Michell has a round lamp to which she wants to add beads the diameter is 12.2 inches what is the circumference

The Alternative Hypothesis, which suggests that the average daily attendance is at least 20,000. The null hypothesis, on the other hand, contradicts this claim and proposes that the average daily attendance is less than 20,000.

Null Hypothesis and Alternative Hypothesis are the two main types of statistical hypotheses in hypothesis testing.

These hypotheses are also known as H0 and H1, respectively. In this question, the amusement park claims that the average daily attendance is at least 20,000.

Hence, the null and alternative hypotheses are as follows.

Null Hypothesis (H0):

The average daily attendance of the amusement park is less than 20,000.

Alternative Hypothesis (H1):

The average daily attendance of the amusement park is at least 20,000.

Note that the claim is the Alternative Hypothesis, which suggests that the average daily attendance is at least 20,000.

The null hypothesis, on the other hand, contradicts this claim and proposes that the average daily attendance is less than 20,000.

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The number sentence 4x7 = (4x3) + (4x4) demonstrates the distributive property.

The distributive property states that for any numbers a, b, and c, the expression a × (b + c) is equal to (a × b) + (a × c). In the given number sentence, we have 4 × 7 on the left side, which can be rewritten as (4 × 3) + (4 × 4) on the right side.

By applying the distributive property, we distribute the factor of 4 to each term inside the parentheses, resulting in (4 × 3) + (4 × 4). This simplifies to 12 + 16, which equals 28.

Therefore, the number sentence 4x7 = (4x3) + (4x4) demonstrates the distributive property, which allows us to break down the multiplication and distribute it over addition or subtraction.

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Some energy workers are considered to work in the agriculture industry because their work relates to providing power and energy solutions specifically tailored for agricultural processes.

These employees are engaged in the creation and execution of environmentally-friendly energy systems specifically designed for agricultural operations and farming facilities.

One possible rephrased sentence could be: In order to produce renewable energy for farming activities such as irrigation and utilizing machinery, farmers could prioritize the implementation of solar panels, wind turbines, or biomass systems.

Moreover, professionals who work with energy in the agricultural sector can focus on enhancing energy effectiveness, incorporating intelligent farming techniques, or incorporating mechanisms for storing energy.

Their primary objective is to advocate for sustainable farming methods by decreasing dependence on conventional energy sources and advancing ecologically sound alternatives.

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To factor the expression, we should first apply difference of squares method. This method is suitable because expression can be written as the difference of two perfect squares, namely (7x^3)^2 - (5y)^2.

The expression 49x^7 - 25y^2 can be rewritten as (7x^3)^2 - (5y)^2, which represents the difference of two perfect squares. The difference of squares method states that for any two perfect squares, say a^2 - b^2, it can be factored as (a + b)(a - b).

In this case, a = 7x^3 and b = 5y. Applying the difference of squares formula, we can factor the expression as follows:

49x^7 - 25y^2 = (7x^3 + 5y)(7x^3 - 5y).

Thus, the first method of factoring to be used for the given expression is the difference of squares method.

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So, option (d) is the correct answer. A triangle with coordinates F(−2, 3), G(−4, 1), and H(−2, −2) is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). The correct rule for the translation is (x, y) → (x - 2, y - 3).

Let's find the distance and direction that the triangle is translated. The coordinates of the image are (0,0), (-2,-2) and (0,-5). We are going to get these coordinates from the original coordinates by applying a translation. Consider the vertex F first.The translation takes F to F'. In other words, we go from (-2,3) to (0,0).What did we do to get from F to F'?We subtracted 2 from the x-coordinate and 3 from the y-coordinate. In other words, we applied the rule(x, y) → (x - 2, y - 3)Thus the rule for the translation is (x, y) → (x - 2, y - 3). Therefore, option (d) (x, y) → (x - 2, y - 3) is the correct answer.

First of all, we will plot the coordinates of the initial and final triangle on the coordinate axis and name the initial triangle as FGH and the final triangle as F'G'H'As per the question, the coordinates of initial triangle are F(-2,3), G(-4,1) and H(-2,-2)The coordinates of final triangle are F'(0,0), G'(-2,-2) and H'(0,-5)Now let's find out the horizontal and vertical translation of the initial triangle to get the final triangle. To get F', we have to move 2 units in the right direction and 3 units in the upward direction. Let's see how this can be calculated:F to F' will move 2 units in the right direction and 3 units in the upward direction.-2 → 0 (2 units to the right)-3 → 0 (3 units upward)Therefore, we can say that the rule of translation is (x,y) → (x-2,y-3). So, option (d) is the correct answer.

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Here are two independent variables that could affect the cost of school supplies:1. Inflation Rate: The inflation rate is a measure of the overall increase in prices over time.

It can impact the cost of various goods and services, including school supplies. If the inflation rate is high, the prices of school supplies may increase, leading to higher costs for purchasing these items.

2. Demand for School Supplies: The demand for school supplies can also influence their cost. Probability of Higher demand typically leads to increased prices, as suppliers may adjust their prices to match the demand. Factors such as back-to-school seasons, educational policies, and population growth can affect the demand for school supplies.

By considering the inflation rate and the demand for school supplies as independent variables, we can better understand how these factors can impact the cost of school supplies.

However, it's important to note that there could be other variables that can also affect the cost, such as production costs, supply chain disruptions, and changes in government policies related to education or trade.

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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies?

In triangle ΔDEF, we are given that ∠F = 90°, EF = 4.9 feet, and DE = 8.3 feet. We need to find the measure of ∠D to the nearest degree.Since ∠F is a right angle (∠F = 90°), triangle ΔDEF is a right triangle.

In a right triangle, the sum of the measures of the two acute angles is always 90°.

Therefore, ∠D + ∠E = 90°.

Since ∠F = 90° and the sum of the angles in a triangle is 180°, we can determine ∠E by subtracting the measures of ∠F and ∠D from 180°.

∠E = 180° - 90° - ∠D

∠E = 90° - ∠D

Now we can use the trigonometric ratio in a right triangle to find the measure of ∠D.

tan(∠D) = opposite/adjacent = EF/DE

tan(∠D) = 4.9/8.3

Using a calculator or trigonometric table, we can find the inverse tangent (arctan) of this ratio:

∠D ≈ arctan(4.9/8.3)

∠D ≈ 32.23°

Therefore, the measure of ∠D to the nearest degree is 32°.

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Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.

We have,

Let's proceed by assuming a general value for the ambient temperature. We'll use 20°C as an approximation.

Given:

V = 7274.69 km/h

T = 20°C = 20 + 273.15 K = 293.15 K (conversion to Kelvin)

c_p = 1005 J/kg°C

Now we can substitute these values into the total temperature equation:

T(0) = T + (V² / (2 x c(p)))

T(0) = 293.15 K + ((7274.69 km/h)² / (2 x 1005 J/kg°C))

First, we need to convert the velocity from km/h to m/s:

V = 7274.69 km/h x (1000 m/km) / (3600 s/h) ≈ 2026.86 m/s

Now we can calculate the stagnation temperature:

T(0) = 293.15 K + ((2026.86 m/s)² / (2 x 1005 J/kg°C))

T(0) = 293.15 K + (4111017.56 m²/s² / 2010 J/kg°C)

T(0) ≈ 293.15 K + 2044.65 K

T(0) ≈ 2337.8 K

Therefore,

Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.

