If U = Set of integers from -10 to 10 A=Set of integers from -1 to 1.

B=Set of first ten whole numbers

Prove that ( A intersection B)©=A©UB©

Hey c is complement

Answers

Answer 1

Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'


Related Questions

Which point is located at (-3, 4)?

Answers

Answer:A

Step-by-step explanation:

-3 to the left and up 4

Help me please! I’ll make you a brainlest show you work!!

Answers

The solution to the following mathematical problems are;

5² -3⁴ / (2³-5)(6² ÷ 9) = - 14/320² ÷ {3(5-9)² + 2} = 884/12 + (5-7)² -72 ÷ 6×2 = -13

Evaluation

Solve using

BODMAS

B - bracketO - offD - division M - MultiplicationA - additionS - Subtraction

5² -3⁴ / (2³-5)(6² ÷ 9)

= 25-81 / (8-5)(36÷9)

= -56 / (3)(4)

= -56/12

= - 14/3

20² ÷ {3(5-9)² + 2}

= 400 ÷ {3(-4)² + 2}

= 400 ÷ {3(16) + 2}

= 400 ÷ (48+3)

= 400 ÷ 50

= 8

84/12 + (5-7)² -72 ÷ 6×2

= 7 + (-2)² - 12 × 2

= 7 + (4) - 24

= 11 - 24

= -13

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On a coordinate plane, parallelogram A B C D has points (3, 6), (6, 5), (5, 1), and (2, 2).

What is the area of parallelogram ABCD?
13 square units
14 square units
15 square units

Answers

Answer:

13 square units

Step-by-step explanation:

We need to find the distance between the points using the  

Pythagorean Theorem, a² + b² = c²

(3,6) and (6,5); 6 - 3 = 3 and 6 - 5 = 1

3² + 1² = c²

9 + 1 = c²

c = √10

(6,5) and (5,1); 6 - 5 = 1 and 5 - 1 = 4

1² + 4² = c²

1 + 16 = c²

c = √17

√17 + √10 = 13.038

A dairy farmer decides to sell three fifth of her 500 cows. How many cows will she be left with after the deal is complete?

Answers

Answer is 200 cows
Step by step
She is selling 3/5 of 500
Multiply across 3/5 x 500
1500/5 divide to get 300 sold
Now 500-300 sold = 200 cows left
Problem solved

Find the distance between the given points.
R(O, O) and S(6, 8)
Distance =

Answers

Answer:

distance = 10

2/7 /(22) = 10

Write the equation for a parabola with a focus at (-4,8) and a directrix at x=-6
x= ?

Answers

The equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

What is the equation for a parabola with a focus at (-4,8) and a directrix at x = -6?

Given that x = -6, it means the directrix is horizontal.

Equation of parabola that opens left or write is expressed as;

( y - k )² = 4p( x - h )

Given that;

Focus: ( -4, 8 )Directrix: y = -6

First, we find the vertex.

The vertex( h, k ) is halfway between the directrix and the focus.

Hence, x coordinate of the vertex is;

x = ( x coordinate of focus + directrix ) / 2

x = ( -4 + (-6) ) / 2

x = -10/2

x = -5

y coordinate of the vertex will be the same as that of the focus.
y = 8

Hence vertex will be;

( -5, 8 )

Next, we find the distance p from the focus to the vertex and from the vertex to the directrix.

Subtract x coordinate of vertex from x coordinate of focus.

p = -4 - ( -5 )

p = -4 + 5

p = 1

Now, we substitute these values into the equation.

( y - k )² = 4p( x - h )

( y - (8) )² = 4(1)( x - (-5) )

( y - 8)² = 4( x +5 )

Therefore, the equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

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Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find the intervals of convergence for f '. find the intervals of convergence for f ''

Answers

Best guess for the function is

[tex]\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}[/tex]

By the ratio test, the series converges for

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1[/tex]

When [tex]x=1[/tex], [tex]f(x)[/tex] is a convergent [tex]p[/tex]-series.

When [tex]x=-1[/tex], [tex]f(x)[/tex] is a convergent alternating series.

So, the interval of convergence for [tex]f(x)[/tex] is the closed interval [tex]\boxed{-1 \le x \le 1}[/tex].

The derivative of [tex]f[/tex] is the series

[tex]\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n[/tex]

which also converges for [tex]|x|<1[/tex] by the ratio test:

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1[/tex]

When [tex]x=1[/tex], [tex]f'(x)[/tex] becomes the divergent harmonic series.

