result, an increase in the money supply can lead to an increase in consumption and investment, as businesses and consumers have more money available to spend.

However, an increase in the money supply can also lead to inflation. This is because more money is chasing the same amount of goods and services, leading to an increase in prices. Inflation can erode the purchasing power of money and lead to a decrease in the standard of living.

In conclusion, when the Federal Reserve increases the money supply, it can lead to a decrease in interest rates and an increase in consumption and investment. However, it can also lead to inflation, which can have negative effects on the economy. Therefore, the correct answer is 1. I and II only.

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After 20 minutes, the temperature of the pan will be approximately 29°F.

Using Newton's Law of Cooling, we can write:

T(t) = To + (T₁ - To)e^(-kt)

where T(t) is the temperature of the pan at time t, To is the temperature of the freezer, T₁ is the initial temperature of the pan, and k is a constant that depends on the properties of the pan and the freezer.

We know that after 15 minutes, the temperature of the pan is 41°F, so we can write: 41 = 0 + (140 - 0)e^(-15k)

Simplifying this expression, we get:

e^(-15k) = 41/140

Taking the natural logarithm of both sides, we get:

-15k = ln(41/140)

Solving for k, we get:

k ≈ 0.056

Now we can use this value of k to find the temperature of the pan after 20 minutes:

T(20) = 0 + (140 - 0)e^(-0.056*20) ≈ 29°F

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After 20 minutes, the temperature of the pan will be approximately 29°F.

Using Newton's Law of Cooling, we can write:

T(t) = To + (T₁ - To)e^(-kt)

where T(t) is the temperature of the pan at time t, To is the temperature of the freezer, T₁ is the initial temperature of the pan, and k is a constant that depends on the properties of the pan and the freezer.

We know that after 15 minutes, the temperature of the pan is 41°F, so we can write: 41 = 0 + (140 - 0)e^(-15k)

Simplifying this expression, we get:

e^(-15k) = 41/140

Taking the natural logarithm of both sides, we get:

-15k = ln(41/140)

Solving for k, we get:

k ≈ 0.056

Now we can use this value of k to find the temperature of the pan after 20 minutes:

T(20) = 0 + (140 - 0)e^(-0.056*20) ≈ 29°F

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Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.

To find h(x, y) = g(f(x, y)), we first need to evaluate f(x, y) and then use the result as input for g(t).
Starting with f(x, y), we have:
f(x, y) = 7x - 6y - 42
Next, we need to use this as input for g(t), which is defined as:
g(t) = t^2*t
Substituting f(x, y) for t, we get:
g(f(x, y)) = (7x - 6y - 42)^2*(7x - 6y - 42)
Simplifying this expression, we can expand the square and get:
h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764
Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.

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The total number of students in the sixth grade is equal to 250.

Percent of students purchased their lunch = 24%

Number of students brought their lunch from home = 190

Let us call the total number of students in the 6th grade 'x'.

We know that all students either purchased their lunch or brought their lunch from home,

x = students who purchased their lunch + students who brought their lunch from home

24% of the students purchased their lunch, so the number of students who purchased their lunch is 0.24x.

And we know that 190 students brought their lunch from home.

Substituting these values into the equation above, we get,

x = 0.24x + 190

Solving for x, we can start by subtracting 0.24x from both sides,

⇒ 0.76x = 190

Then we divide both sides by 0.76 to isolate x,

x = 250

Therefore, there are 250 students in the 6th grade.

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The above question is incomplete, the complete question is:

All students in the 6th grade either purchased their lunch or brought their lunch from home on Monday.• 24% of the students purchased their lunch.• 190 students brought their lunch from home. How many students are in the 6th grade?

The median is the middle value of a set of numbers. To find the median of the sample values provided, we need to first arrange the numbers in order from least to greatest: 3, 7, 11, 18, 24, 27, 32, 35, 41, 46.

Next, we need to determine the middle value or the average of the two middle values, if there is an even number of values in the set.

In this case, we have 10 values in the set, so we need to find the average of the fifth and sixth values: (24 + 27) / 2 = 25.5. Therefore, the median of the sample values is 25.5.

The median is an important measure of central tendency in statistics because it is less sensitive to outliers or extreme values than the mean. It is often used in conjunction with the mean to provide a more complete understanding of a dataset. The sample values provided are relatively close together, so the difference between the median and the mean (if calculated) would likely be small.

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After taking the Laplace transform, we obtain f(s) = (72/s^38) - (20/(s^2 + 25)) * (2/(s + 3)). The Laplace transform of the function f(t) = 2t^36 - 2sin(5t) * 2e^(-3t) can be found by applying the linearity and derivative properties of the Laplace transform.

To find the Laplace transform of f(t) = 2t^36 - 2sin(5t) * 2e^(-3t), we can apply the linearity property of the Laplace transform.

The Laplace transform of 2t^36 can be found using the derivative property of the Laplace transform. Taking the derivative of t^36, we get 36t^35. Then, applying the Laplace transform to 36t^35, we obtain (36!/s^37).

The Laplace transform of 2sin(5t) can be directly found using the standard Laplace transform table. The transform of sin(5t) is 5/(s^2 + 25).

The Laplace transform of 2e^(-3t) can also be found using the standard Laplace transform table. The transform of e^(-at) is 1/(s + a).

