how many ways are there to put $4$ balls into $3$ boxes, given that the balls are not distinguished and neither are the boxes?

If the common difference between every term in a sequence is the same, the sequence is arithmetic. If all of the terms in a sequence have the same common ratio, the sequence is geometric.

Take a look at the sequence 2,4,6,8, and note how each new term is created by adding a constant term, in this case 2, to the one before it.

For instance, the number 4 is created by adding 2 to the previous phrase, in this case the number 2.

Similar to how 2 + 4 = 6, another number is obtained by adding 2 to 4.

As a result, the sequence is arithmetic since there is a common difference between the sequences, which in this case is 2.

Take the numbers 3, 6, 12, etc.

Keep in mind that the ratio of the following and preceding terms is the same (6/3=2 and 12/6=2).

Such a sequence is referred to as a geometric sequence, and the constant ratio is known as the common ratio of the sequence and is typically indicated by the symbol r.

What is arithmetic sequence?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

What is geometric sequence?

Every term in a geometric series is obtained by multiplying the term before it by the same number.

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The width, labelled x in the figure is 162.5 meters

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

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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Answer:

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

Given is a parallelogram

Dennis spent 12 hours practicing.

1.5 hours = 90 mins
90 mins x 8
720 mins = 12 hours

To find: Equation of line parallel to 5x + 3y = -21 and passes through the point (-9, -3)

Solving the given 5x + 3y = -21 for 3y yields  3y = -5x - 21.  

Dividing all three terms by 3, we get:

y = (-5/3)x - 7, indicating that the given line has slope -5/3.

The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.

Start with y = mx + b

Substitute -3 for y, -9 for x, and 3/5 for m

We get,

-3 = (3/5) (-9)  + b

∴  b   = 5/9

Thus, the equation is y = (3/5)x + 5/9 is the required equation of a line parallel to 5x+3y=−21 that passes through the point (-9,-3)

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40 freezers could be shipped in the container.

What is a variable?

A variable is a quality that may be measured and take on several values.

We are given that

A railroad container can hold weight=42,000 pounds

Total number of ovens for ship=90

Weight of each oven=200 lbs

Weight of each freezer=600 pounds

We have to find the number of freezers that can be shipped in the container.

Let x be the number of freezers that can be shipped in the container.

According to the question,

42000=90(200)+600x

42000=18000+600x

600x=42000-18000=24000

x=24000/600=40

Hence, 40 freezers can be shipped in the container.

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Answer:

22.479411764705882352941176470588

Step-by-step explanation:

76.43/3.4

=22.479411764705882352941176470588

The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153

Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up

1.  2.1 x 5.12 =  2 x 5 = 10

Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5

2. 12.3 x 1.6 = 12 x 2 = 24

Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2

3. 6.5 x 3.1 = 7 x 3 = 21

Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3

4. 51.3 x 2.7 = 51 x 3 = 153

Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3

Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively

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Answer:

Step-by-step explanation:

Let's find the equation in the form of y=mx+b that fits the data.  m is the slope and b is the y-intercept (the value of y when x=0).  Slope, m, the the Rise/Run of the line.  It can be found by taking any two points from the table.  Let's choose (0,15) and (2,35), although any two will work.

x    y

0   15

1    25

2   35

3   45

4   55

(0,15)   (2,35)

The Rise is the change in y:  (35 - 15) = 20.

The Run is the change in x for the same points:  (2 - 0) = 2

The slope is the Rise/Run = (20/2) or 10.

The equation has the form y = 10x + b.

Let's find b.  Just enter any of the points in the above equation and solve for b.  I'll choose (3,45).

  y = 10x + b

  45 = 10*(3) + b

b = 45 - 30

b = 15

[Note:  since b is the value of y when x equals zero, we really didn't need to calculate b as we just did.  There is a data point already that tells us the value of y when x = 0:  (0,15)]

Considering an exponential function, it is found that:

a) The half-life of the element is of 39.63 days.

b) The time needed is of 51.82 days.

A decaying exponential function is modeled by the equation presented as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which the variables of the equation are:

In this problem, the parameters are given as follows, from the text:

A(0) = 120, A(11) = 99.

