Based on the graphs of f (x) and g(x), what is (f ⋅ g)(1)?

Symmetry means,  hmmm usually a mirror image.

So when something is symmetry to another, is a way to say, one is the mirror image of the other, or namely they're just identical twins.

Now, if know that B is the midpoint, by definition is cutting AC into two equal halves, so AB is the mirror image of BC, so they're identical twins, there are no flaws, Q.E.D.

Check the picture below.

Answer:

Therefore, the amount that results from the given investment is approximately $579.64.

Step-by-step explanation:

We can use the formula for compound interest to find the amount that results from the given investment:

A = P(1 + r/n)^(nt)

where:

A = the amount

P = the principal (initial investment)

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, P = $500, r = 0.04, n = 4 (since the interest is compounded quarterly), and t = 3.5 years.

Plugging in the values, we get:

A = 500(1 + 0.04/4)^(4*3.5)

A = 500(1.01)^14

A = 500(1.159274...)

A ≈ $579.64

Therefore, the amount that results from the given investment is approximately $579.64.

The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.

To find the z-scores, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.

Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:

z = (39 - 34) / 5

z = 5 / 5

z = 1

So, the z-score for the raw score of 39 is 1.For a raw score of 30:

z = (30 - 34) / 5

z = -4 / 5

z = -0.8

The z-score for the raw score of 30 is -0.8.

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Answer:

x = 65 degrees

Step-by-step explanation:

The sum of all 4 interior (inside) angles in a quadrilateral = 360.

So 82+118+95+x = 360.

295+x = 360

x = 360-295

x = 65

Check that all the angles add up to 360:

82+118+95+65 = 360

Answer:

486 square feet

Step-by-step explanation:

To calculate the area of the path, first find the dimensions of the garden, including the path. Then find the area of this larger outer rectangle and subtract the area of the inner rectangle (the garden without the path).

The garden measures 28ft by 47ft.

The path is 3ft wide, so it adds a total of 6ft to the length (3ft on each side) and 6ft to the width.

The dimensions of the garden, including the path:

Length: 47ft + 6ft = 53ft

Width: 28ft + 6ft = 34ft

Find the area of the outer rectangle (including the path):

Area_outer = Length * Width = 53ft * 34ft = 1802 sq ft

Find the area of the inner rectangle (the garden without the path):

Area_inner = 28ft * 47ft = 1316 sq ft

Now subtract the area of the inner rectangle from the area of the outer rectangle to find the area of just the path:

Area_path = Area_outer - Area_inner = 1802 sq ft - 1316 sq ft = 486 sq ft

So, the area of the path is 486 square feet.

Answer: 486 square feet;

Step-by-step explanation:

Area of the garden = 28 x 47 = 1316ft.²

-

Length of the garden and path = Length of the garden + 3 ft. on both sides

Length of the garden and path = 28 + 3 + 3 = 34 ft.

-

Width of the garden and path = Width of the garden + 3 ft. on both sides

Width of the garden and path = 47 + 3 + 3 = 53ft.

-

Area of the garden and path = Length x Width

Area of the garden and path = 34 x 53 = 1802 ft²  

-

Area of the path = Area of the garden and path - Area of the garden

Area of the path = 1802 - 1316 =  486ft²

-

Answer: 486ft²

The solution is:

[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex]

The partial fraction expansion of a rational fraction is  described as an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.

To solve the above partial fraction decomposition,

[tex]x^3 + x^2 - 2x = x(x^2 + x - 2) = x(x+2)(x-1)[/tex]

we then write the fraction as a sum of partial fractions:

[tex]fx-2dx = \frac{A }{x } + \frac{B}{x + 2 } + \frac{C }{x - 1}[/tex]

We  find the values of A, B, and C by  multiplying  both sides by the common denominator (x)(x+2)(x-1) and  substituting

fx-2dx = A(x+2)(x-1) + B(x)(x-1) + C(x)(x+2)

We set  x = 0

0 = -2A

A = 0.

We set  x = -2

-2 = 20B/(-2)(-4)

-2 = -5B

B = 2/5.

we set  x = 1

1 = 3C

C = 1/3.

fx-2dx = 0/x +  2/5/(x+2) +  1/3/(x-1)

We integrate each term separately and have the solution as :

[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex].

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The slope (m) and y-intercept (b) with the equation of the line in slope-intercept form are given as: m = 2 and b = 5 is y = 2x + 5; m = 3 and b = 5 is y = 3x + 5; m = 5 and b = 4 is y = 5x + 4.

If m represents the slope of a line and b represents its y-intercept, the equation of the line in slope-intercept form is written as: y = mx + b.

Where m = 2 and b = 5, the equation of the line would be expressed as: y = 2x + 5.