When [tex]x=-1[/tex], [tex]f'(x)[/tex] is a convergent alternating series.

The interval of convergence for [tex]f'(x)[/tex] is then the closed-open interval [tex]\boxed{-1 \le x < 1}[/tex].

Differentiating [tex]f[/tex] once more gives the series

[tex]\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)[/tex]

The first series is geometric and converges for [tex]|x|<1[/tex], endpoints not included.

The second series is [tex]f'(x)[/tex], which we know converges for [tex]-1\le x<1[/tex].

Putting these intervals together, we see that [tex]f''(x)[/tex] converges only on the open interval [tex]\boxed{-1 < x < 1}[/tex].

Using flowcharts, programmers can break large systems into subsystems that are easier to understand and code.
a. true
b. false

Answers

It is True that Using flowcharts, programmers can break large systems into subsystems that are easier to understand and code.

What is the use of flowcharts?

A flowchart  serves a picture  consisting the separate steps of a process which is in sequential order and can be used to  break large systems into subsystems during programing.

If a more cohesive module is needed, it can be formed into one unit, having the performance of  multiple functions.

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Evaluate the integral
1
2
sin ¹(x/4)) ² dx
| (si
- 1
2
[(sin ~'(x/4)) ² dx
√16-x²
2
√16-x²
11

Answers

Substitute [tex]y=\sin^{-1}\left(\frac x4\right)[/tex], so that

[tex]dy = \dfrac{dx}{4\sqrt{1-\left(\frac x4\right)^2}} = \dfrac{dx}{\sqrt{16 - x^2}}[/tex]

Then the integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \int y^2 \, dy[/tex]

and by the power rule,

[tex]\displaystyle \int y^2 \, dy = \frac13 y^3 + C[/tex]

so that the original integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \boxed{\frac13 \left(\sin^{-1}\left(\frac x4\right)\right)^3 + C}[/tex]

distribute the problem
2(3-8y)

Answers

Answer:

6-16y

Step-by-step explanation:

Hello!

apply distributive law

[tex]a(b - c) = ab - ac[/tex]

2(3-8y)=2.3-2.8y

2.3=6-2.8y= -16y

=6-16y

Hope it helps!

X=
Help me please asap! Thanks so much :)

Answers

X = 36
To start we know that the three angles make a sum of 180 degrees.
3x-2 + x - 1 + x + 3 = 180
Simplify
5x = 180
Divide by 5
X = 36

23. Which expression is NOT equivalent
to the expression 38 – 14?
A 2(19-7)
B 24
C (19-7)2
D 2(36-12)

Answers

Answer: [D] 2(36-12)

Step-by-step explanation:

    First, we will simplify the given expression.

38 – 14 = 24

    Now, we will see if the other expressions are equivalent or not.

[A] 2(19-7) = 24

[B] 24 = 24

[C] (19-7)2 = 24

[D] 2(36-12) = 48

    The expression is NOT equivalent to the expression 38 – 14 is;

                   [D] 2(36-12)

Hi :)

Let's evaluate all these expressions

———————

[tex]\boldsymbol{\boxed{38-14=24}}}[/tex]

  So Now the question boils down to --

What expression is NOT equivalent to [tex]\boldsymbol{24?}[/tex]

Option (A).

     [tex]\boldsymbol{2(19-7)}[/tex]

     [tex]\boldsymbol{2(12)}[/tex]

     [tex]\boldsymbol{24}[/tex]

Option (A) is ruled out, because we're looking for expressions that are not equivalent to 24.

Option (B)

   Well 24 is always equal to 24!

Option (C)

     [tex]\boldsymbol{(19-7)2}[/tex]

     [tex]\boldsymbol{(12)2}[/tex]

     [tex]\boldsymbol{24}[/tex]

Option (D)

    [tex]\boldsymbol{2(36-12)}[/tex]

     [tex]\boldsymbol{2(24)}[/tex]

     [tex]\boldsymbol{48}[/tex]

[tex]\tt{Learn\;More;Work\;Harder}[/tex]

:)

What is the exact value of cos(c d), given sine c = startfraction 24 over 25 endfraction for c in quadrant ii and cosine d = negative three-fourths for d in quadrant iii?

Answers

The exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

To find the exact value of cos(c+d):

In the second quadrant:

 c = 180° -arcsin(24/25) ≈ 106.26°

In the third quadrant:

 d = 360° -arccos(-3/4) ≈ 221.41°

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

[tex]\frac{21+24\sqrt{7} }{100}[/tex] ≈ [tex]0.84498[/tex]

To prove: Perhaps you want to work this out using the trignometric identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is: cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

Therefore, the exact value of cos(c+d) is (D) [tex]cos(c+d) = \frac{21+24\sqrt{7} }{100}[/tex].

