the area of the state of ohio is about 4000 square miles. at its peak, how did the aztec empire compare? give an area estimate

The value of x is 22.37 and y is 20

What is Interior angle?

An angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon.

What is Exterior angle?

An exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

We know, the sum of interior angle is 180 degree

The given interior angles is ,

3y + 5 and 5y + 15

So, equate to 180°

3y + 5 + 5y + 15 = 180°

Solve for 'y'

8y + 20 = 180

4(2y + 5) = 180

2y + 5 = 45

2y = 45 - 5

2y = 40

y = 20

Now, we know the sum of exterior angle is 360 degree

The given exterior angle is,

17x - 70 and 2x + 5

So, equate to 360°

17x - 70 + 2x + 5 = 360°

Now, solve for 'x'

19x - 65 = 360

19x = 360 + 65

19x = 425

x = 22.368 or 22.37

Hence, the value of x is 22.37 and y is 20

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The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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Answer:

Start at any point on the graph. Move up 1 space and right 2 spaces, and then plot a point.

Explanation:

Look at the coordinates (4, 2) and (6, 3) that I graphed on the chart. If you move 1 space up, and 2 spaces to the right, it leads to the coordinates (6, 3)

The total number of possible choices that John had for making baked goods for the party is 8.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{r!(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

We know that the number of choices with John for his baked goods is only two which are muffins or bread, therefore, the choices of the baked good can be written as \(^2C_1\).

Also, the number of choices with John for flavors is four which are blueberries, bananas, apples, or chocolate chips, therefore, the choices of the flavor can be written as \(^4C_1\).

Now, the total possible choices that John had

= The choices of the baked good x The choices of the flavor

\(=\ ^2C_1 \times ^4C_1\\\\=\ 8\)

Hence, the total number of possible choices that John had for making baked goods for the party is 8.

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The converse of the Pythagorean Theorem is that when the sum of the squares of the other two sides square of the length of the longest side of a triangle, then the triangle is a right triangle.

To understand the Pythagorean Theorem let's assume 2 right-angled triangles with the 2 legs = a and b in each case and the longest side = c in one triangle and e in the other.

Pythagoras' Theorem is = \(a^2 + b^2 = c^2\) (Given)

Also in the other triangle \(a^2 + b^2 = e^2\),  if it is right-angled.

Therefore a^2 = l^2 and a = e.

So the 2 triangles are congruent by SSS.

So m < e  in one triangle = m < e   the angles opposite the hypotenuse

Therefore the second triangle is right-angled

The two triangles are said to be congruent by the SSS rule when all three sides of one triangle are equivalent to the corresponding three sides of the second triangle.

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The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.

In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).

To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).

Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.

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The sample mean for the freshmen reading comprehension test is \(\bar{x}\) = 10.22.

To determine if this sample is significantly different from the population mean μ = 12, a one-sample t-test can be conducted with a significance level of α = .05.

Using the given sample scores, the t-value can be calculated as t = (\(\bar{x}\) - μ) / (s / √n), where s is the sample standard deviation and n is the sample size.

For the given sample, the calculated t-value is t ≈ -1.86.

The critical t-value can be found from the t-distribution table or using statistical software, considering the degrees of freedom (df = n - 1). For α = .05 and df = 8, the critical t-value is approximately t_crit = -2.31 (one-tailed test).

Since the calculated t-value (-1.86) is greater than the critical t-value (-2.31), we fail to reject the null hypothesis. There is not enough evidence to conclude that the sample mean is significantly different from the population mean.

Regarding effect size, Cohen's d is an appropriate measure. It can be calculated as d = (\(\bar{x}\) - μ) / s, where s is the pooled standard deviation. Cohen's d measures the standardized difference between the means. In this case, the calculated Cohen's d is approximately -0.73, indicating a small effect size.

Therefore, the average score for the freshmen reading comprehension test is 10.22.

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Complete question below:

A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is μ = 12, can you conclude that this sample is significantly different from the population. Test with α = .05. Include an effect size measure you find appropriate and explain why you chose what you calculated - you determine the tail and why.

Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10

When testing partial correlation, the impact of a third variable is removed.

Partial correlation is a statistical technique used to measure the relationship between two variables while controlling for the effect of one or more additional variables, known as "covariates" or "control variables." By removing the effect of the covariates, the partial correlation measures the direct relationship between the two variables of interest. This technique is useful when we want to examine the relationship between two variables after accounting for the effect of one or more confounding variables.

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In Utah, if not directly involved in diving activity, motorized vessels and personal watercraft (PWCs) must remain 150 feet from the diver down flags.

