Select the functions f(x)=√x+5 and g(x)=√5-x. Select the Operation fXg and Combine Functions box, and slowly slide the x-slider to the right to graph the function (fg)(x) Note that the graph is a semicircle. Find the equation of this semicircle by simplifying (fXg)(x) Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed.

We traveled to our grandparents for vacation. We drove 234.7 miles before lunch. We got back in the car and drove 37.93 miles before

Answer: 1 km

Step-by-step explanation: For this question, you need to first convert the 20 minutes into hours. You know that an hour is 60 minutes, so dividing 20 by 60 leaves you with 1/3 of an hour. The question says that she can go 3 km/h in her wheelchair, so 3 x 1/3 = 1 km.

Answer:

[tex]d = \frac{29}{10} [/tex]

Step-by-step explanation:

[tex]d = 2 \frac{9}{10} [/tex]

d = 2.9

Answer:

zero

Step-by-step explanation:

the projection of vector RS onto vector PQ is zero

please find the attachment for detail

Answer:

Step-by-step explanation:

The area of a right triangle is A=(1/2)base*height

A=(1/2)(b)(h)

200ft²=(1/2)(10ft)h

200ft²=5ft(h)

40ft=h

Using Pythagorean Theorem for a right triangle a²+b²=c²

a²+b²=c²

(40ft)²+(10ft)²=c²

1600ft²+100ft²=c²

1700ft²=c²

√(1700ft²)=c

10√17=c

41.231056256=c

41.2≅c

Answer:

Step-by-step explanation:

Lets assume the following binary numbers:

a=101,b=10

1)a-b=101-10=91

2)a*b=1010

3)a/ba= ie=b*a=1010

a/ba=101/1010=0.1

4)a-b=101-10=91

5)a/b=101/10=10.1

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Solving the assumed pairs of binary numbers for the operations such as addition, subtraction , multiplication and divisions give 9,090 , 10,212,111 and 9.99

What is binary number?

A binary number system is one of the four types of number system. In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one). The binary numbers here are expressed in the base-2 numeral system. For example, (101)2 is a binary number

Lets assume the following binary numbers:

a=10101, b=1011

1) a-b=10101-1011=9,090

2) axb=10,212,111

3) a/b= 10101 / 1011 = 9.99

4) a + b = 10101 +1011 = 11,112

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The complete question is :

calculate  a−b, a×b , and a÷b, a+b,  for the following pairs of binary numbers : for a=10101 and b=1011.

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

A quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration.

Given that,

The equation for the plane through p0(−1,1,9)

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (-1, 1, 9) that is parallel to the xy-plane has equation

〈x - (-1), y - 1, z - 9〉 • 〈0, 0, 1〉 = 0

x + 1 = 0

y - 1 = 0

z - 9 = 1

z = 1 + 9

z = 10

Therefore,

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

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The slope-intercept format of the linear function in this problem is given as follows:

y = x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

Two points on the graph of the function are given as follows:

(-8, -10) and (12,10).

When x increases by 20, y increases by 20, hence the slope m is given as follows:

m = 20/20 = 1.

Hence:

y = x + b.

When x = 12, y = 10, hence the intercept b is given as follows:

10 = 12 + b

b = -2.

Hence the function is:

y = x - 2.

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The height of the cube calculated from volume 48x⁶y⁵  cubic units, length 6x³y and breadth 4x²y³ is 2xy units.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

The Volume of the cube is 48x⁶y⁵  cubic units

The length of the cube is 6x³y unit

Breadth of the cube is 4x²y³ unit

The height of the cube be H

We know,

volume(V)  = length(L) * breadth(B) * height(H)

⇒ height = V/L*B = (48x⁶y⁵)/(6x³y)*(4x²y³)

⇒ height = (48x⁶y⁵)/(24x⁵y⁴) = 2xy

The height of the cube calculated from volume 48x⁶y⁵  cubic units, length 6x³y and breadth 4x²y³ is 2xy units.

