geometric probability HELP

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

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Answer:

  tan(x) = (√6)/2

Step-by-step explanation:

The tangent identity is ...

  tan = sin/cos

Substituting the given values of sine and cosine, we have ...

  [tex]\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}[/tex]

At this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.

We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...

  [tex]\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}[/tex]

The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.

__

Additional comment

If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)

Answer:

706.86ft² or 225π ft²

Step-by-Step Explanation:

r = 15ft

Now solve the area of the circle! :)

A=πr²

A=π15²

A=225π ft²

or to simplify further!

A=706.86ft²

Using translation concepts, the equation of the new line is:

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

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

Hence the equation of the new line is:

[tex]y = -1 \times \frac{1}{2} \times x = -\frac{1}{2}x[/tex]

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Answer:

(x + 8)(x - 9)

Step-by-step explanation:

(x+8)(x-9)

= x² - 9x + 8x - 72

= x² - x - 72

Then

The factorization of x² - x - 72 is (x+8)(x-9)

1111 is the greatest common divisor of all numbers.

Lets simplify the problem,

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

After it , we get:

5555 _=_ 101 * 11  * 5

7777 = 101 * 11 * 7

9999 = 101 * 11 * 3 * 3

12221 = 101 * 11 * 11

14443 = 101 * 11 * 13

16665 = 101 * 11 * 3 * 5

abcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

Hence we get 1111 is the greatest common divisor.

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Answer:jio

Step-by-step explanation:

Answer: I would go with 3/5, the person who said 7/20 doesn't have any thank you's or ratings besides themselves while 3/5 has thank you's , and confirmation

Step-by-step explanation:

The circumference of the circle of diameter 35cm is 109.9 cm.

Given the diameter of the circle is 35 cm.

We are required  to find the circumference of the circle.

The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.

Formula of circumference=2πr where r is the radius of the circle.

Diameter=35 cm

Radius=35/2 cm (Radius is half of diameter)

Circumference=2π*35/2

=35π

Put the value of π =3.14 (it can be 22/7 as well.)

=35*3.14

=109.9 cm

Hence the circumference of the circle  is 109.9 cm.

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Answer:

I am pretty sure that it is 625.

Answer:

Step-by-step explanation:

please make sure you indicate  whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative

Answer:

x=-4,   y=7

Step-by-step explanation:

-5x-10y=-50...(1)

Multiply both sides by -1:

5x+10y=50

5x=50-10y

x=(50-10y)/5

Substitute x=(50-10y)/5 into second given eqaution:

10(50-10y)/5+8y=16

Cancel out common factor 5:

2(50-10y)+8y=16

100-20y+8y=16

-12y=16-100

-12y=-84

y=84/12

y=7

Substitute y=7 into equation (1)

-5x-10(7)=-50

-5x-70=-50

-5x=-50+70

-5x=20

x=-20/5

x=-4

Answer:

5

Step-by-step explanation:

-2x - y = -3

y = -3x + 2

-2x - (-3x + 2) = -3

-2x + 3x - 2 = -3

x = -1

y = -3*-1 + 2 = 5

The probability that person will be eaten by Maggie is 16.67%.

Given there are 6 sided coloured dice. Colours are red, blue,green,purple, indigo and orange.

We have to find the probability that the person will be eaten by Maggie.

Probability is the likeliness of happening an event among all the possible events. It lies between 0 and 1. The probability is the numberof items divided by the total number of items.

Number of green coloured sides=1

Total number of sides=6

Probability of getting green when the dice is rolled 1 time=1/6=0.1667

We have been told that if green comes then person will be eaten by Maggie so the probability that the person will be eaten by Maggie is 0.1667 which is 16.67%.

Hence the probability that the person will be eaten by Maggie is 16.67%.

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Question is incomplete as the complete question is :

What is the probability that the person will eaten by Maggie?

The correct answer is Option B) 1.67 after rounding off.

Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.

Given here, the number with decimal 1.666 , thus rounding off we get the answer a 1.67

Hence, the correct answer is Option B)

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To start calculating the volume of the cone, we obtain the following data:

To calculate the volume of a cone, we apply the following formula:

[tex]\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}[/tex], where

We solve, substituting our data in the formula:

taking the square root

Multiplying

Dividing

Therefore the volume of the cone is 144 cm³.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}[/tex]

[tex]\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}[/tex]

[tex]\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}[/tex]

[tex]\huge\textbf{What are the labels in your equation?}[/tex]

[tex]\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}[/tex]

[tex]\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{144}{1}}}[/tex]

[tex]\large\boxed{\mathsf{= 144\div1}}[/tex]

[tex]\large\boxed{= \textsf{144}}[/tex]

[tex]\huge\textbf{What is the result to this question?}[/tex]

[tex]\huge\boxed{\frak{144\ cm^3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

While solving the pictogram, we get that the number of hamsters owned  are 4.

Solution:

total number of pets = 33

total number of cats = 12

total number of dogs = 11

total number of rabbits = 6

then total number of hamsters = total pets - total cats, dogs, and rabbits

total number of hamsters = 33 - ( 12 + 11 + 6)

total number of hamsters = 4

also, on the pictogram one block represents 4 animal. then, total number of hamsters will be represented by one block.

view the second attachment for answer.

What is pictogram?

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I hope you are trying to ask the question below in the image

Answer:

C

Step-by-step explanation:

The solution to a system equations is the point(s) of intersection of the 2 graphs.

Assuming that each square grid represents 1 unit, the coordinates of the point intersection is (-2, 2). This is because drawing a vertical line straight down from the point of intersection, we notice that the x-coordinate of the solution is 2 square units on the left of the origin. Drawing a horizontal line from the point of intersection to the y-axis gives us the y-coordinate of y= 2. Thus, the solution is (-2, 2) and the answer is C.

This method of finding the solution is also known as graphical method, where the graphs of the 2 equations are drawn, and the solution is where the lines cuts through each other.

Alternative methods of solving equations include substitution and elimination methods.

*Origin is the point (0, 0) on the graph, and it is the point in which the two axes intersect.

Additional:

For an example of solving by substitution, do check out the following!

Answer:

55

Step-by-step explanation:

Draw a line through the center (horizontally).

Then draw a vertical line through the vertex of the right angle.

You'll get 2 triangles

I'll let you figure this out, it pretty easy

Remember a straight angle add up to 180 degrees, a triangle adds up to 180 degrees.

Answer:

[tex]\sqrt{60}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem a^2 + b^2 = c^2

In this case you are given a and c, so set the equation up like

2^2 + b^2 = 8^2

b^2 = 8^2 - 2^2

b =[tex]\sqrt{8^{2} -2^{2} }[/tex]

b =[tex]\sqrt{60}[/tex]

Answer:

okay so I think its, horizontal shift right 2 and a vertical shift down 1

Step-by-step explanation:

so x says + 2 so right 2 and y says -y so down 1..?

I'm kinda rusty tho so yeah

Answer:

Slope: -1

Y-intercept: 2

Step-by-step explanation:

Line crosses y-axis at 2, the slope is going down so it is negative, and it is going down by 1.

I hope it helps! Have a great day!

bren~

The required value is 70. Using the permutations formula the required value is calculated. I.e.,  P(76, x) = P(76, 70).

The formula for permutations is

nPr = P(n, r) = n!/(n - r)!

Where P -number of permutations,

n - number of objects in the given set

r - number of choosing objects

The given series is

76 × 75 × 74 × ... × 6 = P(76, x)

We know that,

76!  = 76 × 75 × 74 × ... × 1 ...(i)

But to get the required series,

Divide the equation (i) by 6! = (76 - 70)!

Then,

76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6

So, x = 70.

That is,

n!/(n - r)! = P(n, r)

⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108

Hence the required x value is 70.

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The equation of the line is y = 3/2x - 3

The points are given as:

(0, -3), (2, 0), and (4, 3).

Start by calculating the slope (m) using:

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

This gives

m = (3 + 3)(4 - 0)

Evaluate

m = 3/2

The equation is the calculated as:

y = m(x - x1) + y1

This gives

y = 3/2(x - 0) - 3

y = 3/2x - 3

Hence, the equation of the line is y = 3/2x - 3

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With some simple rearrangement, we can rewrite the numerator as

[tex]2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1[/tex]

Then factorizing the difference of squares, [tex]x^2-1=(x-1)(x+1)[/tex], we end up with

[tex]\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}[/tex]

Answer:Divide your speed in feet per minute by 60

Step-by-step explanation:

Answer:

Step-by-step explanation:

25.5625

Answer:

25.5625

Step-by-step explanation:

The solution is in the image

112 men construct 600 meters long wall in 30 days.

What is Time and Work formula?

[tex]\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}[/tex]

We can find the number of persons who can construct 600 meters wall as shown below:

Here, [tex]M_1=70[/tex]

[tex]D_1=12[/tex]

[tex]W_1=150[/tex]

[tex]W_2=600[/tex]

[tex]D_2=30[/tex]

We have to find [tex]M_2[/tex]

Putting in formula

[tex]\frac{70 \times 12}{150}=\frac{M_2\times 30}{600}[/tex]

[tex]M_2=\frac{70\times 12\times 600}{150\times 30}[/tex]

[tex]M_2=112[/tex]

Hence, 112 men can construct 600 meters wall in 30 days.

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Answer:

I guess the first one is correct........

The simplified expression is the one in option B.

Remember that:

[tex]sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)[/tex]

With these two, we can rewrite the numerator as:

[tex]sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)[/tex]

Replacing that in the given expression, we have:

[tex]\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}[/tex]

Now, if we multiply and divide by cos(-x), we get:

[tex]\frac{2*tan(-x)}{1 + 1/cos(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}[/tex]

Now remember that:

[tex]cos(x) = cos(-x)\\sin(-x) = -sin(x)[/tex]

With these two properties:

[tex]\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}[/tex]

Then the correct option is B.

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