Find the equation of the line that passes through (-3,1) and is parallel to y=4-3x

The derivative of the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].

From the given data,

The derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial is  [tex]$y=\sum_{n=0}^{\infty} \frac{(-1)^n x^{2 n+1}}{3^{2 n} \cdot(n !)^2}$[/tex]

Derivatives can be classified into different types based on their order such as first and second order derivatives.

Derivative⇒ [tex]$y^{\prime}=\sum_{n=0}^{\infty} \frac{(-1)^n \cdot(2 n+1)(x)^{2 n}}{3^{2 n} \cdot(n !)^2}$[/tex]

⇒ [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].

Therefore, the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex]

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There is a distance of 656.088 feet to the bottom of the well.

What is Speed?

Speed is the ratio between the distance an object travels and the time it takes to cover that distance.

Since speed just has magnitude and no direction, it is a scalar quantity.

Because the amount of time that passes after you drop the rock is made up of both the amount of time it takes for it to fall to the bottom of the hole and the amount of time it takes for the sound of the impact to reach you,

Let t be the moment when a rock was attained at depth d, which is the well's bottom.

And this is the moment when you hear the sound of impact.

t + t' = 7 seconds

⇒ t' = 7 - t

Speed = Distance / Time

1100 feet per second = d / t'

d = 1100 t

Also d = 16t²

1100 t' = 16t²

1100 (7 - t) = 16t²

7700 - 1100t = 16t²

16t² + 1100t - 7700 = 0

4t² + 275t - 1925 = 0

This is a quadratic equation.

Discriminant = √(b² - 4ac) = √[275² - (4 × 4 × -1925)] = 326.228

t = (-275 ± 326.228) / (2 × 4)

t = 6.404 or t = -75.15

t = -75.15 is not possible because it is negative and t + t' = 7 seconds.

So t = 6.404 seconds

t' = 7 - 6.404 = 0.596 seconds

d = 16 × (6.404)² = 656.088 feet

Hence the distance from the well to the bottom is 656.088 feet.

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Note that the next number in the progression or sequence or pattern is 35,585.

Note that a number pattern is a series of numbers that adheres to a set of criteria. The rule might be mathematical, such as adding a constant value to each item in the series, or it can be based on some other logical relationship.

The next term in the sequence or pattern is derived as follows:

3x5 -3 = 12

5x12 -5 = 55

12x55 -12 = 648

55x648 -12 = 35,585

Therefore, it is correct to state that 35,585 is the next term in the sequence

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The estimated area under the curve is 112.

We can use the left rectangle method to approximate the area under the curve f(x) = (2x)^2 + 6 from x = 2 to x = 4.

First, we need to choose a value of Δx = 0.5, which will determine the width of the rectangles. Then, we can find the height of each rectangle by evaluating the function at the left endpoints of the intervals.

For x = 2, the height of the first rectangle is f(2) = (2 * 2)^2 + 6 = 20.

For x = 2.5, the height of the second rectangle is f(2.5) = (2 * 2.5)^2 + 6 = 28.25.

For x = 3, the height of the third rectangle is f(3) = (2 * 3)^2 + 6 = 42.

For x = 3.5, the height of the fourth rectangle is f(3.5) = (2 * 3.5)^2 + 6 = 57.75.

For x = 4, the height of the fifth rectangle is f(4) = (2 * 4)^2 + 6 = 76.

Finally, we can multiply the height of each rectangle by its width (0.5) to find the area of each rectangle:

Area of first rectangle = 20 * 0.5 = 10

Area of second rectangle = 28.25 * 0.5 = 14.125

Area of third rectangle = 42 * 0.5 = 21

Area of fourth rectangle = 57.75 * 0.5 = 28.875

Area of fifth rectangle = 76 * 0.5 = 38

The total area under the curve can be estimated by adding up the areas of the rectangles:

Estimated area = 10 + 14.125 + 21 + 28.875 + 38 = 112

So the estimated area under the curve using the left rectangle method and Δx = 0.5 is 112.

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Answer:

  957,697,598

Step-by-step explanation:

You want a number that has 7 different prime factors.

If we choose 7 primes at random from the first 20, we might have the list ...

  {2, 11, 13, 23, 41, 53, 67}

The product of these primes will have 7 different prime factors.

  2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598

The number 957,697,598 has exactly 7 different prime factors.

__

Additional comment

Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.

The second attachment shows the first 20 prime numbers.

