The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the shape 13 cm 5.7 cm 16 cm 7.3 cm 6.2 cm ​

Therefore, the solution to fg(x) = gf(x) for the composite functions is x = -1/4.

A function is a mathematical rule that assigns a unique output for every input in a given set. In other words, it is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented using a formula, a graph, or a table of values. Functions are widely used in mathematics, science, engineering, economics, and many other fields to describe the relationship between variables and to make predictions based on data.

Here,

To solve fg(x) = gf(x), we need to find f(g(x)) and g(f(x)), and then set them equal to each other.

f(g(x)) = f(x + 1)

= 2(x + 1)²

= 2(x² + 2x + 1)

= 2x² + 4x + 2

g(f(x)) = g(2x²)

= 2x² + 1

Now we can set them equal to each other and solve for x:

2x² + 4x + 2 = 2x² + 1

Subtracting 2x² from both sides, we get:

4x + 2 = 1

Subtracting 2 from both sides, we get:

4x = -1

Dividing both sides by 4, we get:

x = -1/4

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Answer: 18%

Step-by-step explanation:

Answer:

18%

Step-by-step explanation:

To find what percent 10.08 is of 56, we can use the following formula:

[tex]p=\frac{x * 100}{y}[/tex]

where x is 10.08 and y is 56:

[tex]p = \frac{10.08 * 100}{56}[/tex]

which p is 18%

Answer:

in second equation,

4x+2y=30

2(2x+y)=30

2x+y=15

Now,putting the value of x from above

2×(15-3y)+y=15

30-6y+y=15

30-15=5y

y=3

Then,

x=15-3×3

x=6

#(6,3) is ans

Answer:

(6,3)

Step-by-step explanation:

The surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

To calculate the surface area of a square pyramid, we need to find the area of the square base and the area of each triangular face.

The formula for the surface area of a square pyramid is:

[tex]S = (a^2) + 2as[/tex]

where a is the length of one side of the square base and s is the slant height.

Plugging in the given values, we get:

[tex]S = (6^2) + 2(6)(5)[/tex]

[tex]S = 36 + 60[/tex]

[tex]S = 96[/tex]

Therefore, the surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

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Step-by-step explanation:

you dind't but what we had to anwser

The values of m and be for the line given, can be found to be:

First, we need to pick two points from the line which would be ( 0, 5 ) and ( -5, 2 ).

To find the values of m (slope) and b (y-intercept) for a line with the given coordinates (0, 5) and (-5, 2), we can use the slope formula and the point-slope form of a linear equation.

Calculate the slope (m) using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (2 - 5) / (-5 - 0)

m = (-3) / (-5)

m = 3/5

Find the y-intercept (b) using the point-slope form. The y - intercept is the point where the line crosses the y axis. This means that the value of x at this point would be 0.

The y - intercept can therefore be seen from the point  ( 0, 5 ) which means that 5 is the y - intercept or b.

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Answer: 16

Step-by-step explanation:

4*4 = 16

Answer:

I will try my best with the given info

Step-by-step explanation:

Selection bias occurs when the selection of the sample is not random and is instead influenced by factors that are not related to the study objective. Here are some examples of selection bias in a survey of brown-eyed people:

A survey that only includes brown-eyed people from a specific geographic location, such as a single city or state. This would not be representative of the entire population of brown-eyed people.

A survey that only includes brown-eyed people who are members of a particular organization or club. This would not be representative of the entire population of brown-eyed people, as it would exclude those who are not members of the organization or club.

A survey that only includes brown-eyed people who have a certain level of education or income. This would not be representative of the entire population of brown-eyed people, as it would exclude those with different levels of education or income.

A survey that only includes brown-eyed people who are willing to participate in the study. This could result in a biased sample, as those who are not willing to participate may have different characteristics than those who are willing to participate.

In general, any selection process that is not random and does not provide equal opportunity for all members of the population to be included in the study can result in selection bias.

So, the given triangle is a scalene right triangle.

what is triangle ?

With three consecutive sides and three angles, a triangle is an enclosed plane shape. It is one of the fundamental geometric shapes and is frequently used in physics, maths, and engineering. A triangle's total angles are always 180 degrees. Triangles come in a variety of shapes, such as equilateral triangles, which have three equal sides and angles, isosceles triangles, which have two equal sides and angles, and scalene isosceles (all sides and angles are different).

To determine the type of triangle based on the given side lengths, we can use the following rules:

If all three sides are equal, it's an equilateral triangle.

If two sides are equal, it's an isosceles triangle.

If all three sides are different, it's a scalene triangle.

We can also use the Pythagorean theorem to determine if the triangle is a right triangle. According to this theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.

Let's check the sides of the given triangle using these rules:

The three sides are different, so it's a scalene triangle.

