¿Cuantas permutaciones pueden hacerse con la palabra columna?

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

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Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for [tex]S_{n}[/tex] , that is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + [tex]a_{n}[/tex] )

with a₁ = 5 and [tex]a_{n}[/tex] = a₂₇ = 83 , then

S₂₇ = [tex]\frac{27}{2}[/tex] (5 + 83) = 13.5 × 88 = 1188

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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The ratio of the side length of the side opposite any 30° angle to the length of the hypotenuse is 1/2.

A right triangle has one angle measuring 90°. This angle is also known as the right angle. The side opposite to the right angle is known as the hypotenuse. The other two sides of a right triangle are known as the adjacent side and the opposite side.

The adjacent side is the side adjacent to the angle that is not the right angle, while the opposite side is the side opposite the angle that is not the right angle. A ratio is a comparison of two quantities. In a right triangle, some ratios are of great importance. These ratios are known as trigonometric ratios. The three important trigonometric ratios are sine, cosine, and tangent.

The sine of an angle is the ratio of the opposite side to the hypotenuse. The cosine of an angle is the ratio of the adjacent side to the hypotenuse. The tangent of an angle is the ratio of the opposite side to the adjacent side.  Changing the scale factor of a right triangle results in the creation of similar right triangles. Two triangles are similar if they have the same shape but different sizes.  

When the scale factor is 1, the ratio of the side length of the side opposite angle A to the length of the hypotenuse is 1/2. Change the scale factor to 3. The ratio of the side length of the side opposite angle A to the length of the hypotenuse is still 1/2.What is the ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse?

Therefore, the ratio of the side length of the side opposite any 30° angle to the length of the hypotenuse is 1/2.

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Answer:

12, 14, 16

Step-by-step explanation:

Let's say x is the lowest number:

x+x+2+x+4=42

Simplify the equation:

3x+6=42

Subtract 6 on each side to isolate 3x:

3x=36

x=12

So the lowest number is 12, which means the next number(x+2) would be 14, and the following number(12+4) would be 16.

Happy learning!

Step-by-step explanation:

Answer:

[tex]f=\frac{N^2-H}{6}[/tex]

Step-by-step explanation:

[tex]N^2=6f+H\\\mathrm{or,\ }6f=N^2-H\\\mathrm{or,\ }f=\frac{N^2-H}{6}[/tex]

Work Shown:

A = 7 chilies + 9 beetroots = 16 items that aren't a carrot

B = 7 chilies + 9 beetroots + 11 carrots = 27 items total

P(not a carrot) = A/B = 16/27

Answer:

f * g)(x) = 8x^2 - 2x - 15

Step-by-step explanation:

Since we want to find (f * g)(x), we want to multiply the entire functions and leave the answer in terms of x (in terms of x simply means we do the multiplication and the simplified answer will be in terms of x):

Thus, we have (2x - 3)(4x + 5).  This is a binomial expression and we can multiply binomials using the FOIL method, where

We add all the terms and combine like terms to find (f * g)(x):

(2x * 4x) + (2x * 5) + (-3 * 4x) + (-3 * 5)

8x^2 + 10x - 12x - 15

8x^2 - 2x - 15

Thus, (f * g)(x) is 8x^2 - 2x - 15

The equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, is:

5x + y - 3 = 0.

To determine the equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, we need to find the coordinates of point C.

Since triangle ABC is right-angled at point A, we know that the slope of line BC[tex](m_{BC})[/tex] multiplied by the slope of line AC [tex](m_{AC})[/tex]  is equal to -1 (because the two lines are perpendicular to each other).

The equation of line BC is given as 5y - x = 15.

By rearranging it in the form y = mx + b, we can determine its slope.

The slope of BC[tex](m_{BC})[/tex] is 5.

Using the perpendicularity condition, we have:

[tex]m_{BC} \times m_{AC} = -1[/tex]

[tex]5\times m_{AC} = -1[/tex]

[tex]m_{AC} = -1/5[/tex]

Now, let's find the coordinates of point C.

We have the coordinates of points A and B, so we can find the slope between points A and C using the formula:

[tex]m_{AC} = (N - (-2)) / (m - 1)[/tex]

-1/5 = (N + 2) / (m - 1)

Cross-multiplying, we get:

-5(m - 1) = N + 2

-5m + 5 = N + 2

-5m - N = -3

Rearranging this equation, we obtain:

5m + N = 3

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Answer:  Choice C

Condition 1 fails. [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] does not exist

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

Explanation:

Use a table or a graph to determine that [tex]\ln(\text{x}^2)[/tex] approaches negative infinity as x gets closer to 0.