Where m = 3 and b = 5, the equation of the line would be expressed as: y = 3x + 5.

Where m = 5 and b = 4, the equation of the line would be expressed as: y = 5x + 4.

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Answer:

The length of each side of the square is approximately 4.24 cm.

Explanation:

We can use the Pythagorean theorem to find the length of each side of the square. Let "s" be the length of each side of the square. The diagonal of the square, which is 6 cm, is the hypotenuse of a right triangle whose legs are two sides of the square. So we have:

[tex]s^2 + s^2 = 6^2[/tex]

Simplifying this equation, we get:

[tex]2s^2 = 36[/tex]

Dividing both sides by 2, we get:

[tex]s^2 = 18[/tex]

Taking the square root of both sides, we get:

s ≈ 4.24

Therefore, the length of each side of the square is approximately 4.24 cm.

The amounts of koalas are given as follows:

a. Initially: 47.

b. 13 weeks: 21.

c. 23 weeks: 19.

d. The virus will not kill all the koalas, as when t -> ∞, N(t) -> ∞.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

N(t) = 15 + 96/(t + 3).

For the initial number of koalas, we have that t = 0, hence:

N(0) = 15 + 96/3 = 47.

After 13 weeks, the number is given as follows:

N(13) = 15 + 96/16 = 21.

After 23 weeks, the number is given as follows:

N(23) = 15 + 96/26 = 19.

As t -> ∞, we have that:

N(∞) = 15 + 96/∞ = 15 + 0 = 15.

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By rewriting the 3 given systems, we will see that:

1) Independent and inconsistent.

2) Independent and consistent.

3) Independent and inconsistent..

Let's analyze each system.

Let's look at the first one, we can rewrite it as:

y = 3x - 1

And, 2y - 6x = 4

2y = 6x + 4

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

Now let's look at the second system, we can rewrite it as:

2y = - x + 6

And, 4y + 2x = 12

y = - 1/2x + 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

For the final system we have:

y = 2x + 3

x + y = - 9

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

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It is true that the integers (-4, -2,0, 2, 4) form the set of even integers.

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

Set = (-4, -2,0, 2, 4)

In the above set, we can see that all numbers in the set do not have decimal point

This means that the set of numbers are integers

Also, we can see that the integers are integers that are divisible by 2

This means that the set of integers are set of even integers

Hence, the statement is true

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Complete question

As a integers are integers divisible by 2. The integers (-4, -2,0, 2, 4) form the set of even integers.

True or false

The value of sin (2π/3) is √3/2.

The value of sin (5π/4) is -√2/2.

The value of sin (180) is 0.

The value of cos (π/4) is √2/2.

The value of cos (300) is ¹/₂.

The value of cos (7π/6) is -√3/2.

The value of sin (2π/3) is calculated as follows;

sin (2π/3) = sin (2 x 180 / 3) = sin (120)

sin (120) = sin (60) = √3/2

The value of sin (5π/4) is calculated as follows;

sin (5π/4) = sin (5 x 180 / 4) = sin (225)

sin (225) = - sin (45) = -√2/2

The value of sin (180) is calculated as follows;

sin (180) = sin (0) = 0

The value of cos (π/4) is calculated as follows;

cos (π/4) = cos (180/4) = cos (45)

cos (45) = √2/2

The value of cos (300) is calculated as follows;

cos (300) = cos (60)

cos (60) = ¹/₂

The value of cos (7π/6) is calculated as follows;

cos (7π/6) = cos (7 x 180 / 6) = cos (210)

cos (210) = - cos(30) = -√3/2

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The height of the beaker is 6.35 cm.

To find the height of the beaker, we can use the formula for the volume of a cylinder, which is given by:

Volume = π ×[tex]radius^2[/tex] × height

In this case, we have the volume of the beaker as 1,004.8 cubic centimeters and the radius as 4 cm.

1,004.8 = π × [tex]4^2[/tex] × height

Simplifying the equation:

1,004.8 = 16π × height

To solve for the height, divide both sides of the equation by 16π:

height = 1,004.8 / (16π)

Using a calculator for the approximation of π (pi) as 3.14159, we can calculate the height:

height ≈ 1,004.8 / (16 × 3.14159)

height ≈ 6.35 cm

The height of the beaker is approximately 6.35 cm.

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Based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.

We know that

Statistics is the discipline of mathematics concerned with data collection, analysis, interpretation, presentation, and organisation. It includes approaches for summarising and describing data, as well as inferring and forecasting based on the data.

Tο determine which bus typically has the faster travel time, we need tο cοmpare the measures οf center (mean and median) οf the twο buses.