To check if it's a right triangle, we can find the longest side (53) and see if it satisfies the Pythagorean theorem with the other two sides. Using a calculator, we find that [tex]28^2 + 45^2 = 784 + 2025 = 2809[/tex], and [tex]53^2 = 2809.[/tex]Therefore, the triangle is a right triangle.

So, the given triangle is a scalene right triangle.

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Mathematicians have used probability to determine how likely certain events are to occur. The possible values of  X will be 10, 0, -5 with following probabilities:

P(X = 10 ) = 0.23

P(X = 0 ) = 0.48

P(X = -5) = 0.29

Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.

Given:

The probability distribution of X can be represented as:

X      P(X=x)

-5      0.29

0       0.48

10      0.23

The outcomes is attached as table below.

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The complete question is:

The table below to model the scenario is attached below:

Therefore , the solution of the given problem of triangle comes out to be the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

The centers of the three circles must make an equilateral triangle because they are positioned so that they touch one another. Angles A and C are both 60 degrees, so we know this.

With lengths that are 5.4 and 4.4 in length, we can use the Law of Cosines to determine angle A:

=> cos(A) = (4.4² + 5.4² - 3.4²) / (2 * 4.4 * 5.4)

=> cos(A) = 0.731

=> A = cos⁻¹(0.731)

=>A ≈ 42.5°

We can apply the Law of Cosines once more to determine side b:

=> b² = 4.4² + 5.4^2 - 2 * 4.4 * 5.4 * cos(60)

=> b ≈ 2.15

Finally, we can apply the Law of Sines to determine angle C:

=> Sin(60) / 2.15 = sin(C) / 5.4 =

=> sin(C) ≈ 0.635

=> C ≈ sin⁻¹(0.635)

=> C ≈ 40.3°

As a result, the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.

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Note that the line plot or number line for the data above is given as attached.

1) To create an inequality for a line plot using the given data set, we can use the minimum and maximum distances as the endpoints of the inequality.

The minimum distance is 1 3/8, which is equivalent to 1.375 miles. The maximum distance is 3 1/4, which is equivalent to 3.25 miles.

Therefore, the inequality can be written as:

1.375 ≤ x ≤ 3.25

where x represents the distance of a ski trail in miles.

This inequality states that any value of x (distance of a ski trail) that is between 1.375 and 3.25, inclusive, is a valid value for the data set.


2. The total number of ski trails is 12.

3. The difference in length between the longest ski trail (3 1/4) and the shortest ski trail (1 3/8) is: 3 1/4 - 1 3/8 = 1 7/8

4. The total length of the ski trails that are 2 7/8 is:

2 7/8 + 2 7/8 + 2 7/8 = 8 1/4

5. The sum of the lengths of the shortest (1 3/8) and the longest (3 1/4) ski trails is:

1 3/8 + 3 1/4 = 4 5/8

6. Sam is correct. The longest ski trail is 3 1/4 miles and the shortest ski trail is 1 3/8 miles, so:

3 1/4 > 3 * 1 3/8

10 1/4 > 4 1/8

2.5 > 1

Therefore, the longest ski trail is indeed more than three times the length of the shortest ski trail.

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Step-by-step explanation:

As a salesperson at Trading Cards Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $384. If he sells $700 of merchandise in one month, he is paid $447.

Answer:

Step-by-step explanation:

To solve this problem, we can set up a system of two equations with two variables. Let x be Justin's base pay for the month and y be the commission rate he receives for each dollar of merchandise sold. Then we have:

400y + x = 384 (equation 1)

700y + x = 447 (equation 2)

To solve for x and y, we can use the method of substitution. Solving equation 1 for x, we get:

x = 384 - 400y

Substituting this expression for x into equation 2, we get:

700y + (384 - 400y) = 447

Simplifying and solving for y, we get:

300y = 63

y = 0.21

Substituting this value of y into equation 1, we can solve for x:

400(0.21) + x = 384

x = 304.80

Therefore, Justin's base pay for the month is $304.80 and he receives a commission of 21% on all merchandise sold.

Answer: b

Step-by-step explanation:

Simplify

22 - (-24)

Swap since they are both negatives.

22-(-24) =

22+(24)

22+24

= 46

Which now add in the negative 32 to the problem

46 + (-32)

Recreate the problem to make it more simple:

46 - 32

  = 14

The value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.

What is mean?

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the IQR for the mean of 15 pumpkins, we need to first find the standard error of the mean, which can be calculated using the formula:

SEM = σ / sqrt

where SEM is the standard error of the mean, σ is the standard deviation, and n is the sample size.

Substituting the given values, we get:

SEM = 1.68 / sqrt(15) = 0.433

The interquartile range (IQR) for the mean can be calculated as:

IQR = 1.35 * SEM

where 1.35 is the multiplier for the IQR based on the normal distribution.