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The given function, g(x), is defined piecewise: g(x)=  x+4, & -5 leq x leq -1
2-x, & -1 < x leq 5

To find the value of the function g at different values of x in its domain, we simply need to plug in the value of x into the function. This means that if we know the value of x, we can use the appropriate formula in the piecewise definition to find g(x).

g(-4) when x = -4,  we use the first formula since -5 ≤ -4 ≤ -1:

g(-4) = -4 + 4

g(-4) = 0

Therefore, g(-4) = 0.g(-2)

when x = -2, we use the first formula since -5 ≤ -2 ≤ -1:
g(-2) = -2 + 4

g(-2) = 2
Therefore, g(-2) = 2.g(0)

when x = 0, we use the second formula since -1 < 0 ≤ 5:
g(0) = 2 - 0

g(0) = 2
Therefore, g(0) = 2.g(3)

when x = 3, we use the second formula since -1 < 3 ≤ 5:
g(3) = 2 - 3

g(3) = -1
Therefore, g(3) = -1.g(4)

when x = 4, we use the second formula since -1 < 4 ≤ 5:
g(4) = 2 - 4

g(4) = -2

Therefore, g(4) = -2

The final answers are: g(-4) = 0g(-2) = 2g(0) = 2g(3) = -1g(4) = -2. Therefore, the answer is in 120 words.

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The fruit seller will earn $49 if he sells 49 apples at a cost of $12.25 each.

Here is the word problem that can be solved using the equation 12.25x = 49:
A fruit seller sells apples for $12.25 each. What is the total amount he will earn if he sells 49 apples in his shop?
We can solve the above word problem by using the given equation 12.25x = 49.
Let the cost of one apple be x.
Then, according to the word problem,
Total number of apples sold, x = 49
Cost of one apple, 12.25
The total earnings, E = 12.25x
To find the value of E, we can substitute the given values of x and 12.25 in the equation 12.25x = 49.
12.25x = 49
We need to solve for x to find the total earnings of the fruit seller.
x = 49/12.25
x = 4
Therefore, the cost of one apple is $4.
Now we can calculate the total earnings of the fruit seller by substituting the value of x in the equation:
E = 12.25x
E = 12.25 × 49/12.25
E = 49
Therefore, the fruit seller will earn $49 if he sells 49 apples at a cost of $12.25 each.

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The value of CT is 11.25 units. Given that RT || AC, SR = 25, SA = 15, and ST = 20,

Explanation: we need to find CT.As RT || AC,

we can apply the property, "If a line is parallel to a side of the triangle and it intersects the other two sides of the triangle in two distinct points, then the line divides those sides proportionally.

"Now, using this property, we can say; ST/SA = RT/CT20/15 = RT/CT4/3 = RT/CTCT = 3RT/4

Now, we can apply the Pythagoras theorem in triangle RST,

RS² + ST²

= RT²RT²

= RS² + ST²

= 25² - 20²RT

= √(25² - 20²)

= √225 = 15 units

CT = 3RT/4

= 3 × 15/4

= 45/4 units

= 11.25 units (approx)

Therefore, the value of CT is 11.25 units.

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The greatest common factor (GCF) of the given expressions 24s^3, 12s^4, and 18s is 6s.

To find the GCF, we need to identify the highest power of each variable (s) that appears in all the expressions. In this case, the highest power of s that appears in all the expressions is s^3.Next, we consider the numerical coefficients. The GCF of the numerical coefficients 24, 12, and 18 is 6.

Finally, we combine the GCF of the numerical coefficients (6) with the highest power of the variable (s^3) to obtain the GCF of the entire expressions, which is 6s^3.Therefore, the greatest common factor of 24s^3, 12s^4, and 18s is 6s^3.

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Given that a quadratic equation has a vertical stretch of 4, shift to the left 2 units, and moved up 5 units.In general form the equation for a quadratic function is given by y = ax2 + bx + c

If a is negative, the graph is reflected over the x-axis. And, if a is greater than 1 or less than -1, then the graph will be stretched/compressed in the y-direction and narrow/widen in the x-direction.To obtain the equation for the quadratic function with the given conditions we will use the transformation of quadratic functions. The transformation of a quadratic function

f(x) = ax2 + bx + c

is given by the following formulas:Vertical stretch or compression: g(x) = a · f(x)Horizontal shift:

g(x) = f(x ± h)

Vertical shift: g(x) = f(x) ± k

Therefore, the transformation of

f(x) = ax2 + bx + c to g(x) = a ·

f(x + h) + k is: $$\large

y = a(x-h)^2+k$$Where, a = 4

(vertical stretch), h = 2

(shift to the left) and k = 5

(moved up).Thus, the equation of the quadratic function with the given transformations is:

y = 4(x + 2)² + 5

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Proportion of U.S. Population with Brown Eyes = 41% / 100 = 0.41. In a random group of 1200 U.S. people, you would expect approximately 492 people to have brown eyes.

