Use the given data to make a box-and-whisker plot.
5, 4, 16, 21, 10, 6, 15

The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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The area of the figure as shown in the diagram is 24 in².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The mathemematical sum of the three numbers 1+1+1 would give 3

Addition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.

Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.

Therefore, the sum of the 1+1+1 is 3

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Answer:

? = 7

Step-by-step explanation:

The equation of the line parallel to another line will have the same slope. The given line y = 7x + 2 has a slope of 7.

To find the equation of the line that passes through the point (3, -1) and is parallel to the given line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

So, the equation of the line parallel to y = 7x + 2 and passing through the point (3, -1) is:

y - (-1) = 7(x - 3)

Simplifying this, we get:

y = 7x - 21 - 1

y = 7x - 22

So, the equation of the line is y = 7x - 22.

Given the form of the equation y + 1 = ?(x -3). We then know the answer is y + 1 = 7 (x - 3)

The line's equation is :

Solution:

If two lines are parallel then their slopes are equal.

The slope of [tex]\sf{y=7x+2}[/tex] is 7, so the slope of the line parallel to it is 7.

Now, we should plug the slope and the point into the point slope equation. See, we're even given a hint :

Remember : y - y₁ = m(x - x₁).

This hint tells us the point slope equation.

So I plugin :

[tex]\bf{y-(-1)=7(x-3)}[/tex]

Simplify.

[tex]\bf{y+1=7(x-3)}[/tex]

This is it, we don't have to simplify all the way to slope intercept.

The pairs of alternate exterior angles in the given figure is Option D) ∠1 and ∠7; ∠2 and ∠8

Alternate exterior angles are a pair of angles formed by a transversal line intersecting two parallel lines and located on opposite sides of the transversal and on the exterior of the parallel lines. In other words, if two parallel lines are intersected by a third line (the transversal), then the pairs of angles on opposite sides of the transversal and outside the parallel lines are alternate exterior angles. These angles are congruent to each other.

In the given figure two parallel lines, which are crossed by a transversal line which forms angles.

Now according to the given figure

so, answer is Option D) ∠1 and ∠7; ∠2 and ∠8

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Answer: I have this same exact question

Step-by-step explanation: So someone please help this person, or animal which ever you perfer

53 revolutions will be needed by the wheels to make it travel 300 feet.

Option D is the correct answer.

We have,

To solve this problem, we can use the formula:

Number of revolutions = Distance / Circumference of the wheel

First, let's convert the distance from feet to inches:

300 feet = 300 x 12 = 3600 inches

Next, we need to calculate the circumference of the wheel using the given diameter:

Circumference = π x diameter

Circumference = 3.14 x 22 inches

Circumference ≈ 69.08 inches

(rounded to two decimal places)

Now we can calculate the number of revolutions:

Number of revolutions = 3600 inches / 69.08 inches

= 52.14 revolutions

Rounding to the nearest whole number.

= 52 revolutions.

Therefore,

53 revolutions will be needed by the wheels to make it travel 300 feet.

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The bicycle wheels will need 53 full revolutions to travel 300 feet.

The circumference of a wheel can be calculated using the formula:

circumference = π x diameter

So, circumference = 3.14 x 22

= 69.08 inches

Now, converting feet to inches

300 feet = 300 x 12 inches

300 feet = 3600 inches

So, number of revolutions:

revolutions = distance / circumference

= 3600 / 69.08

≈ 52.11

Therefore, the bicycle wheels will need 53 full revolutions to travel 300 feet.

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Answer:

B, C, E

Step-by-step explanation:

For a rectangle,

area = length × width

Let length = y.

Then the width is y - 5.

A = LW

750 = y(y - 5)

y(y - 5) = 750

y² - 5y - 750 = 0

All equations that can be put in the form above are correct.

A) y(y + 5) = 750

y² + 5y - 750 = 0

No

B) y² – 5y = 750

y² - 5y - 750 = 0

Yes

C) 750 – y(y – 5) = 0

750 - y² + 5y = 0

y²- 5y - 750 = 0

Yes

D) y(y – 5) + 750 = 0

y² - 5y + 750 = 0

No

E) (y + 25)(y – 30) = 0

y² + 25y - 30y - 750 = 0

y² - 5y - 750 = 0

Yes

The equation of the parabola is: y = (1/4)(x-3)²+ 2

In Parabola mathematics, it is defined as a set of points that are equidistant from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.

To find the equation of the parabola, we first need to determine the vertex. The vertex is the midpoint between the focus and the directrix, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of symmetry passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the axis of symmetry is x=3.