Substituting the value of SEM, we get:

IQR = 1.35 * 0.433 = 0.585

Rounding to the nearest thousandth, we get the final answer as:

IQR ≈ 0.585

Therefore, the value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.

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Hence, compared to the second plant, the first plant produces [tex]3x + 14[/tex]more things per day.

Production is the process of creating goods or services that can be used or consumed by individuals or other entities. It involves converting raw materials, labor, and capital into finished products or services that are suitable for sale or distribution in the market.

given

We must take the daily production of the second plant away from the daily production of the first plant in order to calculate how many more things are produced daily by the first plant than the second plant.

The first plant's daily output is equal to [tex]5x + 11.[/tex]

Daily output of the second plant is equal to [tex]2x - 3.[/tex]

As a result, the two facilities' daily production differences are as follows:

[tex](5x + 11) - (2x - 3) = 5x + 11 - 2x + 3[/tex]

[tex]= 3x + 14[/tex]

Hence, compared to the second plant, the first plant produces 3x + 14 more things per day.

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From the above calculations, we can see that the IQR changes the most with a difference of 3°. The new value of the IQR is 34°.

To determine which measure changes the most when a value of 71° is changed to 93°, we need to calculate each measure before and after the change. Mean:

The mean is calculated by adding all the temperatures and dividing by the total number of temperatures.

Before the change:

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 82.3°

After the change:

Mean = (58 + 61 + 93 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 84.8°

The difference between the means is: 84.8° - 82.3° = 2.5°

Median:

The median is the middle value when the temperatures are arranged in order.

Before the change:

Median = 82°

After the change:

Median = 84°

The difference between the medians is: 84° - 82° = 2°

Range:

The range is the difference between the highest and lowest temperatures.

Before the change:

Range = 105° - 57°

= 48°

After the change:

Range = 105° - 58°

= 47°

The difference between the ranges is: 47° - 48° = -1°

IQR:

The IQR is the difference between the third quartile and the first quartile.

Before the change:

Quartiles:

Q1 = 66°

Q3 = 97°

IQR = Q3 - Q1

= 97° - 66°

= 31°

After the change:

Quartiles:

Q1 = 66°

Q3 = 100°

IQR = Q3 - Q1

= 100° - 66°

= 34°                                        

The difference between the IQRs is: 34° - 31° = 3°

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If we take multiple samples of the same size and calculate their means, 90% of the resulting sample which is 69.3 means will fall within 9.02 units of the true population mean for standard deviation.

The following formula must be used to determine the margin of error for a 90% confidence interval for the population mean ():

Margin of error =  [tex]z * (/n)[/tex].

where is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution with a 90% confidence level.

The matching z-value is 1.645 because a 90% confidence interval is what we are looking for. Thus, the margin of error can be determined as follows:

Margin of error: (50 / 77) / 1.645 = 9.02

This indicates that 90% of the sample means obtained when calculating the means of several samples of equal size will be within 9.02 units of the actual population mean.

It is significant to remember that the margin of error lowers with sample size and rises with confidence level. A bigger sample size in this situation would lead to a smaller margin of error, whereas a greater confidence level would lead to a larger margin of error.

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The value of the given percent that satisfied the relation through which it justified it is 6.3 years.

What about percent?

Percent: A percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". For example, if you say that 50% of a group are females, it means that 50 out of every 100 people in the group are female. Percentages are often used to describe the proportion of something or to compare different quantities.

According to the given information:

90 % of 7 years

⇒  [tex]\frac{90}{100}[/tex] x 7 years

⇒ [tex]\frac{630}{100}[/tex]

⇒ 6.3 years

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The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear function.

A linear function is one whose graph on a Cartesian plane is a straight line. The line is always straight even though it can travel in any direction.

Given table:

x        y

-2      -7

-1       -4

0      -1

1         2

2        5

Plot the coordinates on graph:

(-2, -7), (-1, -4),(0,-1),(1,2),(2,5)

The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear.

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Complete question:

Explain, if the given table shows linear or non linear function?

x        y

-2      -7

-1       -4

-0      -1

1         2

2        5

As a result, the system of equations has the following solution: x=-2,y=16,z=11.

In order to resolve the equation system:

x + y - z = 3

x - 3y - 2z = -28 and 4x - y + z = -13

The elimination strategy can be used to find the values of x, y, and z. In order to remove z, we can first add the first and second equations:

3 - 13x + y - z + 4x - y + z

A approach for solving systems of linear equations is the elimination method. The addition method is another name for it. We change an equation system so that one variable "cancels out" in order to solve it by elimination. In this approach, one of the variables is removed by adding or subtracting from the equations. After removing one variable, we can find a solution for the remaining one.