Hence the decay rate r is obtained as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]120 = 99(1 - r)^{11}[/tex]

[tex](1 - r)^{11} = \frac{99}{120}[/tex]

[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]

[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]

1 - r = 0.98266367982

Hence the equation is:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

The half-life is the value of t for which:

A(t) = 0.5A(0).

Hence:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = 0.5[/tex]

[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]

[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]

t = 39.63 days.

For item b, the time is obtained as follows:

[tex]A(t) = 99(0.98266367982)^t[/tex]

[tex]40 = 99(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = \frac{40}{99}[/tex]

[tex](0.98266367982)^t = 0.40404040[/tex]

[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]

t = 51.82 days.

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The width of the rectangle is 12 feet and the length is 30 feet.

The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Given that, The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2:5.

Let the width be 2x and length be 5x,

Perimeter = 2(l+w)

2(2x+5x) = 84

2x+5x = 84/2

2x+5x = 42

7x = 42

x = 42/7

x = 6

Therefore, width = 6x2 = 12

Length = 5x6 = 30

Hence, The width of the rectangle is 12 feet and the length is 30 feet.

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Using the concepts of straight line, we got 7 movies did marc watch between the beginning of week 1 and the beginning of week 5.

From the diagram given, we got that during the week 1 number of movies watch by marc is 2,while at the beginning of the week 5 the number of movies watch by marc is 9.

So, we need total  number of movies watched by marc in between week 1 and week 9 which is given by-

Number of movies watch at the beginning of week 5-Number of movies watch at the beginning of week 1

Number of movies=9-2

=>Number of movies watched by marc=7.

Hence, the number of movies marc watch between the beginning of week 1 and the beginning of week 5 is 7.

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(Complete question)

Marc is keeping track of the total number of movies he has watched over time. The line graph below actually shows the data where the number of movies corresponds to  number of movies that had been watched at the beginning of  week shown on the horizontal axis.

How many movies did Marc watch between  beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.

The proof that shows that lines DC and AB are parallel is shown below.

The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.

When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.

The following proof shows lines DC and AB are parallel lines:

Statement                                              Reasons                                                    

1. AB = CD                                             1. Given

AD = CB                                    

2. Line AC = Line AC                            2. Reflexive property

3. Triangle ADC ≅ Triangle ABC         3. SSS

4. Angle 1 ≅ Angle 4                             4. CPCTC

5. DC║AB                                              5. Converse of alternate interior ∠s theorem

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The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,

n=380

x=95

p=95/380

p=0.25

test=(0.25-0.31)/√(0.28(1-0.28)/380)

test=-2.60

The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.

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Answer:

57 coins are not nickels.

Equation: n + 57 = 70

Step-by-step explanation:

To find how many coins are not nickels, just add up the pennies, dimes, and quarters all together:

26 + 12 + 19 = 57 coins are not nickels.

The equation you could use to find n (nickels) would be:

n + 57 = 70

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Answer:

4 tons of its body weight

Step-by-step explanation:

In this situation you must find 2% of 200. This is simply 4.

Answer: 4 tons

Step-by-step explanation:

the whale eats 2% of itself everyday, so it would be x/200= 2/100 and the whale would eat x tons, which equals 4 so it eats 4 tons of krill a day

Answer:

here is the answer have a good day

Answer:

1. 40/5=8

8 x 3p=24p

8(3p+5)=24p+40

2. 48/8=6

    64/8=8

8(6q-8)=48q-64

Step-by-step explanation:

Randy is 8 years old. His brother is twice as old as Randy. Randy’s sister is three years younger than Randy. Write an expression to represent the age of Randy’s brother.

Randy = R = 8 years

Brother =  B

B = 2R

solving:

B = 2R when R = 8

B = 2(8)

B = 16 years old

Answer: Its 16

Step-by-step explanation:

You need to take randy's age twice so you need to calculate 8x2= 16.

The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9

To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).