Next, we need to find the distance between a point on the parabola and the focus, as well as the distance between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)

The distance between (x,y) and the directrix is simply the absolute value of the difference between y and 1: |y-1|

Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|

Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)

Therefore, the equation of the parabola is: y = (1/4)(x-3)²+ 2

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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.

Complete Question : Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1

The value of the unknown c in the algebraic fraction equation is equal to -24

To solve the simple algebraic fraction equation, we cross multiply to eliminate the fractions, then simplify by solving for the unknown

Given the algebraic equation:

-c/6 = 4

(-c/6) × 6 = 4 × 6

-c = 4 × 6

-c = 24

multiply both sides by -1

-1 × -c = -1 × 24

c = -24

Therefore, the value of the unknown c in the algebraic fraction equation is equal to -24

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Answer:

I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408

Step-by-step explanation:

Thomas Sowell's speech "Morality vs. Sanctimoniousness" addresses the distinction between genuine moral actions and the outward appearance of moral superiority.

The keynote of his speech is to prioritize practical and fruitful measures over merely appearing sensible or righteous. According to Sowell, it is crucial to solve prevalent social problems with pragmatic, yet effective solutions instead of adopting self-righteous attitudes that lack meaningful outcomes.

Essentially, he opines that authentic ethical principles should be anchored in consideration for others' welfare and empirical evidence rather than being fueled by personal moral validation or pretentiousness.

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The measure of p in the diagram is,

m∠P = 45°

We have to given that;

PM is perpendicular to MO.

Now, If m ∠P = m∠2

then it's an isosceles triangle.

And, m ∠M = 90°, therefore it's an isosceles right triangle.

We know that,

the sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

m∠P + m∠2  + m∠M = 180°

Substitute m∠M = 90° and m∠P = m∠2 = x:

x + x + 90° = 180°    

substract 90° from both sides

2x = 90°      

divide both sides by 2

x = 45°

m∠P = 45°

Thus, The measure of p in the diagram is,

m∠P = 45°

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The mode of the data represented in this line plot will be 8.

Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.

The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.

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Answer: To show that log5 7 = 1/(2n-1)(2mn-m-2), we'll start by using logarithmic properties and the given information.

First, let's express log9 75 in terms of the base 5 logarithm, using the change of base formula:

log9 75 = log5 75 / log5 9

Next, let's simplify the expression inside the logarithm by breaking down 75 and 9 into their prime factors:

log5 (3^2 * 5^2) / log5 (3^2)

Now, using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

log5 (3^2) + log5 (5^2) - log5 (3^2)

Simplifying further, we have:

2 log5 3 + 2 log5 5 - 2 log5 3

The 2 log5 3 and -2 log5 3 terms cancel each other out, leaving:

2 log5 5

Now, let's substitute the value of m from the given information (log5 21 = m) into the expression:

2 log5 5 = 2 (log5 (5^2)) = 2(2 log5 5) = 4 log5 5 = 4m

Now, let's substitute the value of n from the given information (log9 75 = n) into the expression:

4m = 4(log5 5) = 4(1/2 log5 (5^2)) = 4(1/2 log5 25) = 4(1/2 log5 (5^2 * 5^2))

Using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

4(1/2 (log5 5^2 + log5 5^2)) = 4(1/2 (2 log5 5 + 2 log5 5)) = 4(1/2 (4 log5 5))

Simplifying further, we have:

4(1/2) (4 log5 5) = 4(2 log5 5) = 8 log5 5 = 8n

Finally, substituting the values of m and n into the expression:

log5 7 = 1/(2n-1)(2mn-m-2) = 1/(2(8) - 1)(2(4m) - m - 2) = 1/(16 - 1)(8m - m - 2) = 1/15(7m - 2)

Therefore, we have shown that log5 7 = 1/(2n-1)(2mn-m-2) = 1/15(7m - 2), using the given values of log5 21 = m and log9 75 = n.

The first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

The system that is equivalent to:

O

O

O

[5-x=9x²

y = 5-x

is: x = -2, y = 7

In the given system, the first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.

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Answer:

V = 381.7 or 121π

Step-by-step explanation:

V=4/3πr³

Radius is half the diameter so, 9/2 = 4.5

r=4.5

V = 4/3π(4.5)³

V=4/3π(91.125)

V = 381.7 or 121π

The solution of expression after subtraction is,

⇒ 8249 L 860 ml

We have to given that;

Subtract measurements 450l 890ml from 8700l 750ml​

Now, WE can simplify as,

⇒ L      ml

8700    750

- 450     890

---------------------------

8249     860

Therefore, After subtraction we get;

⇒ 8249 L 860 ml

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The surface areas and volumes of the solids are listed below:

Case 1: A = 118 cm², V = 70 cm³

Case 2: A = 121.5 in², V = 91.125 in³

Case 3: A = 192 m², V = 144 m²

Case 4: A = 480 ft², V = 576 ft³

Case 5: A = 87.965 yd², V = 62.832 yd³

In this problem we need to determine the surface area and the volume of each solid. The surface area is the sum of the areas of all faces. The area and volume formulas required to answer this question are shown below:

Area

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Circle

A = π · r²

Lateral face of a cylinder

A = 2π · r · h

Volumes

Prism

V = A · h

Where:

Now we proceed to determine the surface areas and volumes of the solids:

Case 1

A = 2 · [(5 cm) · (7 cm) + (5 cm) · (2 cm) + (7 cm) · (2 cm)]

A = 2 · (35 cm² + 10 cm² + 14 cm²)

A = 2 · 59 cm²

A = 118 cm²

V = (5 cm) · (7 cm) · (2 cm)

V = 70 cm³

Case 2

A = 6 · (4.5 in)²

A = 121.5 in²

V = (4.5 in)³

V = 91.125 in³

Case 3

A = 2 · 0.5 · (8 m) · (6 m) + (6 m) · (10 m) + (6 m)² + (8 m) · (6 m)

A = 192 m²

V = 0.5 · (8 m) · (6 m)²

V = 144 m²

Case 4

A = 2 · 0.5 · (12 ft) · (8 ft) + 2 · (10 ft) · (12 ft) + (12 ft)²

A = 480 ft²

V = 0.5 · (12 ft) · (8 ft) · (12 ft)

V = 576 ft³

Case 5

A = 2π · (2 yd)² + 2π · (2 yd) · (5 yd)

A = 87.965 yd²

V = π · (2 yd)² · (5 yd)

V = 62.832 yd³

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The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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The calculated value of the constant in the equation is 75

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

The graph

Where we have

(3, 25) and (5, 15)

The value of the constant in the equation is calculated as

Constant =  Width * Height

So, we have

Constant =  3 * 25

Evaluate

Constant =  75

Hence, the value of the constant in the equation is 75

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The surface area of the rectangular prism is 396 square inches

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

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The perimeter of the rectangular polygon is given by P = 20.2 units

Given data ,

Let the perimeter of the polygon be represented as P

Now , the value of P is

Perimeter P of rectangle = 2 ( Length + Width )

Now , width is 3.8 and the length is 6.3

On simplifying , we get

P = 2 ( 3.8 + 6.3 )

P = 20.2 units

Hence , the perimeter is P = 20.2 units

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The midpoint of this line segment (-3, -5) and (4, 5) is (0.5, 0).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(-3 + 4)/2, (-5 + 5)/2]

Midpoint = [(1)/2, 0/2]

Midpoint = (0.5, 0).

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The volume of the cylindrical shaped pool with water is V = 75.4 feet³

Given data ,

Let the diameter of the pool be d = 8 feet

So , radius r = 4 feet

And , the height of the cylindrical pool is h = 3 feet

Now , the water is half full

So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of water in pool is V = 75.4 feet³

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The equation for g (x) is,

⇒ g(x) = x² -3

Since, The function is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The equation for g (x) is,

g(x) = x² -3

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Answer: C

Step-by-step explanation:

Answer:

D.  (-2, 10)

Step-by-step explanation:

Given inequalities:

    [tex]y > -\dfrac{5}{3}x+2[/tex]

    [tex]y > 3x+2[/tex]

Both inequalities have been given in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The first equation has a negative slope, which means that as x increases, y decreases. Therefore, it is the dashed line that begins in quadrant II and ends in quadrant IV.

The second equation has a positive slope, which means that as x increases, y increases. Therefore, it is the dashed line that begins in quadrant III and ends in quadrant I.

When graphing inequalities, the inequality sign ">" indicates a dashed line and shading above the line.

As both inequalities should be shaded above the lines, the region where the shaded regions overlap is the upper "V" of the graph (see attachment).

A point that satisfies both inequalities is any point that is located in the overlapping shaded region, but not found on the dashed lines.

Therefore, the point that satisfies both inequalities is (-2, 10).

Answer:

∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.

The volume for each cone in this problem is given as follows:

11) V = 94 in³.

12) V = 367 ft³.

13) V = 1005 in³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

For item 11, the dimensions are r = 3 in and h = 10 in, hence the volume is given as follows:

V = π x 3² x 10/3

V = 94 in³.

For item 12, the dimensions are r = 5 ft and h = 14 ft, hence the volume is given as follows:

V = π x 5² x 14/3

V = 367 ft³.

For item 13, the dimensions are r = 8 in(half the diameter) and h = 15 in, hence the volume is given as follows:

V = π x 8² x 15/3

V = 1005 in³.

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