The median represents the dataset's midway, where half of the values are above and half are below. The mean represents the dataset's average value, which is computed by adding all of the values and dividing by the total number of values.

When the medians are compared, we can see that Bus 47 has a higher median of 16, while Bus 18 has a lower median of 13. This shows that Bus 47 may have a faster average trip time.

However, we must also consider the methods. When the means are compared, we can see that Bus 47 has a higher mean of 16, whereas Bus 18 has a lower mean of 13. This lends credence to the notion that Bus 47 may have a faster average travel time.

Therefοre, based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.

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The complete question is:

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13

Bus 47, with a median of 16

Bus 18, with a mean of 13

Bus 47, with a mean of 16

Answer:

C) (-2 , 4)

x = -2

y = 4

Step-by-step explanation:

    We can use substitution method.

     3x + 2y = 2 -------------(I)

    -2x + y  = 8             --------------(II)

Make y as the subject in equation (II)

              y = 8 + 2x ----------------(III)

Substitute y = 8 + 2x in equation (I) and we can find the value of 'x',

          3x + 2*(8 + 2x) = 2

     3x + 2*8 + 2*2x    = 2 {Distributive property}

           3x + 16 + 4x    = 2

           3x + 4x + 16    = 2

Combine like terms,

                      7x + 16 = 2

Subtract 16 from both sides,

                           7x   = 2 - 16

                           7x   = -14

Divide both sides by 7,

                             x  = - 14 ÷ 7

                             [tex]\boxed{\bf x = -2}[/tex]

Substitute x = -2 in equation (III)

           y = 2*(-2) + 8

              = -4 + 8

           [tex]\boxed{\bf y = 4}[/tex]

y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation

The given equation is an equation of an ellipse centered at the origin with a major axis of length 2√7 and a minor axis of length 2√3.

To find two functions defined implicitly by this equation, we can solve for y in terms of x using algebra.

First, we can isolate y²/3 by subtracting x²/7 from both sides:

y²/3 = 1 - x²/7

Multiply by 3 on both sides to eliminate the fraction:

y² = 3 - 3x²/7

y = ±√(3 - 3x²/7)

These are the two functions defined implicitly by the given equation.

The positive square root gives the upper half of the ellipse, while the negative square root gives the lower half.

Hence, y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation

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Answer:

24 years old.

Step-by-step explanation:

Let's say that Elga's age is x years old. Then Alvin's age would be 11 years older than Elga, or x + 11 years old.

We know that the sum of their ages is 59 years old, so we can write an equation:

x + (x + 11) = 59

Simplifying the left side of the equation:

2x + 11 = 59

Subtracting 11 from both sides:

2x = 48

Dividing both sides by 2:

x = 24

Therefore, Elga's age is 24 years old.

Answer: 24

Step-by-step explanation:

Set Elga's age to x and Alvin's age to x+11...

(x+11)+x=59

2x=48

x=24

The ratio of literature books to children books is: a) 4 literature books: 1 children book.

Ratio is simply the numerical quantity that relates two amounts of quantities, showing how much one contains of the other.

The ratio of literature books to children books can be found by dividing the number of literature books by the number of children books:

Ratio of literature books to children books = Number of literature books / Number of children books

Plugging in the given values, we get:

Ratio of literature books to children books = 400 / 100 = 4

So the ratio of literature books to children books is 4:1. Therefore, the answer is option a) 4 literature books: 1 children book.

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Hello

4x² - 28x = -33

4x² - 28x + 33 = 0

(4x² - 6x) + (-22x + 33) = 0

2x(2x - 3) - 11(2x - 3) = 0

(2x - 11)(2x - 3) = 0

2x - 11 = 0               2x - 3 = 0

2x = 11                     2x = 3

x = 11/2                    x = 3/2

The point estimate is given as 0.4688

The standard error = 0.051

P = x / n

= 45 / 96

= 0.4688

The point estimate is given as 0.4688

How to solve for the standard error

SE = √[ p(1 - p) / n ]

Substituting the values we have:

SE = √[ 0.46875 * (1 - 0.46875) / 96 ]

= √[ 0.2482 / 96 ]

The standard error = 0.051

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Question

For the given confidence level and values of x and n, find the following.

=x45, =n96, confidence level 95% find the point estimate and the standard error

Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.

The three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:

1.  Draw a line segment PQ.

2. Place the compass at point P and draw a circle with radius PQ.

3. Without changing the radius of the compass, place the compass at point Q and draw another circle.

4. The intersection of the two circles is point R.

Draw line segments PR and QR to form an equilateral triangle.

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Answer:

Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.

