What is the area of the sector shown in the diagram below?
14 cm
OA. 34.2 cm²
OB. 30.8 cm²
OC. 136.8 cm²
D. 4.9 cm²

Step is the same when constructing an inscribed regular hexagon and an inscribed equilateral triangle is shown below:

Geometric construction is the process of drawing a geometrical figure using two geometrical instruments, a compass, and a ruler.

Construction of an inscribed regular hexagon

1) Set compass width to the radius of the circle

2) Make an arc on the circle with the set radius.

3) From the previous arc draw another arc with the same radius.

4) Continue this process for the other vertex.

5) Connect all the vertices.

Construction of an inscribed equilateral triangle

1) Set compass width to the radius of the circle

2) Make an arc on the circle with the set radius.

3)From the previous arc draw another arc with the same radius.

4)Continue this process for the other vertex.

5) Connect the every other vertices point by drawing  a line between every other adjacent vertex point to form an inscribed equilateral triangle.

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Answer:

17

Step-by-step explanation:

at f(7) means x is 7

7+10 is 17

The mode of a given data set is the number that is repeated most often in a given data set. The mode of the given stem-and-leaf plot is 70.

The mode of a given data set is the number that is repeated most often in a given data set. It can also be described as the number that has the highest frequency of repetition.

As per the given Stem and leaf plot, the number of people who attended the carnival on different days is 54 60 70 70 75 78 79 81 86, since the mode is the number that is repeated very frequently, therefore, the mode of the given data is 70.

Hence, the mode of the given stem-and-leaf plot is 70.

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Answer:

Objects mostly have one or more geometrical shapes like the following. These types of shapes are called three dimensional (3-D) shaped solids. All these geometrical shapes have faces. We have learned about faces like triangular faces, rectangular face, square face and circular face.

The scenario that could be accurately modeled using this diagram is B. Juan Victor gave a 25% gratuity of $12 on a bill that was $48.

Here is the remainder of the question:

Which of the following scenarios could be accurately modeled using this diagram?

Juan Victor gave a gratuity of $25 on a bill that was $48.

Juan Victor gave a 25% gratuity of $12 on a bill that was $48.

Juan Victor gave a gratuity of $12 on a bill that was $100.

Juan Victor gave a 12% gratuity on a bill that was $25.

A conceptual model is a representation of a system to help people understand a subject the model represents.

In this case, the scenario that could be accurately modeled using this diagram is that Juan Victor gave a 25% gratuity of $12 on a bill that was $48.

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For the cosecant we will get:

   [tex]csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}[/tex]

So the correct option is the third one.

First, we can write:

[tex]csc(x) = \frac{1}{sin(x)}[/tex]

Now, remember that:

[tex]cos(x) = \frac{\sqrt{2} }{2} \\\\for\ x = \pm \frac{pi}{4}[/tex]

And for the sine we have:

[tex]sin(pi/4) = \frac{\sqrt{2} }{2} \\\\sin(-pi/4) = -\frac{\sqrt{2} }{2} \\[/tex]

Then the cosecant for these possible values of x gives:

[tex]csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}[/tex]

So the correct option is the third one.

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Answer:

The intersection is at (1,3) and the answer is in the graph. (see image below)

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

1. 4 1/2- 2 1/2= 2

2. 2+1=3

3. 3-2 1/2= 1/2

He has enough

Answer:

A = 16803.2 in^2

Step-by-step explanation:

The area of a regular polygon is [tex]A=\frac{1}{2}(a)\cdot{P}[/tex], where a is apothem and P is the perimeter.

Given side length s = 59 in, and the knowledge that this is an octagon (8 sides): P = 8s.

Now substitute all known values into the area formula: [tex]A=\frac{1}{2}(71.2)\cdot{472}[/tex]

Answer:

Dimensions:  150 m x 150 m

Area:  22,500m²

Step-by-step explanation:

Given information:

Let [tex]x[/tex] = width of the field

Let [tex]y[/tex] = length of the field

Create two equations from the given information:

  Area of field:   [tex]A= xy[/tex]

  Perimeter of fence:   [tex]2(x + y) = 600[/tex]

Rearrange the equation for the perimeter of the fence to make y the subject:

[tex]\begin{aligned} \implies 2(x + y) & = 600\\ x+y & = 300\\y & = 300-x\end{aligned}[/tex]

Substitute this into the equation for Area:

[tex]\begin{aligned}\implies A & = xy\\& = x(300-x)\\& = 300x-x^2 \end{aligned}[/tex]

To find the value of x that will make the area a maximum, differentiate A with respect to x:

[tex]\begin{aligned}A & =300x-x^2\\\implies \dfrac{dA}{dx}& =300-2x\end{aligned}[/tex]

Set it to zero and solve for x:

[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 300-2x & =0 \\ x & = 150 \end{aligned}[/tex]

Substitute the found value of x into the original equation for the perimeter and solve for y:

[tex]\begin{aligned}2(x + y) & = 600\\\implies 2(150)+2y & = 600\\2y & = 300\\y & = 150\end{aligned}[/tex]

Therefore, the dimensions that will give Tanya the maximum area are:

150 m x 150 m

The maximum area is:

[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 150 \cdot 150\\& = 22500\: \sf m^2 \end{aligned}[/tex]

======================================================

Work Shown:

[tex]a = 12\\\\b = 19\\\\c = 20\\\\a^2+b^2 = 12^2+19^2 = 505\\\\c^2 = 20^2 = 400\\\\[/tex]

The values of [tex]a^2+b^2[/tex] and [tex]c^2[/tex] are not the same number

Therefore, there's no way that [tex]a^2+b^2 = c^2[/tex] is possible, which means we do not have a right triangle.