The given polynomial is:

f(x) = 2x³ + ax² + bx + 6

- The polynomial is exactly divisible by (2x-3) means:

f(3/2) = 0

2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0

27 + 9a + 6b + 24 = 0

9a + 6b = - 51 (equation 1)

- f(x) divided by (x+3) has remainder -28

f(-3) = -28

2. (-3)³ + a(-3)² + b(-3) + 6 = -28

9a - 3b = 20  (equation 2)

Substract equation 2 from equation 1

9a + 6b = -51

9a - 3b =  20 _

      9b = -71

         b = -71/9

9a - 3(-71/9) = 20

9a = 131/3

a = 131/27

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The slopes of the given lines are:

1. 2/5.

2. -1.

If a line passes through points on a graph, [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], the formula that can be employed to find the slope of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

1. Using two points on the line, (3, 1) and (-2, -1):

Slope of the line = m = (-1 - 1)/(-2 - 3)

Slope of the line (m) = -2/-5

Slope of the line (m) = 2/5

The slope of the graph is 2/5.

2. Using two points on the line, (-3, 2) and (2, -3):

Slope of the line = m = (-3 - 2)/(2 -(-3))

Slope of the line (m) = -5/5

Slope of the line (m) = -1

The slope of the graph is -1.

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The equation which has exactly one solution is 6x - 6 = 15x + 15.

The correct answer option is option A

Check all that applies:

6x - 6 = 15x + 15

6x - 15x = 15 + 6

- 9x = 21

divide both sides by -9

x = 21/-9

x = -2.33

6x + 15 = 6x + 15

6x - 6x = 15 - 15

0 = 0

False

6x - 15 = 6x + 15

6x - 6x = 15 + 15

0 = 30

False

6x - 6 = 6x + 15

6x - 6x = 15 + 6

0 = 21

False

In conclusion, the 6x - 6 = 15x + 15 has only one solution.

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Events A and B are non-overlapping. Option(2) is correct.

When two sets A and B have at least one element in common, they are said to be overlapping.

The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.

A red die and a blue die are rolled.

Assume that Event A is receiving the number 9.

Event B: You receive a double.

Whether events A and B overlap or not is what we want to determine.

When two red dice and two blue dice are thrown, a sample space is then provided by,

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}

The two dice are rolled, and there are a total of 36 outcomes.

n(S)=36

Assume that Event A is receiving the number 9.

The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)

And let's say that you receive a double in Event B.

The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.

Therefore events A and B are non-overlapping

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The measures of the angles BCA and ABD are equal because they are both right angles.

The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.

Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.

∠BCA = (1/2)×180° = 90°

Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.

∠ABD =  90°

Hence, both the angles are equal to each other.

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Equations B and D are true.

The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]

What are mixed numbers?

A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.

Given,     [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]

             [tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]

             [tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]

              [tex]= \frac{26}{9} +\frac{50}{9}[/tex]

               [tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]

Hence, the required answer for the given term is  [tex]8\frac{4}{9}[/tex] .

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Gregg manages a small cleaning business. He has 16 employees. The cleaners get  $13/hour. The cleaning supervisors get paid $18/hour. then Gregg employed 11 cleaners and 5 cleaning supervisors.

Set up a system of equations where c is the number of cleaners and s is the number of cleaning supervisors:

c + s = 16

13c + 18s = 233

Solve by substitution by solving for c in the first equation:

c + s = 16

c = 16 - s

Then, plug in 18 - s as c into the second equation:

13c + 18s = 233

13(16 - s) + 18s = 233

Solve for s:

208 - 13s + 18s = 233

208 + 5s = 233

5s = 25

s = 5

Then, plug in 5 as s into the first equation:

c + s = 16

c + 5 = 16

c = 11

So, Gregg employed 11 cleaners and 5 cleaning supervisors.

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A graph of the inequality (-2x + y ≥ -6) is shown in the image attached below.

A graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rearrange and simplify the given equation in slope-intercept form as follows:

-2x + y ≥ -6

Adding 2x to both sides of the inequality, we have the following equation:

-2x + y + 2x ≥ -6 + 2x

y ≥ -6 + 2x

Rearranging the equation in slope-intercept form, we have the following equation:

y ≥ 2x - 6

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