To find the expected number of people with brown eyes in a group of 1200 U.S. people, we need to calculate the proportion of people with brown eyes in the U.S. population and then apply that proportion to the group size.

First, let's calculate the proportion of people with brown eyes in the U.S. population based on the given eye color ratios:

Percentage of U.S. Population with Brown Eyes = 41%

Next, we convert this percentage to a decimal:

Proportion of U.S. Population with Brown Eyes = 41% / 100 = 0.41

Now, we can find the expected number of people with brown eyes in the group of 1200 U.S. people:

Expected Number of People with Brown Eyes = Proportion of U.S. Population with Brown Eyes * Group Size

Expected Number of People with Brown Eyes = 0.41 * 1200 = 492

Therefore, in a random group of 1200 U.S. people, you would expect approximately 492 people to have brown eyes.

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Katie completed 15 math problems. That is 5 times as many math problems as Katie completed.

Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.

Eric completed 75 math problems. That is 5 times as many math problems as Katie completed. How many math problems did Katie complete?Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.

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Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W).

To determine Shelly's total cost after 4 years of attending community college and transferring to the university, we need to consider the costs associated with each institution separately.

Community College:

Let's assume the cost of tuition per year at the community college is $X.

Shelly will attend the community college for 2 years, so the total cost for tuition at the community college would be 2 * X.

In addition to tuition, there may be other expenses such as textbooks, supplies, and fees. Let's assume these additional expenses for each year at the community college amount to $Y per year. So, the total additional expenses for 2 years would be 2 * Y.

Therefore, the total cost for Shelly's education at the community college for 2 years would be:

Total cost at community college = (2 * X) + (2 * Y)

University:

Let's assume the cost of tuition per year at the university is $Z.

Shelly will transfer to the university for 2 years, so the total cost for tuition at the university would be 2 * Z.

Similarly, there will be additional expenses for each year at the university, which we'll assume amount to $W per year. Thus, the total additional expenses for 2 years at the university would be 2 * W.

Therefore, the total cost for Shelly's education at the university for 2 years would be:

Total cost at university = (2 * Z) + (2 * W)

To calculate the total cost for Shelly's education after 4 years, we sum up the costs at the community college and the university:

Total cost after 4 years = Total cost at community college + Total cost at university

Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W)

Please note that the values of X, Y, Z, and W represent the respective costs per year at the community college and the university, and these values are not provided in the question.

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The degree of the polynomial is 3.True. The degree of the polynomial is determined by the highest power of x, which is 3 in this case.The coefficient of the x^3 term is 2.True. The coefficient of the x^3 term is indeed 2.

The y-intercept is (0, 3).True. The y-intercept is found by setting x = 0, which results in f(0) = 2(0)^3 + 3 = 3.The graph of the function is always increasing.False. The graph of the function may not always be increasing. It depends on the sign of the coefficient of the x^3 term and the values of x. The function is an even function. False. The function is not an even function because it does not exhibit symmetry around the y-axis (i.e., f(-x) ≠ f(x)). The given function is f(x) = 2x^3 + 3. By analyzing the properties of the function and its equation, we can determine the truth or falsehood of each statement. The degree and coefficient of the x^3 term can be identified directly from the equation. The y-intercept is obtained by substituting x = 0. To determine whether the graph is increasing, we would need to examine the derivative or analyze the function's behavior at different intervals. The evenness or oddness of a function can be determined by evaluating f(-x) and comparing it to f(x).

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The given statement describes a relationship between two angles that are not adjacent, stating that they do not form a linear pair. The different types of logical statementsstatements from this statement are the converse statement, inverse statement, contrapositive statement, and conditional statement.