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∫10∫1∫ ∫01∫x1∫xy dzdydx as an iterated integral in the order dydzdx then the sum of the six limits of integration =  [tex]\int\limits^x_0\int\limits^2_1 f(x,y) dydx[/tex]

Let D be the region bounded by the lines y = 1, y = 2, x = 0, and x = x. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.

[tex]\int\limits^x_0\int\limits^2_1 f(x,y) dydx[/tex]

The region is bounded by the lines y = 1, y = 2, x = 0, and x = x. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and x = 0 being the base of the triangle. Then, we can express the double

integral as: [tex]\int\limits^x_0\int\limits^2_1 f(x,y) dydx[/tex]where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.

Therefore,

∫10∫1∫ ∫01∫x1∫xy dzdydx as an iterated integral in the order dydzdx then the sum of the six limits of integration =  [tex]\int\limits^x_0\int\limits^2_1 f(x,y) dydx[/tex]

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The turning point of the function is (37, -232)

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

y = f(x) has a turning point of (-33, 22)

For the transformed function f(x + 70) -254, we have

Turning point = (-33 + 70, 22 - 254)

Evaluate the like terms

Turning point = (37, -232)

Hence, the turning point is (37, -232)

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hope help you keep smiling a =7.35*3.44

On solving the provided question, we can say that the coordinates are (-2,0) and (0,2) slope is = m = 2-0/0+2= 1 and slope intercept equation is y-2 = x+2 => x-y = 0

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

the coordinates are (-2,0) and (0,2)

slope is = m = 2-0/0+2= 1

slope intercept equation is y-2 = x+2

x-y = 0

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Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] - [tex]\frac{1}{12}[/tex]

[tex]\frac{1}{6}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{12}[/tex]   ([tex]\frac{2}{2}[/tex] is another name for 1, so we are just multiplying [tex]\frac{1}{6}[/tex] x 1)

[tex]\frac{1}{6}[/tex] is equivalent to [tex]\frac{2}{12}[/tex]

[tex]\frac{2}{12}[/tex] - [tex]\frac{1}{12}[/tex] = [tex]\frac{1}{12}[/tex]

A line passes through the two points (4, 7) and (2, 3).

The equation of the line is y = 2x + 1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line passes through the two points (4, 7) and (2, 3).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 7 = {(3 -7)/(2 -4)} (x - 4)

y - 7 = 2(x - 4)

y = 2x + 1

Therefore, the equation of the line is y = 2x + 1.

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The side of the square will be 47 cm.

A quadrilateral is a four-sided polygon, having four edges and four corners.

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal.

Given that the side is x cm

each side of the square is increased by 4cm

Then side will be x+4 cm

The area is increased by 392cm².

x²+392=(x+4)²

x²+392=x²+16+8x

392-16=8x

376=8x

Divide both sides by 8

x=376/8

x=47

Hence, the side of the square will be 47 cm.

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The area of the circle that has a diameter of 78 cm is: 4,778.4 cm².

The area of a circle can be calculated using the following formula:

A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (the distance from the center of the circle to its edge).

Given that the diameter of the circle = 78 cm, therefore:

Radius (r) = 78/2 = 39 cm

Area of the circle = π * r² = π * 39²

Area of the circle = 4,778.4 cm²

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The value of the fraction is given by the equation A = (x - 6) / (x + 2) (3x - 2)

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the equation will be

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

On simplifying the equation , we get

Finding the common denominator and LCM , we get

A = [ ( 3x - 2 ) - 2 ( x + 2 ) ] / (x + 2) (3x - 2)

On further simplification , we get

A = ( 3x - 2 - 2x - 4 ) / (x + 2) (3x - 2)

A = ( x - 6 ) / (x + 2) (3x - 2)

Hence , the fraction is A = ( x - 6 ) / (x + 2) (3x - 2)

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the expected value of perfect information is not the same as the expected value with perfect information then it is a true statement

For a decision alternative the weighted average of the payoffs is known as the Expected Value.

