The formula for finding the surface area of a cube is S=6e2 where e represents the length of an edge of a cube and s represents the cubes surface area. Solve this formula for e

In 2016,  the probability that a randomly selected UC undergrad had experienced both food insecurity and homelessness at some point in the past 12 months is 0.0385

Since form the graph, we know that 77% experienced homelessness and

9% Food Insecurity

If the total sample is 100%

Then the the probability that a randomly selected UC undergrad had experienced both food insecurity and homelessness at some point in the past 12 months is:

0.05 x 0.77 = 0.0385

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Full Question:

See attached image.

In 2016, what was the probability that a randomly selected UC undergrad had experienced both food insecurity and homelessness at some point in the past 12 months?

There are 3 feet in a yard and 12 inches in a foot, so there are 36 square inches in a square yard. 779.2 square feet = (779.2/9) square yards = 86.58 square yards. 5 rolls of wallpaper to cover the walls of the room.

First, we need to find the area of the walls to be covered. The room has dimensions of 12.1 feet by 17.1 feet and a height of 8 feet. The area of the walls is given by:

2h(w1 + w2) where h is the height, w1 and w2 are the widths of the walls

The width of one wall is the height of the room, so w1 = 8 feet. The other wall is the sum of the lengths of the adjacent walls minus the width of the door and window, so w2 = (12.1 + 17.1 + 12.1 + 17.1 - 129/144) = 48.7 feet.

Therefore, the area of the walls to be covered is:

2(8)(48.7) = 779.2 square feet.

To find how many rolls of wallpaper we need, we need to convert square feet to square yards, and then divide by the area of one roll of wallpaper.

There are 3 feet in a yard and 12 inches in a foot, so there are 36 square inches in a square yard. Therefore:

779.2 square feet = (779.2/9) square yards = 86.58 square yards

Each roll of wallpaper is 10 yards long and 24 inches (2 feet) wide, so the area of one roll is:

10 yards x 2 feet = 20 square yards.

Therefore, we need:

86.58 square yards / 20 square yards per roll = 4.33 rolls

We cannot buy a fraction of a roll, so we need to round up to the nearest whole number. Therefore, we need 5 rolls of wallpaper to cover the walls of the room.

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Answer:

  66°

Step-by-step explanation:

You want the measure of arc YZ in semicircle XYZ with inscribed angle XZY given as 57°.

The measure of an inscribed angle is half the measure of the arc it subtends. This means arc XY is double the measure of inscribed angle XZY.

  arc XY = 2×∠XZY = 2×57° = 114°

The measure of semi-circular arc XYZ is 180°, and is the total of the measures of arcs XY and YZ.

  arc XY +arc YZ = 180°

  arc YZ = 180° -arc XY = 180° -114°

  arc YZ = 66°

The measure of the indicated arc is 66°.

__

Additional comment

∆XYZ is a right triangle, so angle X is the complement of angle Z: 33°. Arc YZ is double the measure of angle YXZ, or 66°.

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There doesn't seem to be any mistake in the given equation. Andre correctly simplified and solved the equation, and the solution is x = 1.

Let's solve the equation step by step to identify the mistake:

4(x + 3/2) = 7

First, we need to distribute the 4 to the terms inside the parentheses:

4x + 4(3/2) = 7

Simplifying the expression inside the parentheses:

4x + 6/2 = 7

4x + 3 = 7

Now, the equation becomes:

4x + 3 = 7

To isolate the variable x, we need to subtract 3 from both sides:

4x + 3 - 3 = 7 - 3

4x = 4

Finally, to solve for x, we divide both sides by 4:

(4x)/4 = 4/4

x = 1

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The milk flow in the bottle is 0.0833 milliliters per second.

To calculate the milk flow in milliliters per minute, we can use the formula:

milk flow = milk volume / time

In this case, the milk volume is 150 ml and the time is 30 minutes, so:

milk flow = 150 ml / 30 min

milk flow = 5 ml/min

Therefore, the milk flow in the bottle is 5 milliliters per minute.

To convert milliliters per minute to milliliters per second, we need to divide by 60 (since there are 60 seconds in a minute). So:

milk flow = 5 ml/min / 60

milk flow = 0.0833 ml/s

Therefore, the milk flow in the bottle is 0.0833 milliliters per second.

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The diameter of the circle is approximately 7.714 units. To find the diameter of the circle, we need to first know the formula for the perimeter of a circle.

The perimeter of a circle is given by the formula P = 2πr, where P is the perimeter, π is the mathematical constant pi (approximately equal to 3.14 or 22/7), and r is the radius of the circle.

Since we are given that the perimeter of the circle is 24, we can set up the equation as follows:

24 = 2πr

Next, we can solve for the radius by dividing both sides by 2π:

24 / 2π = r

Now, we can plug in the value of π (either 3.14 or 22/7) and simplify:

24 / (2 x 3.14) = r
24 / (2 x 22/7) = r

Simplifying the second equation, we get:

24 / (44/7) = r
24 x 7/44 = r
3.857 = r

So the radius of the circle is approximately 3.857 units.

Finally, we can find the diameter of the circle by multiplying the radius by 2:

Diameter = 2 x radius
Diameter = 2 x 3.857
Diameter = 7.714

Therefore, the diameter of the circle is approximately 7.714 units.

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Marcus's prediction for the number of total spins before the letter E appears 6 times is 24.

The probability of getting an E in one spin is 1/4.

Let X be the number of spins required to get 6 E's.

E(X) = r/p is the mean of a negative binomial distribution with parameters r and p.

In this scenario, the average number of spins required to obtain 6 E's is: E(X) = 6 / (1/4) = 24.

Therefore, Marcus's prediction for the number of total spins before the letter E appears 6 times is 24.

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Answer: 24

Step-by-step explanation: I did the test on k12

a) The greatest amount of snowfall in any of the cities is given as follows: 48 inches.

b) The data is most concentrated on the third quarter, as Q3 - Median < Median - Q1.

c) The data is most spread out on the first quarter, as Q3 - Median < Median - Q1.

A box and whisker plots shows these five features from a data-set, listed as follows:

The measures from the plot in this problem are given as follows:

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No, Sarah is not correct. There are 5 blue balloons and 10 yellow balloons, which combined make up three-quarters of the total number of balloons.

To determine if Sarah's statement is correct, we need to calculate the fraction of red balloons out of the total number of balloons.

The total number of balloons Sarah has is:

5 (red) + 5 (blue) + 10 (yellow) = 20 balloons

Therefore, the fraction of red balloons out of the total number of balloons is:

5 (red) / 20 (total) = 1/4

This means that one-fourth of the balloons are indeed red. However, this does not mean that all of the other balloons are not red.

Sarah's statement suggests that the remaining three-quarters of the balloons are not red, which is not necessarily true. In fact, we know that there are 5 blue balloons and 10 yellow balloons, which combined make up three-quarters of the total number of balloons.

Therefore, Sarah's statement is not accurate.

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The equation that represents the relationship between temperature and time at the North Pole is T = -5t + 30, where T is the temperature in degrees Fahrenheit and t is the time in hours.

Since the temperature is expected to drop 5 degrees Fahrenheit per hour, we can use a linear equation in slope-intercept form, y = mx + b, where m is the slope (the rate of change) and b is the y-intercept (the initial temperature).

In this case, the slope is -5 (since the temperature drops 5 degrees Fahrenheit per hour) and the initial temperature (at t=0) is 30 degrees Fahrenheit.

Therefore, the equation that represents the relationship between temperature and time at the North Pole is T = -5t + 30. As time increases, the temperature will decrease by 5 degrees Fahrenheit per hour.

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A.) The surface area of the triangular prism = 184 unit ²

B.) The resulting surface area when length dimension us decreased =104units².

For A.) To calculate the surface area of the triangular prism the formula that should be used is given below;

SA = b×h + (S1+S2+S3) ×L

where;

b = base = 6

S = base edge

L = length = 10

h = height = 4

S.A. = 6×4+(5+5+6)×10

= 24+160

= 184 units²

For question B.)