Now, using the linearity property of the Laplace transform, we can combine the transforms of each term:

f(s) = (72/s^37) - (20/(s^2 + 25)) * (2/(s + 3)).

Thus, the Laplace transform of f(t) is f(s) = (72/s^37) - (40/(s^2 + 25)(s + 3)).

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Answer:

$1,134 + $926 + $562 + $333 + $55 + $130

+ $1,500 + $313 = $4,953

(A) qualitative and quantitative categories. (A) True. (C) is highly susceptible when used outside tested range of X values.

Data is broken into (A) qualitative and quantitative categories, which refers to the nature of the data being analyzed. Qualitative data is non-numeric and describes characteristics or attributes, while quantitative data is numeric and describes quantities or measurements.

The statistical calculation r shows the correlation between variables (Y, X) in a regression analysis. This statement is true. The correlation coefficient r is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

Linear regression used for estimation of A is susceptible when used outside the tested range of X values. This statement is true. Linear regression models are based on the assumption of a linear relationship between the dependent variable Y and the independent variable X within a certain range of X values. When used outside of this range, the linear regression model may not accurately predict the values of Y. This is because the linear relationship between Y and X may not hold outside of the tested range, or other factors may come into play that were not accounted for in the model. Therefore, it is important to carefully consider the range of X values used in the regression analysis and to exercise caution when making predictions outside of this range.

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The overall gain or loss from Peter's moves is 12.

The correct option is C.

To find the overall gain or loss from Peter's moves, we need to consider the direction and magnitude of each move. A positive value represents a gain or moving forward, while a negative value represents a loss or moving backward.

In this case, Peter had a gain of 5 spaces, followed by a loss of 2 spaces, a gain of 12 spaces, a gain of 7 spaces, and finally a loss of 10 spaces. When we add up these individual gains and losses, we find that the total sum is 12.

This means that, overall, Peter gained a net total of 12 spaces from all his moves. It indicates that he moved forward more than he moved backward. The positive value suggests a net gain in terms of spaces on the game board.

Therefore, the answer C) 12 represents the overall gain or loss from Peter's moves.

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The probability of the price of milk being between $2.8 and $3.0 is 0.1359 or 13.59% (rounded to two decimal places).

To solve this problem, we need to standardize the values using z-scores, which is calculated as (x - μ) / σ where x is the value, μ is the mean, and σ is the standard deviation.

For the lower limit of $2.8, the z-score is

(2.8 - 3.4) / 0.20 = -3.00.

For the upper limit of $3.0, the z-score is

(3.0 - 3.4) / 0.20 = -2.00.

We can then use a standard normal distribution table or calculator to find the probability of the z-score being between -3.00 and -2.00, which is the same as the probability of the price being between $2.8 and $3.0.

The probability of a z-score being between -3.00 and -2.00 is approximately 0.1359.

In other words, there is a 13.59% chance that a randomly selected vendor sells milk between $2.8 and $3.0, assuming the price of milk follows a normal distribution with a mean of $3.4 and a standard deviation of $0.20.

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The amount of the substance that will be left after 5 half life is 5.94 grams

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.

The time required for half of the original population of radioactive atoms to decay is called the half-life.

Half life = 1/2

5 half life = 1/2 × 1/2 × 1/2 × 1/2 × 1/2

= 1/32

This means 1/32 of tht original mass will be left after 5 half life.

Therefore;

The mass of the substance left = 190 × 1/32

= 5.94 grams

therefore 5.94g of the mass of the substance will be left.

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Shaylen's score is at the 42nd percentile, which means that 42% of the students who took the test scored lower than Shaylen.

To find the percentile for Shaylen's score, we can use the formula:

percentile = (number of scores below Shaylen's score / total number of scores) x 100

We are given that Shaylen's score of 455 was higher than the scores of 4226 students. This means that there were 7246 - 4226 = 3020 students who scored higher than Shaylen. Therefore, we can calculate the percentile as:

percentile = (3020 / 7246) x 100

= 0.417 x 100

= 42 (rounded to the nearest percent)

So Shaylen's score is at the 42nd percentile, which means that 42% of the students who took the test scored lower than Shaylen.

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The width of the rectangle is 2n^9 - 5n^3 + 28.

To find the width of the rectangle, we need to use the formula for the area of a rectangle:
Area = Length x Width

We are given that the area of the rectangle is:
12n^12 - 30n^6 + 168n^3

And we know that the length of the rectangle is:
6n³

So we can plug these values into the formula and solve for the width:

Area = Length x Width
12n^12 - 30n^6 + 168n^3 = 6n^3 x Width

Dividing both sides by 6n^3:
2n^9 - 5n^3 + 28 = Width

Therefore, the width of the rectangle is 2n^9 - 5n^3 + 28.

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Thus, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.

In △ABC, you have given B = 51°, b = 35, and a = 36. To find the two possible values for angle A, we can use the Law of Sines.

The Law of Sines states: (sinA)/a = (sinB)/b

Plugging in the given values, we get:
(sinA)/36 = (sin51°)/35

Now, solve for sinA:
sinA = 36 * (sin51°)/35 ≈ 0.923

Since sinA = 0.923, we can find the two possible values for angle A using the inverse sine function:

1. A = arcsin(0.923) ≈ 67.4°
2. A = 180° - arcsin(0.923) ≈ 112.6°

So, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.

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Answer:

5

Step-by-step explanation:

you see here you go to red and green and their you see it.. I might be right