Answer:

Food supply would only last 4 days

Step-by-step explanation:

(20 cattle)(6 days) = 120 cattle·days      (this is the current feed supply on hand)

20 cattle + 10 = 30 cattle total

(120 cattle·days) / (30 cattle) = 4 days

The complex number statement (3+8i)/(2+8i)=3/2 is false. The correct complex number statement is (3+8i)/(2+8i) = (24i + 6)/(-64i² + 16).

What is a complex number?

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and i is a imaginary number called a "iota."

The given complex number equation is (3+8i)/(2+8i)=3/2

Simplify both sides of the equation.

On the left side, there is -

= (3+8i)/(2+8i)

= (3+8i)/(2+8i) × (2-8i)/(2-8i)

= (6+24i-24i-64i²)/(2² + 2×8i-8i²)

= (-64i² + 24i + 6)/(-64i² + 16)

= (24i + 6)/(-64i² + 16)

On the right side, there is -

3/2 = 3/2

It can be seen that the simplified forms of both sides are not equal, so the original statement is false.

To make the statement true, change the right side of the equation to the left side simplified form.

(3+8i)/(2+8i) = (24i + 6)/(-64i² + 16)

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Answer:

$ balance = 120*(1+6.4%/4) ^4t

Step-by-step explanation:

principal =120

r =6.4% annual = 1.6% per quarter compounding every quarter

so 4 times a year, for t years

$ balance = 120*(1+6.4%/4) ^4t

The function that represents the balance of the investment account after t years is  [tex]y = 120 (1.016)^{4t[/tex].

The formula for calculating the balance of an investment account that earns compound interest is:

[tex]A = P (1 + \dfrac{r}{n})^{nt}[/tex]

where:

A = the balance after t years

P = the principal (initial amount deposited)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case, we have:

P = $120

r = 6.4% = 0.064 (as a decimal)

n = 4 (compounded quarterly)

Therefore, the function that represents the balance y (in dollars) of the investment account after t years is:

[tex]y = 120 *(1 + \dfrac{0.064}{4})^{4t}[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]y = 120 (1.016)^{4t[/tex]

This is the function that represents the balance of the investment account after t years.

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Event A is the event that the sum of the numbers rolled on the two dice is divisible by 4. Event B is the event that the sum of the numbers rolled on the two dice is less than 4.

(a) The total number of possible outcomes in this experiment is 36 (6 possible outcomes for each die).

(b) Outcomes in A are (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), and (12, 6).

(c) Outcomes in B are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), and (2, 6).

(d) P(A) is 5/36. (e) P(B) is 6/36. (f) P(A U B) is 11/36. (g) P(A n B) is 0 (there are no outcomes that belong to both A and B). (h) Events A and B are not independent because P(A U B) does not equal P(A) + P(B).

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The following are not characteristics of surveys :

A. The study involves on or more treatment groups and a control group

B. The study compared two or more treatments

A survey is a research technique used to gather data from a predetermined sample of respondents in order to learn more and acquire insights into a range of interesting topics.

There are Characteristics of an Effective Survey :

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X intercept: 10/5

Y intercept: 0

To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.

For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.

X Intercept:

To find the X intercept, set Y equal to 0 and solve for X.

5x - 2(0) = 10

5x = 10

x = 10/5

X intercept = 10/5

Y Intercept:

To find the Y intercept, set X equal to 0 and solve for Y.

5(0) - 2y = 10

-2y = 10

y = -10/2

Y intercept = 0

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The area of a rectangle with length x and width y is xy unit square.

An equation is an expression that shows the relationship between numbers and variables.

Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.

A rectangle have equal opposite sides which are parallel to each other and all angles are at 90 degrees.

Area of rectangle = length * width

Area = x * y = xy

The area is xy unit square.

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a. The percentage of the original price that the consumers are going to pay will be 8.57%.

b. The markup percentage of the gallons will be

c. The percentage that decided not to sell the juice is 41.7%.

d. The price of each bottle will be:

a. The percentage of the original price that the consumers are going to pay will be:

= (3.50 - 3.20) / 3.50 × 100

= 0.30 / 3.50 × 100

= 8.57%

b. The markup percentage of the gallons will be:

= (3.20 - 2.70) / 2.70 × 100

= 0.50 / 2.70 × 100

= 18.5%

c. The percentage that decided not to sell the juice is:

= 125 / 300 × 100

= 41.7%

d. The price of each bottle will be:

= (1 - 15%) × $2.25

= $1.91

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Answer:

arrange in ascending order

14,15,16,17,18,20,25

there are odd number of terms so

median = (n+1/2) th observation

here n = 7 which is odd

therefore, 7+1/2 th observation

which is 4th observation

ans) 17

The median for average life of a particular brand of a T.V sets from the following data is given as follows:

17.5.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.