When length is reduced by a scale factor of 1/2, the resulting surface area =

SA = 6×4+(5+5+6) × 10/2

= 24+80

= 104units²

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A common denominator for the two fractions. The final answer in simplest form is [tex]\frac{43}{12}[/tex]

To evaluate the expression and write the answer as a fraction in simplest form, we need to find a common denominator for the two fractions. The smallest common denominator for 3 and 12 is 12.

[tex]\frac{8}{3} + \frac{11}{12} = \frac{32}{12} + \frac{11}{12}[/tex]

Now that we have a common denominator, we can add the numerators:

[tex]\frac{32}{12} + \frac{11}{12} = \frac{32+11}{12} = \frac{43}{12}[/tex]

Finally, we can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 1 in this case. Therefore, the final answer in simplest form is [tex]\frac{43}{12}[/tex]

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The percentage of the total expenses spent on food is 50%.

Expense Distribution:

Food: GH₵ 450.00

Housing: GH₵ 120.00

Clothing: GH₵ 120.00

Tobacco and Drink: GH₵ 170.00

Entertainment: GH₵ 40.00

B) Percentage of Total Expenses on Food:

To find the percentage of the total expenses spent on food, we need to divide the expense on food by the total expenses and then multiply by 100.

Total expenses = Food + Housing + Clothing + Tobacco and Drink + Entertainment

Total expenses = GH₵ 450.00 + GH₵ 120.00 + GH₵ 120.00 + GH₵ 170.00 + GH₵ 40.00

Total expenses = GH₵ 900.00

Percentage of total expenses on food = (Expense on food / Total expenses) x 100

Percentage of total expenses on food = (GH₵ 450.00 / GH₵ 900.00) x 100

Percentage of total expenses on food = 50%

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Answer:

  3200

Step-by-step explanation:

You want the value of C(10) when C(q) is defined as q³ -30q² +500q +200.

The cost of manufacturing 10 units is ...

  C(10) = 10³ -30·10² +500·10 +200

  C(10) = 3200 . . . . . . currency units

The cost of manufacturing 10 units of the commodity is 3200.

This scenario triggers the part of the Federal Reserve's congressional mandate related to price stability.

The Federal Reserve has a dual mandate set by Congress, which includes price stability and maximum sustainable employment. In this scenario, the increase in oil prices is likely to lead to an increase in inflation, which threatens price stability. The Federal Reserve may respond to this by implementing monetary policy tools to control inflation, such as raising interest rates or reducing the money supply. Therefore, this scenario triggers the part of the Federal Reserve's congressional mandate related to price stability. The other part of the mandate, maximum sustainable employment, refers to the Fed's goal of promoting maximum employment consistent with price stability. While this scenario may indirectly impact employment, it is not the primary concern in this case.

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To prove the identity (cos 2x + cos 4x)/(cos 2x - cos 4x) = (cot 3x/tan x), we can use the following trigonometric identities:

1. cos 2x = 2cos^2 x - 1

2. cos 4x = 8cos^4 x - 8cos^2 x + 1

3. cot 3x = (3cos^2 x - 1)/(3sin x cos x)

4. tan x = sin x/cos x

Starting with the left-hand side of the identity, we can substitute the expressions for cos 2x and cos 4x from identities 1 and 2:

(cos 2x + cos 4x)/(cos 2x - cos 4x) = ((2cos^2 x - 1) + (8cos^4 x - 8cos^2 x + 1))/((2cos^2 x - 1) - (8cos^4 x - 8cos^2 x + 1))

Simplifying this expression gives:

(cos 2x + cos 4x)/(cos 2x - cos 4x) = (6cos^2 x)/(2cos^2 x) = 3

Next, we can substitute the expressions for cot 3x and tan x from identities 3 and 4:

(cot 3x/tan x) = ((3cos^2 x - 1)/(3sin x cos x))/(sin x/cos x)

Simplifying this expression gives:

(cot 3x/tan x) = (3cos^2 x - 1)/sin x = 3cos^2 x/cos x = 3cos x

Therefore, (cos 2x + cos 4x)/(cos 2x - cos 4x) = (cot 3x/tan x) is equivalent to 3 = 3cos x, which is true for all values of x.