Symbolically [tex]\displaystyle \lim_{\text{x} \to 0}\ln(\text{x}^2) = -\infty[/tex]. Since this result is not a finite number, we consider the limit to not exist. Write "DNE" as shorthand for "does not exist".

Therefore, [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x}) = -\infty[/tex] making [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] not exist as well.

Answer:

AC = 3 + 2√15

Step-by-step explanation:

Call the center of the circle O.

(OB)² = 2² + 3²

(OB)² = 13

OD = OB

(OD)² + (DC)² = (CO)²

13 + 51 = (CO)²

(CO)² = 64

(CX)² + 2² = (CO)²

(CX)² = 64 - 4

(CX)² = 60

CX = √60 = 2√15

AX = BX = 3

AC = AX + CX

AC = 3 + 2√15

In terms of length, 218 inches is greater than 6 yards.

To determine which is more, 6 yards or 218 inches, we need to convert one or both of the measurements to a common unit of measurement. In this case, we can convert yards to inches or inches to yards for comparison.

Since there are 36 inches in a yard, we can convert 6 yards to inches by multiplying it by 36:

6 yards * 36 inches/yard = 216 inches.

Now, we can compare the converted measurements: 216 inches and 218 inches.

Since 218 inches is greater than 216 inches, we can conclude that 218 inches is more than 6 yards.

This comparison can also be verified by considering the conversion factors. 6 yards is equivalent to 216 inches, which is smaller than 218 inches.

It is important to note that when comparing measurements, it is crucial to ensure that both measurements are in the same unit for an accurate comparison. Converting them to a common unit helps provide a clear understanding of which value is greater or smaller.

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The analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.

The function g(x) = 3^(2x-1) is an exponential function with a base of 3. In this case, the base is raised to the power of (2x-1).

To determine the behavior of the function, we can analyze the exponent (2x-1).

When x is a positive number, 2x-1 will increase as x increases. This means that the function will experience exponential growth as x increases.

When x is a negative number, 2x-1 will decrease as x decreases. This indicates that the function will exhibit exponential decay as x decreases.

Now, let's analyze the options to identify the graph that best represents the function g(x).

Graph (A): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be slower than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (A) does not accurately represent the given function.

Graph (B): This graph shows exponential growth. As x increases, the function increases. The rate of growth appears to match the behavior we would expect for the function g(x)=3^(2x-1). Therefore, graph (B) is a potential candidate.

Graph (C): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be faster than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (C) does not accurately represent the given function.

Considering the analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.

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Question

Which of the following graphs represents the function g(x)=3^2x-1

Answer:

x-2 and y(-1) -1

Step-by-step explanation:

Explained
it made a reflection of the y-axis (-1) and lowered it by 1 unit (-1)

It moved to the left by two units so x-2

X-2 and y(-1) -1

The yearly installment that Thabo has to pay to the bank is c. R202.

We shall use the formula for calculating the amortized loan payment to estimate the yearly installment that Thabo has to pay to the bank:

Installment = (Loan amount (L) * Interest rate (I)) / (1 - (1 + Interest rate)^(-Number of years (N))):

In short: Installment = (L * I) / (1 - (1 + I)⁽⁻ⁿ⁾)

Given:

L = R700

I = 6% = 0.06

N = 4

Plugging the values into the formula, we have the yearly installment:

Installment = (700 * 0.06) / (1 - (1 + 0.06)⁽⁻⁴⁾)

= 42/(1 - (1 + 0.06)⁽⁻⁴⁾ )

= 42/ (1 - (1.06)⁽⁻⁴⁾ )

= 42/(1 - 0.792)

= 42 / 0.2079 ≈ 202.01

Installment ≈ 202.01

Therefore, the yearly installment that Thabo has to pay to the bank is  R202.

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The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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If each bus holds ten students and there are three buses, then the total number of students going to the show is 10 x 3 = 30 students.

The mass of the bus, 1900, is most likely measured in kilograms (kg) because kilograms are a commonly used unit for measuring the mass of large objects like vehicles.

If there are five rows in the theatre and Mr. Murray wants an equal number of students to sit in each row, then the number of students in each row would be the total number of students (30) divided by the number of rows (5), which is 30 / 5 = 6 students per row.