The diver down flag is a banner that is used by vessels to indicate that divers are in the water. It is typically a red flag with a white diagonal stripe that is used to indicate the presence of divers in the water. The flag must be at least 12 x 12 inches in size and must be clearly visible from all directions. When the flag is raised, boaters are expected to keep a safe distance from the divers and to take extra precautions to ensure that they do not pose a hazard to the divers.The diver down flag should be used whenever there are divers in the water. This includes scuba divers, free divers, and anyone else who is swimming or diving underwater. The flag should be raised before the divers enter the water and should be lowered when they exit the water. In addition to the flag, divers are required to use other means of indicating their presence in the water, such as lights and audible signals, to ensure that boaters can see and hear them. Motorized vessels and personal watercraft (PWCs) must remain at least 150 feet from the diver-down flag. This means that they must keep a safe distance from the divers and take extra precautions to ensure that they do not pose a hazard to the divers. If a motorized vessel or PWC is directly involved in the diving activity, such as transporting divers to and from the dive site, they may operate closer to the flag, but they must still maintain a safe distance from the divers at all times.

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Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8. Therefore, the correct options are B. 10 and E. 8.

To determine the possible values for the length of the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given sides of lengths 5 and 13, we can check which values satisfy the triangle inequality:

The sum of the lengths of the two sides must be greater than the length of the third side:

5 + 13 > Third side

18 > Third side

Now let's check each given value:

A. 2: Not possible, since 18 > 2 does not hold true.

B. 10: Possible, since 18 > 10 holds true.

C. 24: Not possible, since 18 > 24 does not hold true.

D. 5: Not possible, since the given length is already one of the sides.

E. 8: Possible, since 18 > 8 holds true.

F. 19: Possible, since 18 > 19 does not hold true.

Based on the calculations, the values that could be the length of the third side are B. 10 and E. 8.

Therefore, the correct options are B. 10 and E. 8.

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Answer:

Area = 31.5 squared inches

Step-by-step explanation:

I am assuming d1 and d2 diagnol lengths, so if that's true, then answer would A=(d1*d2)/2    (3.5*18)/2 = 63/2 = 31.5 squared inches

Answer:

3x³ - 2x² + x - 5

Hope this helps!

The slope is \(-2\).

(Please comment if you want explanation)

Ok, My answer is marked wrong and I don't know why. Ok, kindakait asked for the slope of the line in the graph.

To find the slope of the line is \(\frac{∆y}{∆x} \\\) or so they call \(\frac{rise}{run} \\\).

We can clearly see that to be at (-2,1) from (-4,5). You have to rise by -4 units and run by 2 units. Therefor:

\(m = \frac{rise}{run} \\ m = \frac{-4}{2} \\ m = -2\).

If you are not satisfied yet. Let's try another points. (0,-3) and (1,-5) and this is obvious by just eyeballing it.

\(m = \frac{rise}{run} \\ m = \frac{-2}{1} \\ m = -2\).

Answer:

slope is -4

Step-by-step explanation:

(-1, 1) (0, -3)

(-3 - 1)/(0 + 1) = -4/1 = -4

y + 3 = -4(x - 0)

y + 3 = -4x + 0

y = -4x - 3

Answer:

x=3 or C

Step-by-step explanation:

I just did the math and got it correct on my FLVS quiz

The value of Ay-dy for the given function and values is approximately 2.7.

To calculate Ay-dy for the function y = x - 3x + 7, with x = -4 and Δx = -0.9, follow these steps:

1. Determine the original function value: y = (-4) - 3(-4) + 7
2. Calculate the new x value: x_new = -4 + (-0.9) = -4.9
3. Find the new function value: y_new = (-4.9) - 3(-4.9) + 7
4. Calculate Δy: Δy = y_new - y
5. Calculate Ay-dy: Ay-dy = Δy - Δx

Now, let's compute the values:

1. y = (-4) - 3(-4) + 7 = -4 + 12 + 7 = 15
2. x_new = -4 - 0.9 = -4.9
3. y_new = (-4.9) - 3(-4.9) + 7 ≈ -4.9 + 14.7 + 7 ≈ 16.8
4. Δy = y_new - y ≈ 16.8 - 15 ≈ 1.8
5. Ay-dy = Δy - Δx ≈ 1.8 - (-0.9) ≈ 2.7

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Kay deposited (c)$93.44  in cash and coins.

Money or coins that are legal tender can be used to pay for goods, debts, or services. Additionally, as stated by a corporation, it occasionally includes the worth of assets that can be quickly converted into cash. In its physical form, cash is another name for money. Bank accounts and marketable securities, such as government bonds and banker's acceptances, are typically included in the definition of "cash" in a business context.

We proceed from the whole backward. The amount deducted for cash received is first added back,

498.01+213.51 = 711.52

Each cheque that was deposited is then subtracted:

711.52-40.25 = 671.27

671.27-57.68 = 613.59

613.59-520.15 = 93.44

She started with (c) $93.44 in cash and coins.

Correct Question :

How much did kay deposit in cash and coins? a. $404.57 b. $213.51 c. $93.44 d. $284.50

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The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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The cοffee shοp that typically sells the mοst amοunt οf cοffee per hοur is Perks A Lοt, with a mean value οf 5.75 gallοns. Sο cοrrect οptiοn is C.