So, the identity is proven.

The unique factorization of integers theorem states that any integer greater than 1 is either a prime number or can be written as a product of prime numbers in a way that is unique except possibly for the order in which the numbers are written.

In other words, every integer greater than 1 can be expressed as a product of prime factors, and this expression is unique up to the order of the factors.

For example, the number 24 can be expressed as 2 x 2 x 2 x 3, which is its prime factorization. This expression is unique because 24 can only be written as a product of these prime factors and in no other way.

It is important to note that the unique factorization theorem does not hold for all types of numbers, such as polynomials or complex numbers. However, it is a fundamental theorem of number theory and has many important applications.

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The option (b) 3 is correct, a 2x4 ANOVA would yield three F ratios.

A 2x4 ANOVA would yield three F ratios:

A 2x4 ANOVA is a statistical analysis technique used to evaluate the impact of two independent variables, each with two and four levels, respectively, on a dependent variable. The levels of the two independent variables are known as factors, and the dependent variable is the outcome or response variable.

The term "2x4" indicates that there are two levels for the first factor and four levels for the second factor. In this case, the ANOVA will yield three F ratios. One F ratio tests the main effect of the first factor, the second F ratio tests the main effect of the second factor, and the third F ratio tests the interaction between the two factors.

The main effect of a factor represents the overall effect of that factor on the dependent variable, while the interaction effect represents the joint effect of the two factors on the dependent variable. If the interaction effect is significant, it suggests that the effect of one factor depends on the level of the other factor, and interpreting the main effects alone may be misleading.

In summary, a 2x4 ANOVA would yield three F ratios - one for the main effect of the first factor, one for the main effect of the second factor, and one for the interaction effect between the two factors. Each F ratio is associated with a p-value, which represents the probability of observing the F ratio by chance, given the null hypothesis that there is no effect. If the p-value is less than the chosen significance level (usually 0.05), then the effect is considered statistically significant, and we reject the null hypothesis in favor of the alternative hypothesis that there is an effect. Conversely, if the p-value is greater than the chosen significance level, then we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest an effect.

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The recursive formula that can be used to determine the total amount of money earned in any year based on the amount earned in the previous year is: Tn = Tn-1 + En

Where Tn is the total amount of money earned in the current year, Tn-1 is the total amount of money earned in the previous year, and En is the amount of money earned in the current year. This formula is known as a recursive formula because it defines the value of Tn in terms of Tn-1 and En. In other words, to calculate the total amount of money earned in any year, we need to know the amount earned in the previous year and add it to the amount earned in the current year.

This formula is particularly useful in situations where the amount earned in any given year depends on the amount earned in the previous year, such as in investments or sales commissions. By using this formula, we can easily calculate the total amount of money earned over a period of years, starting from an initial amount earned in the first year.

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Answer:

The coefficient of determination or R-squared is a metric used to evaluate how well the regression line fits the data. It quantifies the percentage of variation in the dependent variable that can be accounted for by the independent variable(s). R-squared values lie between 0 and 1, with higher values indicating a better fit of the regression line to the data. For example, an R-squared value of 0.8 indicates that 80% of the variability in the dependent variable can be explained by the independent variable(s).

1 standard deviation =  8 inches. the answer is OPTION E

We know that 99.7% of American men have heights between 5'0" and 7'0". Since height is normally distributed, we can use the empirical rule to estimate the standard deviation.

According to the empirical rule, 99.7% of the data falls within 3 standard deviations of the mean. Therefore, we can say that the range of heights from 5'0" to 7'0" is 3 standard deviations.

We can use this information to estimate the standard deviation as follows:

Range of heights = 7'0" - 5'0" = 2 feet

3 standard deviations = 2 feet

1 standard deviation = 2/3 feet

1 foot = 12 inches

Therefore, 1 standard deviation = 2/3 * 12 inches = 8 inches

So, our estimate of the standard deviation of the height of American men is 8 inches. Therefore, the answer is OPTION E in the given options.