Converse statement: The converse of a conditional statement switches the hypothesis and the conclusion. In this case, the converse statement would be: If two angles do not form a linear pair, then they are not adjacent.
Inverse statement: The inverse of a conditional statement negates both the hypothesis and the conclusion. The inverse statement would be: If two angles are adjacent, then they form a linear pair.
Contrapositive statement: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. The contrapositive statement would be: If two angles form a linear pair, then they are adjacent.
Conditional statement: The original statement itself is the conditional statement. It follows the form: If two angles are not adjacent, then they do not form a linear pair.
These different logical statements provide alternative ways to express the relationship between angles that are not adjacent and their formation of a linear pair.

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The simplified equivalent expression for the sum (5x – 2) + (2x + 9) is 7x + 7.

This can be obtained by combining like terms, which involves adding the coefficients of x and the constant terms separately.

In the given expression, we have (5x – 2) and (2x + 9). To simplify, we can add the coefficients of x together: 5x + 2x = 7x. Similarly, we can add the constant terms: -2 + 9 = 7. Therefore, the simplified expression becomes 7x + 7, where 7x represents the combined coefficient of x and 7 represents the combined constant term.

Overall, by combining like terms, we obtain the simplified equivalent expression of the sum (5x – 2) + (2x + 9) as 7x + 7.


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An hour before show time, only people are seated for a. According to ticket sales, % of the people have yet to arrive. How many tickets were sold for the ​?

Solution:Since only 200 people are seated for a show an hour before the showtime, the remaining number of people who have yet to arrive can be found by subtracting the number of people who are seated from the total number of tickets sold.Let the total number of tickets sold be t.Then the number of people who have yet to arrive is `t - 200`.The percent of people who have yet to arrive is given to be More than 250 percent. Since percentages cannot be greater than 100%, this is impossible and the problem is incorrectly stated. Therefore, the number of tickets sold cannot be determined from the given information.

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The profit from selling the DVDs for the ski trip is £850.

To calculate the profit, we need to determine the total revenue and the total cost.

The total revenue is calculated by adding the revenue from selling 300 DVDs at £2 each (£600), the revenue from selling 250 DVDs at £2 each (£500), and the revenue from selling the remaining DVDs at £6 each (£300). This gives us a total revenue of £1,400.

The total cost is calculated by adding the cost of purchasing 300 DVDs (£300) and the cost of purchasing 250 DVDs (£250), which gives us a total cost of £550.

To find the profit, we subtract the total cost (£550) from the total revenue (£1,400), resulting in a profit of £850.

Therefore, the profit from selling the DVDs for the ski trip is £850.

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The cost of the lifetime membership in the movie club is $96.  To find the cost of the lifetime membership, we can subtract the cost of the movies from the total amount paid by Andrea.

The average cost per movie is $16, and she has purchased 24 movies. Therefore, the total cost of the movies is $16 * 24 = $384.

Since the membership fee is included in the average cost per movie, we can calculate the cost of the lifetime membership by subtracting the total cost of the movies from the total amount paid. So, the lifetime membership fee is $384 - ($12 * 24) = $96.

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The correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

The answer to the question is option C) The speed is decreasing because the distance traveled during each time increment is increasing.

Explanation:A group of students collected distance versus time data for a model car. There could be many types of data that can be collected with respect to distance and time.

For instance, distance could be in miles or kilometers, whereas time could be in seconds, minutes, or hours.In this case, the relation between the distance and time of a model car is given, and we have to describe how the speed of the car is changing over time. If the distance traveled during each time increment is increasing, then the speed is decreasing.

Thus, the correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

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There were 7 students who signed up but did not attend the field trip. There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up.

On the day of the field trip, only 29 students were present out of the 36 students who initially signed up.

There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up. This means that 7 students who had originally signed up did not attend the trip.

The difference between the initial number of sign-ups (36) and the number of students present (29) gives us the number of students who did not show up:

36 - 29 = 7.

Therefore, there were 7 students who signed up but did not attend the field trip.