If Mrs. Stewart has two times as many students as Mr. Murray, and Mr. Murray has 30 students, then Mrs. Stewart would have 2 x 30 = 60 high school students in the theatre for the show.

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The equation in standard form for the circle passing through (5/2, -6) and centered at the origin is [tex]4x^2 + 4y^2 = 169.[/tex]

To write the equation in standard form for the circle passing through (5/2, -6) and centered at the origin, we'll use the general equation of a circle:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) represents the center of the circle and r represents the radius.

Given that the circle is centered at the origin (0, 0), we can substitute these values into the equation:

[tex](x - 0)^2 + (y - 0)^2 = r^2\\x^2 + y^2 = r^2[/tex]

Now, we need to determine the radius of the circle. Since the circle passes through the point (5/2, -6), we can find the distance between the origin (0, 0) and this point, which represents the radius.

Using the distance formula:

d = √([tex](x2 - x1)^2 + (y2 - y1)^2)[/tex]

Substituting the values of the point (5/2, -6) and the origin (0, 0):

r = √([tex](5/2 - 0)^2 + (-6 - 0)^2)[/tex]

r = √(([tex]5/2)^2 + (-6)^2)[/tex]

r = √(25/4 + 36)

r = √(25/4 + 144/4)

r = √(169/4)

r = 13/2

Now, we can substitute the value of the radius (r = 13/2) into the equation:

[tex]x^2 + y^2 = (13/2)^2\\x^2 + y^2 = 169/4[/tex]

Multiplying both sides of the equation by 4 to eliminate the fraction:

[tex]4(x^2 + y^2) = 4(169/4)\\4x^2 + 4y^2 = 169[/tex]

Therefore, the equation in standard form for the circle passing through (5/2, -6) and centered at the origin is:

[tex]4x^2 + 4y^2 = 169.[/tex]

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Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;

1. The mean deviation about the mean, median mode are;

2.653, 3.709, and 3.709, respectively

The coefficients of variation are;

0.364, 0.337, 0.337, respectively

The variance is about 9.462

The standard deviation is about 3.076

2. Section A has a higher relative dispersion than section B

3. City 2

4. a. Mean ≈ 43.85

b. Mode 40 - 54 inches

c. Median ≈ 45.16

The variance ≈ 125.8056

Standard deviation ≈ 11.216

Coefficient of variation ≈ 0.268

The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.

The mean for the data can be calculated as follows;

Mean  = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29

The median is the 86/2 value = 43rd value

10 + 15 + 25 = 50

Therefore, the median is in the class with a frequency of 25, which is 11

The mode of the data, which is the value with the highest frequency in the data set is 11

The mean deviation from the mean is therefore;

(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653

The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364

The mean deviation about the median is therefore;

(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)

The mean deviation about the median = 319/86 ≈ 3.709

The coefficient ≈ 3.709/11 ≈ 0.337

The median = The mean deviation about the mode ≈ 3.709

The coefficient is about 0.337

The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462

The standard deviation, s ≈ √(9.462) ≈ 3.076

2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;

CV = Standard deviation/( The mean of the data)

Therefore; CV for section A = 23/79 ≈ 0.2911

CV for section B = 11/64 ≈ 0.172

The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B

3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;

City 1; Mean = 23

Variance = 50/4

Standard deviation, City 1 = (√(50))/2 = 5·√2/2

City 2; Mean = 21.8

Sample variance = 2.2

Standard deviation, City 2 = √(2.2) ≈ 1.483

City 3; Mean = 29.2

Sample variance = 18.7

Standard deviation, City 3 = √(18.7) ≈ 4.324

The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature

4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f

Therefore; The mean obtained using an online tool is; 43.85

The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches

The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches

The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16

The standard deviation found for the grouped data, using an online tool is as follows;

Variance, σ² ≈125.8056

The standard deviation, σ ≈ √(125.8056) ≈ 11.216

The coefficient of variation is; 11.216/41.83 ≈ 0.268

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A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

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1.)The length of the diagonal of the square would be = 5.7

2.) The perimeter of the equilateral triangle = 12.

To calculate the length of the diagonal of a given square, the Pythagorean formula should be used and it's given below as follows:

1.) C² = a² + b²

But the perimeter = 16

The length = 16/4 = 4

C² = 4²+4²

= 16+16

= 32

C = √32= 5.7

2.) The perimeter of the equilateral triangle = length×3 = 36.