Put another way: since [tex]a^2+b^2 \ne c^2[/tex], this means we don't have a right triangle.

Refer to the converse of the pythagorean theorem for more information.

Side note: because of that same theorem, and because [tex]a^2+b^2 > c^2[/tex] is the case, this means we have an acute triangle based on what is shown below.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so a line perpendicular to that one above will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}[/tex]

Answer:

5:9

Step-by-step explanation:

the circumference is d*pi

so you must find the diameter of both circles

31/pi = 9.86760647

which is about 10

57/pi = 18.1436635

which is about 18

10:18 is your ratio

but you can simplify this down to

5:9

Answer:

12

Step-by-step explanation:

127491733816383827i 9273

The probability that the next elk that will be caught will be unmarked is 5400/ 5625, 0.96 and 96%

The probability that the next wolf that will be caught will be unmarked is 696 / 928,  0.75 and 75%.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the next elk that will be caught will be unmarked = number of unmarked elks / total number of elks

number of unmarked elks  = 5625 - 225 = 5400

5400/ 5625 = 0.96 = 96%

The probability that the next wolf that will be caught will be unmarked = number of unmarked wolfs / total number of wolfs

number of unmarked wolfs  = 928 - 232 = 696

696 / 928 =  0.75 =  75%.

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The best definition of the phrase "like terms" is as follows: terms that have identical variable parts.

Like terms is used to describe terms that contain the same variable which is raised to the same power.

Algebra is an aspect of mathematics that involves the system of computation using letters or other symbols to represent numbers.

For example; in the algebraic expression: x² + 3 - 2x², x² and 2x² are like terms because they are terms that have identical variable parts.

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We know the slope formula

Parallel lines have equal slope so it has m=-2

Using proportions, it is found that 804.54 pounds of vegetables will be transported to the market in August.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the weight increases by 15% every month, the August amount will be the July's amount multiplied by 1.15, hence:

A = 1.15 x 699.60 pounds = 804.54 pounds.

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Answer:

Model the expression as 3 groups of x+2.

There are 3 x-tiles.

There are 6 +1 tiles.

The equivalent expression is 3x+6

Step-by-step explanation:

see image. This program is trying to help you learn algebra (here it looks like distributive property) by using a physical model. The bars are x's and the +1's are numbers. The little squares are 1 each (positive or negative, but you only need the positives for this question)

see image.

The lesson is:

3(x+2) = 3x + 6

Answer: -6, -7

Magnitude = 9.22

Step-by-step explanation:

Answer:

Step-by-step explanation:

The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. The confidence interval for the given sample is 48.07656, 45.9234.

The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. The percentage is used to represent the location of a population mean between an upper and lower interval.

Given the random sample is 81, while the sample means is 47, the standard deviation is 5.89. Therefore, the confidence interval for 90% of the population mean is,

[tex]CI = \bar{x} \pm z \dfrac{s}{\sqrt{n}}\\\\CI = 47 \pm 1.645 \dfrac{5.89}{\sqrt{81}}\\\\CI= 47 \pm 1.07656\\\\CI = 48.07656, 45.9234[/tex]

Hence, the confidence interval for the given sample is 48.07656, 45.9234.

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Answer:

A got it right

Step-by-step explanation:

got it right

Add the two trips together for total Km’s:

4500 + 11700 = 16,200 km.

divide total km by speed:

16,200 / 1,100 = 14.727272 hours

0.727272 x 60 minutes per hour = 43.636363 minutes, round up to 44 minutes

total time: 14 hours and 44 minutes

Answer:

11 points

Step-by-step explanation:

Claire had 11 points  because 18-7=11

C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

Two or more expressions with an Equal sign is called as Equation.

Given that Ava scored 18 points in a basketball game.

Let Ave score be represented as A.

Ave scored seven points more than Claire.

Let C be the Claire score.

A=7+C

As given Ava scored 18 points in a basketball

so the value of A is 18

18=7+C

Now let us find the value of C

Subtract 7 from both sides

18-7 =C

11=C

Hence, C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

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Answer:

13.4meters

Step-by-step explanation:

13.4×3×1.5 = 60.3

vol = L X W X H

60.3 = 3 X 1.5 X H

60.3 / 3 / 1.5 = H

Based on the above, it can be inferred that the best option to produce the 15,000 units is the factory with the lowest cost per unit.

Unit cost is a term to refer to the value per unit of a product that a factory charges to produce it.

In this case, the best alternative to produce 15,000 products is the factory with the lowest cost per unit, since this will reduce the cost of the order.

To find the cost per unit we divide the total cost of the order by the number of units. For example:

To know which one is more convenient, I must divide the total value by the number of units

According to the above, the second option would be the cheaper.

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Answer:

.53 facory B

Step-by-step explanation:

10000/15000 =.66

8000

The object reaches the lowest height at 5 seconds

The function is given as:

f(t) = -2t² +22t + 6

Differentiate the function

f'(t) = -4t +22

Set to 0

-4t +22 = 0

Subtract 22 from both sides

-4t = -22

Divide both sides by -4

t = 5.5

Remove decimal points

t = 5

Hence, the object reaches the lowest height at 5 seconds

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Answer:

9 units

Step-by-step explanation:

Using Pythagorean Theorem

12^2 + x^2 = 15^2

144 +x^2 = 225

x^2 = 81

x = 9