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The function that represents the total of the flight times is h(x) = 0.0045x - 2.To find the total flight time, we need to multiply the respective functions for Flight A and Flight B

Flight A is represented by the function f(x) = 0.003x - 1.2, and Flight B is represented by the function g(x) = 0.0015x^0.8. Multiplying the two functions together, we get h(x) = f(x) * g(x): h(x) = (0.003x - 1.2) * (0.0015x^0.8) Simplifying the equation, we can distribute the terms and combine like terms: h(x) = 0.0045x^1.8 - 0.0018x^0.8 Since x^1.8 is not equivalent to x, and we want the answer in the form h(x) = mx + b, we can rewrite the equation as: h(x) = 0.0045x - 0.0018x^0.8 Simplifying further we can rewrite x^0.8 as √(x^1.6): h(x) = 0.0045x - 0.0018√(x^1.6) To express the equation with rational exponents, we can rewrite it as: h(x) = 0.0045x - 0.0018x^(0.8/2) Simplifying the exponent, we get: h(x) = 0.0045x - 0.0018x^0.4 Finally, x^0.4 is equivalent to the square root of x, so the equation becomes: h(x) = 0.0045x - 0.0018√x Simplifying further, we get: h(x) = 0.0045x - 0.0018√x = 0.0045x - 2Therefore, the function that represents the total flight time is h(x) = 0.0045x - 2

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To determine the age of the counsellor, we can set up a system of equations based on the given information. By solving the equations simultaneously, we find that the counsellor is currently 28 years old.

Let's denote the counsellor's present age as x and the campers' age as y. Based on the given information, we can set up the following equations:

Equation 1: x + 4 = 2y

Equation 2: x - 5 = (3/4)(y + 8)

To solve this system of equations, we can substitute the value of x from Equation 1 into Equation 2:

(2y - 4) - 5 = (3/4)(y + 8)

2y - 9 = (3/4)(y + 8)

Multiplying both sides by 4 to eliminate the fraction:

8y - 36 = 3y + 24

5y = 60

y = 12

Substituting the value of y back into Equation 1:

x + 4 = 2(12)

x + 4 = 24

x = 20

Therefore, the counsellor is currently 28 years old.

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The width of the rectangle is 10 inches, as it is calculated by finding the square root of the ratio of the area to the length.

Let's denote the width of the rectangle as "w" inches. According to the given information, the length of the rectangle is 4 times its width, so the length can be expressed as "4w" inches.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is 400 square inches, so we have the equation:

Area = Length × Width

400 = (4w) × w

400 = 4w^2

To find the width, we can rearrange the equation and solve for "w":

4w^2 = 400

w^2 = 100

w = √100

w = 10

Therefore, the width of the rectangle is 10 inches. This means that the length of the rectangle is 4 times the width, which is 40 inches.

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A right triangle is a triangle that has a right angle, which is an angle of 90 degrees. The Pythagorean theorem applies to any right triangle. It is named after the ancient Greek mathematician Pythagoras.

The theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. It is commonly written as: c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. In the given triangle, since ∠E = 90°, △DEF is a right triangle.

Therefore, the Pythagorean theorem applies. We can use DE, DF, and EF to represent the lengths of the sides. Using the theorem, we can write the equation as: DE^2 + DF^2 = EF^2Since △DEF is a right triangle, DE and DF are the legs, and EF is the hypotenuse. Thus, the square of the length of the hypotenuse (EF) is equal to the sum of the squares of the lengths of the legs (DE and DF).

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The number that should be placed in the empty box is 13.

In the given division problem, we start by dividing 4498 by 346. The quotient obtained is written above the solid line as 13. Then, we subtract 13 times 346 (which is 4498) from 4498 itself and write the result, -3900, below the line. Next, we bring down the 598 and subtract 598 from -3900, resulting in -3498.

We continue the process, bringing down the minus sign and subtracting 78 from -3498, which gives us -3576. Finally, we bring down the 0 and subtract 0 from -3576, resulting in 0. Since there is no remainder, the division is complete. Therefore, the number that should be placed in the empty box is 13.

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