The length = 36/3 = 12

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Answer:

y - 3 = 1(x - 6)  or y - 4 = 1(x - 7)

Step-by-step explanation:

to find the slope: m = (3-4) / (6-7) = -1 / -1 = 1

next, substitute the values into the equation: y2 - y1 = m(x2 - x1)

you can use any x or y value from the given.

y - 3 = 1(x - 6)

or

y - 4 = 1(x - 7)

If the height of the cone were increased to 16 inches and the diameter stayed the same, the volume of the cone would increase by approximately 12π or around 37.7 cubic inches.

The formula for the volume V of a cone is given by:

V = 1/3 * π * r² * h

The height of an object is denoted as "h" and its base radius as "r", while the constant π is approximately equal to 3. 1416

Initially, it is crucial to determine the initial capacity of the triangular object.

The radius r is half the diameter, so r = 6/2 = 3 inches. Substituting the given height h = 12 inches and r = 3 inches into the formula, we get:

V1 = 1/3 * π * (3²) * 12 = 36π cubic inches

Then, calculate the new volume of the cone, using the same radius but the new height of 16 inches:

V2 = 1/3 * π * (3²) * 16 = 48π cubic inches

The increase in volume is the difference between the new volume and the original volume:

ΔV = V2 - V1 = 48π - 36π = 12π cubic inches

Therefore, if the height of the cone were increased to 16 inches and the diameter stayed the same, the volume of the cone would increase by approximately 12π or around 37.7 cubic inches.

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The Complete Question

Suppose you have a cone with a height of 12 inches and a base diameter of 6 inches. If the height of the cone were increased to 16 inches and the diameter stayed the same, by approximately how much would its volume increase?

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

La sucesión que se describe tiene un primer término de 1/2 y aumenta constantemente en 1/3 en cada término subsiguiente. Podemos encontrar los primeros 10 términos de la sucesión calculando cada término de manera sucesiva.

El primer término es 1/2.

Para encontrar el segundo término, sumamos 1/3 al primer término:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

El segundo término es 5/6.

Para encontrar el tercer término, sumamos 1/3 al segundo término:

5/6 + 1/3 = 10/12 + 4/12 = 14/12 = 7/6

El tercer término es 7/6.

Podemos continuar este proceso para encontrar los siguientes términos:

4to término: 7/6 + 1/3 = 14/12 + 4/12 = 18/12 = 3/2

5to término: 3/2 + 1/3 = 9/6 + 2/6 = 11/6

6to término: 11/6 + 1/3 = 22/12 + 4/12 = 26/12 = 13/6

7mo término: 13/6 + 1/3 = 26/12 + 8/12 = 34/12 = 17/6

8vo término: 17/6 + 1/3 = 34/12 + 4/12 = 38/12 = 19/6

9no término: 19/6 + 1/3 = 38/12 + 8/12 = 46/12 = 23/6

10mo término: 23/6 + 1/3 = 46/12 + 4/12 = 50/12 = 25/6

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

Si tienes más preguntas, ¡no dudes en hacerlas!

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The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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The value of a/b is 10/3.

We start by simplifying the expression under the square root:

√((4/5) * (5/4) * (6/5) * (x/a) * (b/x)) = 2

We can observe that the terms (4/5) and (5/4) cancel out, leaving us with:

√(6/5 * (x/a) * (b/x)) = 2

Next, we square both sides of the equation to eliminate the square root:

6/5 * (x/a) * (b/x) = 2²

Simplifying the right hand side, we get:

6/5 * (x/a) * (b/x) = 4

Multiplying both sides by 5/6, we get:

(x/a) * (b/x) = (5/6) * 4

x and b cancel out, and we are left with:

a = 10/3

Therefore, the value of a/b is:

a/b = (10/3) / 1

a/b = 10/3

So the value of a/b is 10/3.

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Step-by-step explanation:

This is a law of sines problem.

Law of sines states that

A / sin (a) = B(sin b) = C (sin c)

5 / sin (60) = 9 / sin (x)

Simplifying this equation gives us sin (x) = (9 * sin (60)) / 5. Now we take the arc sin of both sides, to get that x = arc sin ((9 * sin (60)) / 5). Plugging this into a calculator gives us..... no solutions

I think thats the right solution as I plugged it into a law of sines calculator as well.

Answer:

[tex]6,10[/tex]

Step-by-step explanation:

Method 1:

[tex]\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 1:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 2:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]