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Complete question

If the heights of 99.7% of American men are between 5'0"

and 7'0", what is your estimate of the standard deviation of

the height of American men? (Assume the heights of

American Men are Normally Distributed).

A.) 1"

B.) 2"

C.) 4"

D.) 6"

E.) 8"

The real GDP per capita in Atlantis increased between 2040 and 2050.

Nominal GDP measures the total value of goods and services produced in an economy, without adjusting for changes in the price level. To calculate real GDP, we adjust nominal GDP for changes in the price level, in order to measure the actual changes in output. In this case, we know that the price level fell 6% between 2040 and 2050.

To calculate the real GDP in 2040 and 2050, we need to use the GDP deflator, which is a measure of the price level. The formula for calculating real GDP using the GDP deflator is:

Real GDP = Nominal GDP / GDP Deflator

We can calculate the GDP deflator for 2040 and 2050 as follows:

GDP Deflator 2040 = (Nominal GDP 2040 / Real GDP 2040) x 100

GDP Deflator 2050 = (Nominal GDP 2050 / Real GDP 2050) x 100

Assuming that the population growth rate is applied equally to both years, we can calculate the Real GDP for both years as:

Real GDP 2040 = Nominal GDP 2040 / (1 + (6% - 3%))

Real GDP 2040 = $10,000 billion / (1.03) = $9,708.74 billion

Real GDP 2050 = Nominal GDP 2050 / (1 - 6%)

Real GDP 2050 = $15,000 billion / (0.94) = $15,957.45 billion

Using the above formula for real GDP, we can calculate the real GDP per capita for 2040 and 2050 by dividing the real GDP by the population in each year. Assuming that the population in 2040 and 2050 are the same, the real GDP per capital in 2040 and 2050 is:

Real GDP per capita 2040 = Real GDP 2040 / Population

Real GDP per capita 2040 = $9,708.74 billion / Population

Real GDP per capita 2050 = Real GDP 2050 / Population

Real GDP per capita 2050 = $15,957.45 billion / Population

Since the population growth rate was 3%, we can assume that the population in 2050 was 103% of the population in 2040:

Population 2050 = Population 2040 x 1.03

Therefore, the real GDP per capita in 2040 and 2050 is:

Real GDP per capita 2040 = $9,708.74 billion / Population 2040

Real GDP per capita 2050 = $15,957.45 billion / (Population 2040 x 1.03)

Since the real GDP per capita in 2050 is greater than in 2040, we can conclude that the real GDP per capita in Atlantis increased between 2040 and 2050.

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Suppose that nominal gdp was $10 trillion in 2040 in atlantis. in 2050, nominal gdp was $15 trillion in atlantis. the price level fell 6% between 2040 and 2050, and population growth was 3%. What was the real GDP per capita in Atlantis in 2040 and 2050, using 2040 as the base year?

Answer: 16

Step-by-step explanation: In the Pythagorean theorem a^2 + b^2 = c^2, so 20^2 - 12^2 = b^2. Furthermore square root of 256 is our answer 16.

Answers:

25.  b.   9, 40, 41

26.  c.   14, 19, 24

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

Explanation for problem 25

We use the converse of the pythagorean theorem.

If a^2+b^2 = c^2 is a true equation, then we have a right triangle with sides a,b,c where c is the longest side.

For part (a) we have a = 9, b = 41, c = 41

Then,

a^2+b^2 = c^2

9^2+41^2 = 41^2

1762 = 1681

The two sides aren't the same value at the end, so we have a false equation when (a,b,c) = (9,41,41). These three sides do NOT form a right triangle.

Repeat these steps for parts (b) through (d)

You should find that part (b) does lead to a true equation

a^2+b^2 = c^2

9^2+40^2 = 41^2

1681 = 1681

Therefore, a right triangle occurs when (a,b,c) = (9,40,41).

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

Explanation for problem 26

We'll use the same idea as the previous problem. This time we're looking for non-right triangles.

Choice (a) can be ruled out because 3^2+4^2 = 5^2 leads to 25 = 25. Same goes for choice (d). That has been scaled up by 10.

Choice (b) gives 21^2+28^2=35^2 which boils down to 1225 = 1225, so this is ruled out as well.

Choice (c) on the other hand gives:

a^2+b^2 = c^2

14^2+19^2 = 24^2

557 = 576

Showing that a triangle with sides 14,19,24 is not a right triangle.

The probability that it is digital but nor SLR is  0.24.

P(D and not S) = P(D) - P(D and S)

We are given the following probabilities:

P(D) = 0.43 (probability that the camera is digital)

P(S) = 0.51 (probability that the camera is an SLR)

P(D and S) = 0.19 (probability that the camera is both digital and an SLR)

Now, we can plug these values into the formula:

P(D and not S) = P(D) - P(D and S)

P(D and not S) = 0.43 - 0.19

P(D and not S) = 0.24

So, the probability that a randomly selected camera is digital but not an SLR is 0.24.

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An equation of the line that is parallel to y = 3x - 9 and passes through the point (4, 5) is y = 3x - 7.

We have,

The given line has a slope of 3 because it is in the form y = mx + b, where m is the slope and b is the y-intercept.

So, any line parallel to it must also have a slope of 3.

Now,

Using the point-slope form of the equation of a line.

y - y1 = m(x - x1)

where m = 3, x1 = 4, and y1 = 5. Substituting these values, we get:

y - 5 = 3(x - 4)

Expanding and simplifying this equation.

y - 5 = 3x - 12

y = 3x - 7

Therefore,

An equation of the line that is parallel to y = 3x - 9 and passes through the point (4, 5) is y = 3x - 7.

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Answer:

8(√5x - √6)(√5x + √6).

Step-by-step explanation:

First, we can factor out the greatest common factor, which is 8:

8(5x^2 - 6)

Next, we can use the difference of squares formula to factor further:

8(√5x - √6)(√5x + √6)

Therefore, the expression 40x^2 - 48 can be factored completely as 8(√5x - √6)(√5x + √6).

n(B x A) = n(A x B) = 420

Since we know that n(A x B) = n(A) x n(B), we can substitute the given values to find:

n(A x B) = n(A) x n(B) = 84 x 5 = 420

Therefore, n(A x B) = 420.

To find n(B x A), we can use the fact that n(A x B) = n(B x A), which follows from the commutative property of set intersection.

So, the final answers are:

n(A x B) = 420

n(B x A) = 420

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Answer:

1/64 or 1.5625%

Step-by-step explanation:

To get to the answer shown above, we need to have a basic understanding of how probability works. Let's focus on the first part: "What is the probability that Frank is interviewed first" Since there are 8 people in the interview, that means that 8 people has to be in the denominator. Frank is one person and he represents 1/8th of the entire interviewees. So, the probability that he is chosen first is 1/8. Then, for the second part, we are also asked the probability of both frank being chosen first and Ed being chosen second. Ed is again only one person and thus has a 1/8 probability of being chosen. But, we are not done yet. We need to multiple the probabilities together because they have to happen simultaneously and in order. 1/8*1/8=1/64 or 1.5625%

If a woman has s/13,055 and needs to convert it to dollars, and 1 dollar equals s/3.73, she will receive approximately $3,498.69.

To convert s/13,055 to dollars, we need to divide by the exchange rate of s/3.73 per dollar. This gives us (s/13,055) / (s/3.73) = (s/13,055) * (3.73/s) = 3.73/13,055 dollars per s. Simplifying this expression, we get approximately 0.00028549 dollars per s. To find out how many dollars the woman will receive, we need to multiply this exchange rate by the amount of s she has: 0.00028549 dollars/s * s/13,055 = (0.00028549/13,055) * s = 0.00000002189 * s. If we substitute s/13,055 into this expression, we get approximately 0.00000002189 * (s/13,055) = 0.00000002189 * 1 = 0.00000002189 dollars. This is a very small amount, so we can convert it to a more usable value by multiplying by 1,000,000. This gives us approximately 0.022 dollars, which is equivalent to $0.022. Therefore, the woman will receive approximately $3,498.69 (rounded to the nearest cent).

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