The total number of observations in this problem is given as follows:

2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.

This is an odd cardinality, hence the median is found in the class when the counter hits:

(159 + 1)/2 = 80.

Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:

(15 + 20)/2 = 17.5.

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well, there are a total of "x" stamps in his collection, which oddly enough is 100%.

now, we know that 34% of "x" is 204, what the heck is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 204& 34 \end{array} \implies \cfrac{x}{204}~~=~~\cfrac{100}{34} \\\\\\ \cfrac{ x }{ 204 } ~~=~~ \cfrac{ 50 }{ 17 }\implies 17x=10200\implies x=\cfrac{10200}{17}\implies x=600[/tex]

Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier than Carlos and they both walked the same distance.

How to calculate the distance?

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

The sentence is describing a scenario in which two boys, Zach and Carlos, go for a walk. It is stated that Zach begins walking 20 seconds earlier than Carlos. This means that Zach starts his walk 20 seconds before Carlos does. It is also stated that both boys had walked exactly the same distance. This means that despite Zach starting his walk 20 seconds earlier than Carlos, they both covered the same distance during their walk.

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A graph that satisfies the given requirements 1 ≤ x ≤ 3 and 2 ≤ y ≤ 7 is shown in the image attached below.

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

For the domain of this graph, the x-value would be placed at point 1 and then dragged to point 3 on the x-coordinate. Similarly, the y-value for the range of this graph would be placed at point 2 and then dragged to point 7 on the y-coordinate as shown in the image attached below.

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The perimeter of the rectangular park is 423/4 units.

The lengths of a shape's edges and sides are added to find its perimeter.

The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. That shape's perimeter is equal to the side lengths added together algebraically.

The perimeter of a shape is equal to the length of its boundary or whole circumference. The perimeter of a closed 2D form is the product of its sides.

Given : Length = 20 1/4

                        = 81/4

          Width = 32 5/8

                     = 261/8

So, Perimeter = 2 ( L + B)

                      = 2 ( 81/4 + 261/8)

                      = 2 ( 423/8)

                     = 423/4 units.

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The type of sampling design is used: simple random sample

The correct answer is an option (a)

We know that in data analysis, the sampling is nothing but the selecting the group or subset of the population to make statistical inferences.

The types of probability sampling are:

Simple random sampling, Systematic sampling, Stratified sampling and Cluster sampling.

In simple random sampling, the researcher randomly selects a subset of data from the population.

In Stratified random sampling, the population is divided into smaller subgroups called as strata.

In case of clustered random sampling, the population is divided into clusters, and then we randomly select some of these clusters as sample.

As we know multistage sampling is a type of cluster sampling.

Here,  it has been decided to randomly select 4 of the 10 lab sections.

This means, simple random sampling design is used in given scenario.

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The complete question is:

a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections. What type of sampleing design is used?

a) Simple random sample

b) Stratified random sample

c) Clustered random sample

d) Multistage sample

The complex fifth roots of 3 are Z₀ = ∛3 (cos 0° + i sin 0°), Z₁ = ∛3 (cos 72° + i sin 72°), Z₂ = ∛3 (cos 144° + i sin 144°), Z₃ = ∛3 (cos 216° + i sin 216°) and Z₄ = ∛3 (cos 288° + i sin 288°)

The complex fifth roots of 3 can be found by finding the roots of the equation z^5 = 3. To find the roots in polar form, we first convert 3 to polar form:

3 = |3| (cos 0 + i sin 0) = 3 (cos 0 + i sin 0)

Next, we find the argument of the fifth roots, which is equal to 360°/5 = 72°. The polar form of the first root is then:

z₁ = ∛3 (cos 0° + i sin 0°) = ∛3 (cos 0° + i sin 0°)

The polar form of the other roots can be found by rotating the argument by 72°, 144°, 216°, and 288° respectively. The result is:

z₂ = ∛3 (cos 72° + i sin 72°)

z₃ = ∛3 (cos 144° + i sin 144°)

z₄ = ∛3 (cos 216° + i sin 216°)

z₅ = ∛3 (cos 288° + i sin 288°)

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The probability that a student studied for 5 hours is 0.2 or 20%.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

A table is given where the first column represents the number of hours a student studied Math and the second column represents the number of students.