The median is a measure οf central tendency in statistics that represents the middle value οf a dataset when the data is arranged in οrder frοm least tο greatest.

Tο find the median οf a dataset, yοu first arrange the values in οrder. If the dataset has an οdd number οf values, the median is the middle value. Fοr example, in the dataset {2, 3, 5, 6, 8}, the median is 5 because it is the middle value.

If the dataset has an even number οf values, the median is the average οf the twο middle values. Fοr example, in the dataset {2, 3, 5, 6, 8, 10}, the median is (5+6)/2 = 5.5 because it is the average οf the twο middle values.

Tο determine which cοffee shοp typically sells the mοst amοunt οf cοffee per hοur, we need tο cοmpare the central tendency οf the data fοr bοth shοps.

The measure οf center that we can use here is either the mean οr the median. The mean is the average value οf the data, while the median is the middle value οf the data when it is arranged in οrder.

Tο calculate the mean, we can add up all the values and divide by the number οf values. Tο calculate the median, we can arrange the values in οrder and find the middle value.

Fοr Perks A Lοt:

Mean = (10 + 3.5 + 3 + 5 + 2.5 + 7 + 8 + 5.5 + 9.5 + 6 + 9 + 4.5) / 12 = 5.75 gallοns

Median = (3 + 3.5 + 5 + 5.5 + 6 + 7 + 8 + 9 + 9.5) / 9 = 5.75 gallοns

Fοr Wide Awake:

Mean = (2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 15 + 6 + 5 + 2.5) / 11 = 6.36 gallοns

Median = (3 + 4 + 4 + 5 + 6.5 + 6 + 10 + 15 + 18) / 9 = 4.5 gallοns

Cοmparing the mean and median values, we can see that Perks A Lοt has bοth a mean and median value οf 5.75 gallοns, while Wide Awake has a mean value οf 6.36 gallοns and a median value οf 4.5 gallοns.

Therefοre, the cοrrect measure οf center tο determine which shοp typically sells the mοst amοunt οf cοffee per hοur is the mean, and the cοffee shοp that typically sells the mοst amοunt οf cοffee per hοur is Perks A Lοt, with a mean value οf 5.75 gallοns.

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The ratio of the weight of a semi-truck trailer tire compared to the weight of a mobile home will be 51: 52.

The utilization of two or more additional numbers that compares is known as the ratio.

The weight of the semi-truck trailer tire is 102 pounds.

The weight of the mobile home is 104 pounds.

The ratio of the weight of a semi-truck trailer tire to a mobile home is given as.

Ratio = 102 / 104

Ratio = 51 / 52

Ratio = 51: 52

The ratio of the weight of a semi-truck trailer tire to a mobile home will be 51: 52.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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2 is 4/6, 8/12

3 is 2/4, 4/8

4 is 8/10, 16/20

5 is =

6 is >

7 is >

8 is =

9 is =

10 is <

11 is =

12 is >

Correct option is E. In line 24, "sense" most nearly means impression

The word 'sense' is used in the following extract from the passage: "There was simply the sense that she found wings and meant to use them". In this context sense implies an impression that the speaker got from looking at her. Thus the best answer is option E.

Important Strategy to Solve Comprehension Passages -

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The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

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Answer:

B. x =  -3 or x = 2

Step-by-step explanation:

There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.

2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60

60 possible arrangements for the 4 grade levels

60 * 6 (the number of ways to arrange 6 people) = 360

360 * 6 (the number of ways to arrange 6 people) = 2160

2160 * 6 (the number of ways to arrange 6 people) = 12,960

12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720

6,720 possible arrangements for the school dance committee.

The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.

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The expression is 8n – 3; The 100th term is 797

The nth term of an arithmetic sequence is given by:

an=a1+(100-1)d          ....[1]

where

a1  is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

Given the sequence:

5, 13, 21, 29, 37, 45, …

This is an arithmetic sequence with first term  = 5 and common difference(d) = 8

Since;

13-5 = 8,

21-13 = 8,

29-21 = 8  and so on....

We have to find the 100th term in the sequence

Substitute in [1] we have;

an=a1+(100-1)d

an=5+(n-1)8=5+8n-8 = 8n-3

Substitute the given values and n=100 we have;

a100= 800 - 3 = 797

Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;

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Answer:

x<4, not sure which graph it is tho, I can't see it clearly

Step-by-step explanation:

-4(-2x+8)-2x<-8

8x-32-2x<-8

8x-2x<-8+32

6x<24

x<4

Answer:

c

Step-by-step explanation:

Edge 2020 - 2021

Good luck on your quiz :)

Graph (a) represents an exponential decay.

Here, two graph are shown and we have to check which represent exponential decay.

What is exponential decay?

Exponential decay occurs when a quantity decreases by the same factor over equal intervals of time.

Now,

From the graph, we have

In graph (a), as x increases the function decreases.

Hence this graph shows exponential decay.

In graph (b), as x increases the function increases.

So, Graph (a) represents an exponential decay.

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