For a chance node, it is the weighted average of the payoffs. The weights are the state-of-nature probabilities.  A weighted average is an average that multiplies each component by a factor representing its frequency or probability. The expected value is the return or cost you can expect on average, given many trials. The payoff of a game is the expected value of the game minus the cost.

The expected value is the return or cost you can expect on average, given many trials. A weighted average is an average that multiplies each component by a factor representing its frequency or probability. A weighted average is like a regular average except the data is often given to you in summary form.

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Therefore, the state with the highest improvement in SAT score from 2011 to 2014 is Wyoming


EXPLANATION:

Step-1:
a.

Obtain the two SAT score distributions by using graph, using MINITAB.

For SAT 2011.

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2011.

4: Click OK.

Step-2:
For SAT 2014

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2014.

4: Click OK.

Conclusion:

The frequency of SAT score in 2014 is comparatively higher than that of SAT score of 2011.There is an increase in frequency of SAT score in between 1500 and 1600, from 2011 to 2014.However there is a sudden decrease in SAT score of 1600, from 2011 to 2014, and again rise of the score between 1700 to 1800.


step-3
b.

Summarization:

Obtain a graph for the difference in the SAT scores of 2014 and 2011, using MINITAB.

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2014.

4: Click OK.

step-4:
c.

Interpretation:

In part (b), maximum of the times, there is no difference in SAT score from 2011 to 2014. However in some cases, there is an increase in SAT score in 2014, than in 2011.

In part (a), individual SAT score was found, and hence no conclusion was drawn on whether the SAT score increases or decreases form 2011 and 2014. The difference and the comparison of the score is observed in part (b) of the exercise.

d.
Observe the state with the highest improvement in SAT score from 2011 to 2014.

The state with the highest improvement in SAT score from 2011 to 2014 is Wyoming, with a difference of 65 scores from 2011 to 2014.

Therefore, the state with the highest improvement in SAT score from 2011 to 2014 is Wyoming.

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Don't worry, I gotchya :)

50% of 2006 is ⇒1003

2006% of 50 is ⇒1003

So 2006% of 50 + 50% of 2006 = 1003 + 1003

1003+1003 = 2006

Hope this helped you!

Answer:

.................                

Step-by-step explanation:

        /..........

The most appropriate statement is that C. The shaded area represent both 2/3 and 6/9 of the whole shape.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Given a square.

This square is divided in to 9 equal sized squares, with 3 rows and 3 columns.

Out of the 9 equal sized squares, 6 squares are shaded.

We can write the fraction of shaded squares to total number of squares as 6/9.

In the same way, we have in the question that, 6 squares which are shaded is the squares in the first two columns, where each column has three squares.

So we can say that, out of 3 equal sized columns, two columns are shaded.

Fraction of shaded columns to total columns is 2/3.

So 2/3 = 6/9.

Hence shaded area represent both 2/3 and 6/9 of the whole shape.

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The region that minimizes the value of ∫∫R(x² + y² - 9)dA is the unit circle centered at (0, 0) with radius 3.

To see why this is the case, consider that x² + y² is the equation of a circle with center at the origin. The value of the integrand, x² + y² - 9, is minimized when x² + y² = 9, which is a circle with radius 3 centered at the origin.

The double integral ∫∫R(x² + y² - 9)dA represents the total area under the graph of x² + y² - 9 over the region R. The minimum value of this integral would be achieved when the region R is the smallest possible region that covers the minimum value of the integrand.

In this case, the smallest region that covers the minimum value of the integrand is the unit circle centered at (0, 0) with radius 3.

Therefore, the region that minimizes the value of ∫∫R(x² + y² - 9)dA is the unit circle centered at (0, 0) with radius 3.