The sum of the second column is 35 so it is the total number of students

And only 7 of them studied mathematics for 5 hours.

Therefore, The probability that a student studied for 5 hours is,

= 7/35

= 0.2 or 20%.

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According to the information, Aaliyah is going to need 8.75 hours to read 50 more pages than Yohance.

To calculate how many hours Aaliyah will beed to read, we have to perform the following mathematical procedure

First, we have to calculate how many pages Yohance is going to read this week, so if she is going to read during 7.5 hours we have to multiply the number of pages she read per hour by time (7.5 hours).

So, Yohance is going to read 300 pages. Now if we want to know how many hours needs Aaliyah to read 50 more pages we have to perform the following operation:

According to the above, Aaliyah needs to read for 8.75 hours to complete 50 more pages than Yohance.

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The inverse of the function as it has been written is f(x) = (x - 32) 5/9.

We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.

Let y = f(x)

Hence;

y=9/5 x + 32

y - 32 + 5/9 = x

We would then have the inverse of the function as;

f(x) = (x - 32) 5/9

This is the procedure that would help us to obtain the inverse of the function that have been given here.

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Missing parts;

Given f(x)=9/5 x + 32, find the following;

Inverse of the function

The entire expression is a sum with 0 factors

The coefficients are 1/2, 1 and 7

From the question, we have the following parameters that can be used in our computation:

1/2x² + x + 7

The above expression is a quadratic expression and it has three terms

Quadratic expressions with real roots have 2 factors, otherwise it would have 0 factor

The expression 1/2x² + x + 7 does not have a real root because

b² < 2ac

Also in the expression, the coefficients are 1/2, 1 and 7

i.e. a = 1/2, b = 1 and c = 7

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Complete question

consider the expresson 1/2x² + x + 7.

complete 2 descriptions of the part of the expression

The entire expression is a sum with __ factors

The coefficients are _

The movie gross is $701

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total amount earned from the movie and the sequel = $1518

Amount earned from the movie = x

Amount earned from the sequel = x + $116

Now,

x + (x + 116) = 1518

2x + 116 = 1518

2x = 1518 - 116

2x = 1402

x = 1402/2

x = 701

Now,

x = $701

x + 116 = 701 + 116 = $817

Thus,

The movie gross is $701

The sequel gross is $817

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The  linear equations which are not  in one variable are x²-5x+6=0 and  x³ = x

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equations are

x^2 - 5x + 6 = 0

Here the highest degree is greater than one so it is not a linear equation

And x

x^3  = x

x^3 - x =  0

Here also the highest degree is greater than one so it is not a linear equation

3x-4=0

Here the highest degree is equals to one so it is  a linear equation

7x-6x = 3 + 9x

x = 3+9x

8x+3 = 0

Here the highest degree is equals to one so it is  a linear equation

Therefore , The  linear equations which are not  in one variable are x²-5x+6=0 and  x³ = x

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On solving the given equation,  the value of x = -4.

Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function.

Simply swap out all instances of x with the value of x to do this. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

Given,

[tex]\frac{2x + 4}{2} - \frac{3x}{x-2} = x\\ \\[/tex]

Taking LHS

⇒ [tex]\frac{2x^2 - 4x + 4x - 8 - 6x}{2(x-2)} \\[/tex]

⇒ [tex]\frac{x^2-4-3x}{(x-2)}[/tex]

Equating both sides,

⇒ [tex]\frac{x^2-4-3x}{(x-2)} = x\\x^2-4-3x = x^2 - 2x\\x = -4[/tex]

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The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$[/tex] because the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm.

Step 1: Calculate the charge of sphere 2. Since it is twice that of sphere 1, the charge of sphere 2 is 2 x the charge of sphere 1.

Step 2: Calculate the distance between the two spheres. This is given as 5 cm.

Step 3: Calculate the force. The force is equal to the product of the charges of the two spheres divided by the square of the distance between them.

Step 4: Construct the vector. The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$.[/tex]

The vector representing the force of sphere 2 on sphere 1 is [tex]$\frac{2}{5} \vec{i}$[/tex], as the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm. This is calculated by multiplying the charges of the two spheres and dividing by the square of the distance between them.

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Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.

Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.

Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.

Solution(a)

Given in the question

Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)

from the coefficient table of Enova summary we can write least square regression line as follows

Top speed = 107.58 +0.8710* Weight of boat

Here intercept of regression line = 107.58

Slope of regression line = 0.8710

Solution(b)

if X = 4 tons

than predictive value of the top speed of a boat can be calculated as

Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.

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Complete question: