Imagine you are the Ghost of Pheidippides. Write the whole story of the Battle of Marathon from your point of view.


Make sure to include all the important events of the Battle

Answer:

angle 1 = 72 angle 2= 36 angle 3 = 18 angle 4=144

Step-by-step explanation:

take 90 and subtract 18

thats 72

72 is direct opposite of angle 1

so angle 1 =72

so the top triangle is 18+18=36

180-36=144

adjcent angle 4 is congruent so 4 =144

angle 2+4=180

angle 2 =36

angle 3=18 due to top triangle is congruent

Step-by-step explanation:

5.

y = 3

yes, that's it for this here too.

it means that any value for x is valid, and all have the assigned y value 3.

6.

remember, the usual equation for a line is

y = ax + b

"a" being the slope, "b" the y-intercept (the y-value when x = 0).

we see the y-value for x = 0 is 3. that is "b".

for the slope we need 2 points and calculate the x- and y- coordinate differences.

always look for points with integer coordinates.

I see e.g. (0, 3) and (3, 2).

x changes by +3 (from 0 to 3).

y charges by -1 (from 3 to 2).

the slope "a" = -1/+3 = -1/3

the equation is then

y = (-1/3)x + 3

7.

we do exactly the same things.

we see the y-value for x = 0 is +1. that is "b".

I see e.g. these points : (0, 1) and (3, 2).

x changes by +3 (from 0 to 3).

y changes by +1 (from 1 to 2).

the slope "a" is +1/+3 = 1/3.

the equation is

y = (1/3)x + 1

8.

and again the same things.

we see the y-value for x = 0 is +3. that is "b".

I see e.g. these points : (0, 3) and (-3, 0).

x changes by -3 (from 0 to -3).

y changes by -3 (from 3 to 0).

the slope "a" is -3/-3 = 3/3 = 1.

the equation is

y = x + 3

Answer: B and E

Step-by-step explanation:

Edge

Answer:

BE

Step-by-step explanation:

just took test

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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9514 1404 393

Answer:

  77.3 cm

Step-by-step explanation:

The distance FA is the diagonal of rectangle ABFE. We know the length AB, so we need to find the length BF. That is found using the trig relation ...

  cos(25°) = BC/BF

  BF = BC/cos(25°) ≈ (60 cm)/0.906308 ≈ 66.203 cm

Then the diagonal length FA is found using the Pythagorean theorem:

  FA = √(AB² +BF²)

  FA = √(40² +66.203²) ≈ √5982.79 ≈ 77.349 . . . cm

The diagonal length FA is about 77.3 cm.

Answer:

the second dimension 2D

The function f(x) = -6.7sin(x)5.8cos(x) represents a periodic function with a combination of sine and cosine terms. Tthe maximum value of the given function f(x) is 38.86, and the minimum value is -38.86.

1. To find the maximum and minimum values of this function, we need to examine the behavior of both the sine and cosine functions.

2. In the given function, the sine and cosine terms are multiplied together. Since the maximum absolute value of the sine function is 1 and the maximum absolute value of the cosine function is also 1, the maximum absolute value of their product is 1.

3. Therefore, the maximum value of the function occurs when the product of the sine and cosine terms is positive and equal to 1. In this case, the maximum value of the function is 6.7 * 5.8 = 38.86.

4. Similarly, the minimum value of the function occurs when the product of the sine and cosine terms is negative and equal to -1. In this case, the minimum value of the function is -6.7 * 5.8 = -38.86.

5. In summary, the maximum value of the given function f(x) is 38.86, and the minimum value is -38.86. These values are obtained when the product of the sine and cosine terms is equal to 1 and -1, respectively.

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6.45 written as a fraction is 645/100.

645/100 can also be written as 6 45/100

*proof*

100x6=600

600+45=645

So, therefore

6.45 as a mixed number is 6 45/100.

Hope this helps!

y[n] = {0, 1, 4, 2, -4, 0, 0}.

To determine y[n] = x[n] * h[n], we need to perform the convolution operation between the sequences x[n] and h[n].

Given x[n] = {1, 2, -2} and h[n] = {0, 1, 2, 3}, we can compute y[n] as follows:

For n = 0: y[0] = x[0] * h[0] = 1 * 0 = 0

For n = 1: y[1] = x[1] * h[0] + x[0] * h[1] = 2 * 0 + 1 * 1 = 1

For n = 2:y[2] = x[2] * h[0] + x[1] * h[1] + x[0] * h[2] = -2 * 0 + 2 * 1 + 1 * 2 = 4

For n = 3: y[3] = x[3] * h[0] + x[2] * h[1] + x[1] * h[2] = 0 * 0 + (-2) * 1 + 2 * 2 = 2

For n = 4: y[4] = x[4] * h[0] + x[3] * h[1] + x[2] * h[2] = 0 * 0 + 0 * 1 + (-2) * 2 = -4

For n = 5: y[5] = x[5] * h[0] + x[4] * h[1] + x[3] * h[2] = 0 * 0 + 0 * 1 + 0 * 2 = 0

For n = 6: y[6] = x[6] * h[0] + x[5] * h[1] + x[4] * h[2] = 0 * 0 + 0 * 1 + 0 * 2 = 0

Therefore, y[n] = {0, 1, 4, 2, -4, 0, 0}.

To sketch the sequence y[n], we plot the values of y[n] on the y-axis against the corresponding values of n on the x-axis:

n | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

y[n] | 0 | 1 | 4 | 2 | -4 | 0 | 0 |

The plot will consist of discrete points representing the values of y[n] at each value of n. Connect the points with lines to visualize the sequence.

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Answer:

7x - 4 + x = 12

7(2) - 4 + (2) = 12

True x = 2

Step-by-step explanation:

I used a calculator, pls let me know if im incorrect

Answer:wertyuiop[]\]

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Step-by-step explanation:

One reason for Emma's extreme hunger after working for five straight hours on her psychology paper without eating is that her blood glucose level has dropped. Option C.

Our body's supply of glucose is drained when we participate in lengthy mental or physical activity without eating, which lowers blood sugar levels. The brain receives messages from the stomach-dropping that indicate a need for food.

Emma's body sent hunger signals since the prolonged period of intense work had drained her glucose supplies. Several hormones, notably the appetite-stimulating hormone ghrelin, influence this hungry response. Emma's hunger in this situation is mostly caused by the decline in blood glucose levels.

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The complete question is:

Emma worked for five straight hours on her psychology paper and did not stop to eat. After finishing her paper she felt extremely hungry. One reason for her hunger is that her:

A. leptin levels are high

B. blood glucose level has increased

C. blood glucose level has dropped

D. ghrelin production is low

An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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Answer:

C) 15.5 units

Step-by-step explanation:

1. Total person-years of observation = 48 + 20 + 30 + 730 = 828 person-years.

2. The incidence rate of breast cancer in this population is approximately 1,449.28 cases per 100,000 person-years of observation.

1- To calculate the number of person-years of observation, we need to consider the duration of follow-up for each individual and sum them up.

For the women who developed breast cancer:

12 women were followed for 4 years each, totaling 12 * 4 = 48 person-years.

For the women who remained healthy but were lost to follow-up:

10 women were followed for 2 years each, totaling 10 * 2 = 20 person-years.

For the women who died of heart disease:

5 women were followed for 6 years each, totaling 5 * 6 = 30 person-years.

For the remaining women who remained healthy and were followed for 10 years:

100 - 12 - 10 - 5 = 73 women were followed for 10 years each, totaling 73 * 10 = 730 person-years.

Total person-years of observation = 48 + 20 + 30 + 730 = 828 person-years.

2- The incidence rate can be calculated by dividing the number of new cases (12 women who developed breast cancer) by the total person-years of observation (828 person-years) and multiplying by a constant (e.g., 100,000) to express it per 100,000 person-years.

Incidence rate = (Number of new cases / Total person-years) * 100,000

Incidence rate = (12 / 828) * 100,000

Incidence rate ≈ 1,449.28 per 100,000 person-years.

Interpretation: The incidence rate of breast cancer in this population is approximately 1,449.28 cases per 100,000 person-years of observation.

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The table becomes:MonthAprilMayJuneAds onSocial Media12825696Ads onSearch Sites484836

The ratio between the number of ads on social media to the number of ads on search sites that Li buys ads for a clothing brand is always 8: 3. Given that, we can complete the table.MonthAprilMayJuneAds onSocial Media12825696Ads onSearch Sites4896.

To get the number of ads on social media and the number of ads on search sites, we use the ratios given and set up proportions as follows.

Let the number of ads on social media be 8x and the number of ads on search sites be 3x. Then, the proportions can be set up as8/3 = 128/48x = 128×3/8x = 48Similarly,8/3 = 256/96x = 256×3/8x = 96.

Similarly,8/3 = 96/36x = 96×3/8x = 36

Therefore, the table becomes:MonthAprilMayJuneAds onSocial Media12825696Ads onSearch Sites484836.

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There are 18 blocks in the first row

Calculate the number of blocks on the first row

The ruin is given as:

Ruin = 49

The common difference is given as:

d = -2

The number of block on each row is then represented as:

Blocks = 48 - 2n

Where n represents the number of rows.

In this case, the first row would have a value of n = 15

So, we have:

Blocks = 48 - 2 * 15

Evaluate

Blocks = 18

Hence, there are 18 blocks in the first row

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Though a time series could be defined more widely, the common simplification is required for analysis is discrete time.

Time series analysis is a specialized method of analyzing a series of data points collected over a period of time. In time series analysis, analysts record data points at consistent intervals over a set period of time, rather than recording data points intermittently or randomly.

What makes time series data different from other data is that analysis can show how a variable changes over time. In other words, time is a key variable that dictates how the data is adjusted over the course of the data points and the final result. It provides an additional source of information and a specified ordering of dependencies between data.

Time series analysis typically requires a large number of data points to ensure consistency and reliability. Using a large data set ensures a representative sample size and allows the analysis to cut out noisy data. Additionally, time series data can be used for forecasting. Predict future data based on historical data.

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Answer:

D. 44.79

Step-by-step explanation:

\(\frac{43}{96}\) who worked 8 or more years said that e-mail was their favorite communication method.

\(\frac{43}{96}\) ≈ \(\frac{44.79}{100}\)

So around 44.79% who have worked 8 years or more said that email were their preferred communication method. Our answer is D. 44.79.

Answer:

44.79%

Step-by-step explanation:

Answer:

I'm think it is 40hours (or 1 1/2 days)

Answer:

1. x=−11

2. No solution

3.x=5t−28

4.y=-11

Step-by-step explanation:

Answer:

1. x=11

2.p=8

3.5t-21-x+7

4. y=8

Step-by-step explanation:

1. 3(1-3x)=2(4x+7)

3-9x=8x+14

x=11

2.8p+4(4p-3)=4(6p+4)-4

8p+16p-12=24p+24-4

25p-12=24p-4

p=8

3. -3(t-1)+8(t-3)=6x+7-5x

-3t+3+8t-24=6x+7-5x

5t-21=x+7

4. 3(2-3y)=2(-4y+7)

6-9y=-8y+14

y=8

Answer:

25

solution

50=3x

or, 50/3=x

or, x=16.66

hence,imran father will 16 years

Answer:

\( \displaystyle a) \: {x}^{ \circ} = 21.8 ^{ \circ} \)

Step-by-step explanation:

we are given opposite and adjacent

we want to figure out x°

remember that,

\( \displaystyle \: \tan( \theta) = \frac{opp}{adj} \)

where our opp is 5 and adj is 12.5

let \(\theta\) be x°

so

\( \displaystyle \: \tan( {x}^{ \circ} ) = \frac{5}{12.5} \)

\( \displaystyle \: {x}^{ \circ} = \arctan \left( \frac{5}{12.5} \right)\)

by using calculator

\( \displaystyle \: {x}^{ \circ} = 21.8\)

hence,

our answer is a

The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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Answer:

79.2% (to the nearest tenth)

Step-by-step explanation:

use the percent change formula:

PC = [ (difference between initial value and final value) ÷ initial value] x 100

= [(77-16) ÷77] x 100

= 79.22077922...

= 79.2% (to the nearest tenth)

The possible zeros of the function f(x)=x³- 4x² + 5x + 6 are

To find the possible zeros of the function f(x)=x³- 4x² + 5x + 6  using the Rational Zeros Theorem, we need to consider the factors of the constant term (6) divided by the factors of the leading coefficient (1).

The factors of 6 are: ±1, ±2, ±3, ±6

The factors of 1 (leading coefficient) are: ±1

Using the Rational Zeros Theorem, the possible zeros can be obtained by taking all possible combinations of the factors and their negations. Therefore, the possible zeros are:

±1, ±2, ±3, ±6

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Answer:

21

Step-by-step explanation:

This triangle is isosceles ( I added a photo of my solution)

Using linear approximation, the approximate value of f(9.001) is 36.018.

Linear approximation is the process of approximating the value of a function by using the tangent line at a particular point.

To approximate the value of 9.001 using linear approximation, we need to find the tangent line to the function f(x) = x^2 at x = 9 and then evaluate it at x = 9.001.

The equation of the tangent line to f(x) = x^2 at x = 9 is given by: y - 81 = 18(x - 9) y = 18x - 135 Now, we can use this equation to approximate the value of f(9.001) as follows: f(9.001) ≈ y(9.001) f(9.001) ≈ 18(9.001) - 135 f(9.001) ≈ 36.018.

Therefore, using linear approximation, the approximate value of f(9.001) is 36.018.

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As per the borrowed amount, the value of IRR is 6.40%

The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.

Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.

Now, we have to calculate the value of IRR,

The general form of the IRR formula is written as,

=> NPV = \(\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0\)

where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.

Here we apply the values on it, then we get,

=> \(NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000\)

When we simplify this one then we get,

=> Internal Rate of Return = 6.402%

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