When we simplify this equation, we obtain:

5x = -10

When we multiply both sides by 5, we get:

x = -2

Knowing x now allows us to solve for y by substituting it into the first equation:

-2 + y - z = 3

When we simplify this equation, we obtain:

y - z = 5

In order to solve for z, we may now enter x and y into the third equation:

-2 - 3y + 2z = -28

When we simplify this equation, we obtain:

-3y + 2z = -26

by replacing  y - z = 5 to this equation gives us:

-3y + 2(y - 5) = -26

When we simplify this equation, we obtain:

-y - 10 = -26

To both sides of the equation, add 10, and we get:

-y = -16

Adding -1 to both sides gives us:

y = 16

Knowing x and y now allows us to solve for z by substituting them into the first equation:

-2 + 16 - z = 3

When we simplify this equation, we obtain:

z = 11

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There are 2500 Shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.

1. First, analyze the given diagram and observe the pattern. Notice that there are alternating shaded and unshaded squares, with the shaded squares being on the main diagonal.

2. Next, identify the sequence in the pattern. It appears that there is a continuous increase of shaded squares, starting from 1 and increasing by 2 each time. This forms an arithmetic sequence: 1, 3, 5, 7, and so on.

3. To find the number of shaded squares in the 100x100 square, calculate the sum of the first 50 terms of the sequence (since there are 100 rows/columns and each shaded area covers 2 rows/columns). The formula for the sum of an arithmetic sequence is: Sn = n * (a1 + an) / 2, where Sn is the sum of the sequence, n is the number of terms, a1 is the first term, and an is the last term.

4. In our case, n = 50, a1 = 1, and an = 99 (the 50th term in the sequence). Plugging these values into the formula, we get: S50 = 50 * (1 + 99) / 2 = 50 * 100 / 2 = 2500.

5. Thus, there are 2500 shaded squares in the 100x100 square.

6. To find the number of unshaded squares, subtract the number of shaded squares from the total number of squares in the 100x100 square. The total number of squares is 100 * 100 = 10,000.

7. Now, calculate the number of unshaded squares: 10,000 - 2500 = 7500.

In conclusion, there are 2500 shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.

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The grοwth rate (r) represented as a percentage is 4%, which is οptiοn (c).

A percentage is a number οr ratiο expressed as a fractiοn οf 100. It is οften denοted using the percent sign, "%", althοugh the abbreviatiοns "pct.", "pct" and sοmetimes "pc" are alsο used. A percentage is a dimensiοnless number; it has nο unit οf measurement.

The given pοpulatiοn grοwth mοdel is:

P = 6191(1.04)¹

Here, P represents the pοpulatiοn after οne year, 6191 represents the initial pοpulatiοn, and 1.04 is the grοwth factοr.

The grοwth factοr is calculated as:

grοwth factοr = 1 + grοwth rate

where the grοwth rate is a decimal representatiοn οf the percentage increase in pοpulatiοn.

Sο, in this case, we can calculate the grοwth rate as:

grοwth rate = grοwth factοr - 1 = 1.04 - 1 = 0.04

Tο cοnvert this tο a percentage, we multiply by 100:

grοwth rate as a percentage = 0.04 * 100% = 4%

Therefοre, the grοwth rate (r) represented as a percentage is 4%, which is an οptiοn (c).

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Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.

A triangle is considered to be correct when one of its angles is 90 degrees. Moreover, a right angle is one that measures 90 degrees or more.

The non-right angle measurements of right triangles must add up to 90 degrees, which is a crucial condition. This results from the fact that a triangle's total number of angles equals 180 degrees.

In right triangle, the longest side is called hypotenuse.

Then,

hypotenuse H = 98 inches

Let Side S1 = 63 inches,

Let Side S2 = 73 inches,

Then, Pythagorean theorem must satisfy for right triangle

H² = (S1)² + (S2)²

98² = (63)² + (73)²

9604 = 3969 + 5329

9604 = 9298

But, 9604 ≠ 9298

Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.

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Answer:

B) 102

Step-by-step explanation:

To find x, we need to simplify and solve the equation (5x+6)=(7x-12):

5x + 6 = 7x - 12 // distribute the 5 and 7

6 + 12 = 7x - 5x // group the x terms and constants

18 = 2x

Now, we can solve for x by dividing both sides by 2:

18/2 = x

9 = x

Therefore, x is 9.

To find the solution if x = 9, we can simply substitute 9 for x in the given expressions:

(5x+6) = (5(9) + 6) = 51

(7x-12) = (7(9) - 12) = 51

Therefore, both expressions are equal to 51 when x = 9.

Answer:

G

Step-by-step explanation:

The diagonal of a square is equal to the diameter of the circle in this case

d = 16 cm

r = 0,5 × d

r = 0,5 × 16 = 8 cm

The circumference of the circle is equal to:

[tex]c = 2\pi \times r[/tex]

[tex]c = 2\pi \times 8 = 16\pi \: {cm}^{2} [/tex]