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If Vector A = [15, 80 degrees] and Vector B = 12i - 16j, the magnitude of Vector A - Vector B is 32.17

We are given Vector A = ( 15, 80° )

It can be written as: Vector A = 15 cos 80° i + 15 sin 80° j

                   Vector A = 2.6 i + 14.77 j

Also, Vector B = 12 i - 16 j

Now, Vector A - Vector B = 2.6 i + 14.77 j - ( 12 i - 16 j )

                                          = -9.4 i + 30.77 j

We are asked to calculate the Magnitude of Vector A - Vector B = | A - B|

                                                        = ((-9.4)² + (30.77)²)^0.5

                                                        = (88.36 + 946.79)^0.5

                                                        = 32.17

Therefore, the magnitude of Vector A - Vector B is 32.17

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Answer:

35

Step-by-step explanation:

To find the value of x that makes the median and mean equal, we first need to determine the median of the data set. In this case, the median is the middle value when the data is arranged in order. Since there are 7 values, the median is the fourth value, which is 11.

To find the mean of the data set, we add up all the values and divide by the number of values.

Mean = (6 + 8 + 3 + 11 + 5 + 13 + x) / 7

To find x, we need to make the median and mean equal.

11 = (6 + 8 + 3 + 11 + 5 + 13 + x) / 7

Multiply both sides by 7

77 = 6 + 8 + 3 + 11 + 5 + 13 + x

Subtracting the sum of the other values from both sides

77 - 42 = x

x = 35

So, the value of x that makes the median and mean equal is 35.

There are 4 possible answers for each question, so there are 4^10 = 10,048 different ways to answer the quiz.

This is because for each question, there are 4 choices, and since there are 10 questions, the total number of choices is 444444444*4 = 4^10, which equals 10,048.

Answer:

1. Answer is A 43 degrees

2. Answer is c 65 degrees

Step-by-step explanation: Hope this helps! :))

A cardioid is a mathematical curve that is commonly studied in geometry and calculus. It is defined by the equation r = 1 + cos(θ), where r is the radial distance from the origin and θ is the polar angle. The cardioid has a distinctive heart-shaped form, and it is a smooth curve that can have tangent lines at certain points.

Horizontal Tangent Line:

A horizontal tangent line is a tangent line that is parallel to the x-axis. To find the points on the cardioid at which there is a horizontal tangent line, we need to find the points where the derivative of the curve is equal to zero in the x direction. The derivative of r = 1 + cos(θ) with respect to θ is -sin(θ), and the derivative of r with respect to x is cos(θ). Setting these two derivatives equal to zero, we have:

-sin(θ) = 0

cos(θ) = 0

The first equation has a solution when θ = n * π, where n is an integer. The second equation has solutions when θ = (2n + 1) * π/2, where n is an integer. When θ = n * π, the cardioid is at its maximum value, and when θ = (2n + 1) * π/2, the cardioid is at its minimum value. These points correspond to horizontal tangent lines on the cardioid.

Vertical Tangent Line:

A vertical tangent line is a tangent line that is perpendicular to the x-axis. To find the points on the cardioid at which there is a vertical tangent line, we need to find the points where the derivative of the curve is equal to zero in the y direction. The derivative of r with respect to y is sin(θ), and setting this derivative equal to zero, we have:

sin(θ) = 0

This equation has solutions when θ = (2n) * π/2, where n is an integer. These points correspond to vertical tangent lines on the cardioid.

Singular Point:

A singular point is a point on the curve at which the curve is not smooth and its tangent line is undefined. To find the singular points on the cardioid, we need to find the points where the second derivative of the curve is equal to zero. The second derivative of r = 1 + cos(θ) with respect to θ is -cos(θ), and setting this derivative equal to zero, we have:

-cos(θ) = 0

This equation has solutions when θ = n * π, where n is an integer. These points correspond to singular points on the cardioid.

In conclusion, the points on the cardioid at which there is a horizontal tangent line are given by θ = n * π and θ = (2n + 1) * π/2. The points at which there is a vertical tangent line are given by θ = (2n) * π/2. The singular points are given by θ = n * π. These points can be used to study the properties and behavior of the cardioid in more detail.

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