How to explain the triangle

The three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:

1.  Draw a line segment PQ.

2. Place the compass at point P and draw a circle with radius PQ.

3. Without changing the radius of the compass, place the compass at point Q and draw another circle.

4. The intersection of the two circles is point R.

Draw line segments PR and QR to form an equilateral triangle.

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[1st Picture] Answer: x = 3.98

Step-by-step explanation:

    We are given the opposite side and adjacent side from our reference angle. This will use the tangent function. tanθ = [tex]\frac{opposite}{adjacent}[/tex].

tan(53°) = [tex]\frac{x}{3}[/tex]

3tan(53°) = x

x = 3.98

[2nd Picture] Answer: x = 3.13

Step-by-step explanation:

    Here, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex].

sin(23°) = [tex]\frac{x}{8}[/tex]

8sin(23°) = x

x = 3.13

[3rd Picture - #6] Answer: θ = 63.4°

Step-by-step explanation:

    Again, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex]. To find the angle measurement of theta at the end, we will use the inverse of sine.

sin(θ) = [tex]\frac{6}{6.71}[/tex]

[tex]sin^{-1}[/tex](sin(θ)) = [tex]sin^{-1}[/tex]([tex]\frac{6}{6.71}[/tex])

θ = 63.4°

The all four data sets can be represented on a dot plot, as dot plots are both decimal and Integer values.

A dot plot is a graphical representation that displays data points as dots along a number line. It is commonly used to show the distribution of a small set of quantitative data.

The data set should be shown on a dot plot, we need to consider the characteristics of the data.

1. Data Set 1: {0.012, 0.078, 0.093, 0.147, 0.187}

This data set consists of decimal values. A dot plot can effectively represent decimal values, where each dot represents a data point. Therefore, Data Set 1 should be shown on a dot plot.

2. Data Set 2: {1.3, 1.9, 2.5, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0}

Similar to Data Set 1, this data set consists of decimal values. Hence, it can also be effectively represented on a dot plot. Each value would be represented as a dot along the number line.

3. Data Set 3: {712, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730}

This data set consists of integer values. Dot plots are commonly used for discrete data, including integers. Therefore, Data Set 3 can be appropriately represented on a dot plot.

4. Data Set 4: {16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97}

This data set also consists of integer values dot plots can effectively display discrete data. Hence, Data Set 4 can be shown on a dot plot.

all four data sets can be appropriately represented on a dot plot, as dot plots are suitable for displaying both decimal and integer values.

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The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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The profit did you make from your investment is $20

To determine how much profit you made from your investment, we need to find the value of P that makes your friend's profit equal to the initial investment of $20.

In other words, we need to solve the equation:

0.4P - 20 = 20

Adding 20 to both sides, we get:

0.4P = 40

Dividing both sides by 0.4, we get:

P = 100

if the football is sold for $100, your friend's profit will be $100 - $50 = $50, and your profit will be 40% of $50, or $20.

This means that you have made back your initial investment of $20, and have earned an additional profit of $20.

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The circumference of a circle with a radius of 21 centimeters is 132 centimeters.

The circumference is the distance around the boundary of a closed curve or shape. In the case of a circle, the circumference is the total length of the circular boundary.

To find the circumference of a circle with a radius of 21 centimeters, we can use the formula C = 2πR, where R is the radius and π is the mathematical constant approximately equal to 22/7.

Substituting the given values:

C = 2 x (22/7) x 21

C = (44/7) x 21

C = 924/7

C ≈ 132 centimeters

Therefore, the circumference of a circle with a radius of 21 centimeters is 132 centimeters.

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The first time that Account X will have more money than Account W, excluding the initial deposits, is in the fifth month.

To determine when Account X will contain more money than Account W, we need to compare the balances of the two accounts each month until Account X surpasses Account W.

Let's analyze the balances of the two accounts month by month:

Month 1:

Account W: $0 + $100 = $100

Account X: $1 + 80% × $1 = $1 + $0.80 = $1.80

Month 2:

Account W: $100 + $100 = $200

Account X: $1.80 + 80% × $1.80 = $1.80 + $1.44 = $3.24

Month 3:

Account W: $200 + $100 = $300

Account X: $3.24 + 80% × $3.24 = $3.24 + $2.592 = $5.832

Month 4:

Account W: $300 + $100 = $400

Account X: $5.832 + 80% × $5.832 = $5.832 + $4.6656 = $10.4976

Month 5:

Account W: $400 + $100 = $500

Account X: $10.4976 + 80% × $10.4976 = $10.4976 + $8.39808 = $18.89568

Please note that the values provided in this calculation assume no withdrawals and no interest earned on the balances.

As we can see, by the fifth month, Account X will contain more money than Account W. The first time that Account X will have more money than Account W, excluding the initial deposits, is in the fifth month.

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