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The complete question is given below:

What is the exact value of cos(c+d), given sine c = start fraction 24 over 25 end fraction for c in quadrant ii and cosine d = negative three-fourths for d in quadrant iii?

(A) Negative StartFraction 47 Over 100 EndFraction

(B) Negative 1 and StartFraction 3 Over 100 EndFraction

(C) StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction

(D) StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

12.50h = 2500.75

Step-by-step explanation:

He earned $12.50 for 1 hour of work.

For 2 hours, he earned $12.50 × 2.

For 3 hours, he earned $12.50 × 3.

For h hours, he earned $12.50 × h which can be simply written as 12.50h

He earned altogether $2500.75, so 12.50h must equal 2500.75.

Answer: B 12.50h = 2500.75

Answer:

[tex]12.50 h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

12.50 x h = 2500.75

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

[tex]h=\frac{2500.75}{12.50}[/tex]

= 200.6 Hours

In which step does a mistake first occur? 8 2 (3 x 3 -2) step 1: 8 2 (3 x 1) step 2: 8 2 3 step 3: 4 3 step 4: 7

Answers

Answer: Step 1

Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.

T-shirts and sweatshirts were sold at a local shop. One salesperson sold three T-shirts and seven sweatshirts for a total amount of $240.50. Another salesperson sold six T-shirts five sweatshirts for a total amount of$220.00. Based on this information, what is the cost of a T-shirt and sweatshirt?

A. T-shirt for $9.00 and sweatshirt for $30.50
B. T-shirt for $12.50 and sweatshirt for $29.00
C.T-shirt for $11.67 and sweatshirt for $30.00
D. T-shirt for $23.70 and sweatshirt for $24.20

Answers

Answer:

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

Step-by-step explanation:

A. - Three T-Shirts and Seven Sweatshirts: $27 + $213.50 = $240.50

   - Six T-Shirts and Five Sweatshirts: $54 + $152.5 = $206.5

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

C. - Three T-Shirts and Seven Sweatshirts: $35.01 + $210 = $245.01

   - Six T-Shirts and Five Sweatshirts: $70.02 + $150 = $220.02

Mark as Branliest Please! :)

if a skip rope is a meter long and its a cm less how much is it pls answer

Answers

Answer:

99cm

Step-by-step explanation:

A meter is equal to 100cm

The rope is a metre (m) long but a centimetre (cm) less.

100cm - 1cm = 99cm

I need help answering this!

Answers

Based on the odometer on Missy's car, her total trip is equal to 1,449 miles.If her car had travelled 68,000 kilometers, the speedometer should have been lubricated 4 times.The next lubrication would be at 80,000 kilometers.Missy's car ticket would be equal to $232.

How to solve Part A?

Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object or land is taken, especially for use in a scientific research and experiment such as direct comparison.

From the odometer on Missy's car, we have the following information:

Initial reading = 23,678 miles.

Final reading = 25,127 miles.

Trip = Final reading - Initial reading

Trip = 25,127 - 23,678

Trip = 1,449 miles.

How to solve Part B?

Lubrication mileage = 16,000 kilometers.

Total mileage = 68,000 kilometers.

Lubrication time = Total mileage/Lubrication mileage

Lubrication time = 68,000/16,000

Lubrication time = 4.25 ≈ 4.

Next Lubrication time = (16,000 × 0.25) + 68,000

Next Lubrication time = 16,000 - (16,000 × 0.25) + 68,000

Next Lubrication time = 80,000 kilometers.

How to solve Part B?

Rate = $29 per mile

Speed limit = 35 mph

Missy's car speed = 43 mph

Difference = 43 - 35

Difference = 8 mph.

Ticket = 29 × 8

Ticket = $232.

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I was wondering what C and how to solve for it because i dont really understand the problem

Answers

The measure of angle C is 35°.

Given that, ΔABC≅ΔDEF, ∠A=70°, ∠E=3x and ∠F=x+10.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

In ΔABC and ΔDEF, corresponding angles are equal.

That is, ∠A=∠D=70°, ∠B=∠E=3x and ∠C=∠F=x+10

Now, ∠A+∠B+∠C=180° (∵angle sum property)

⇒70°+3x+x+10=180°

⇒4x=100°

⇒x=25°

Thus, ∠C=x+10=35°.

Therefore, the measure of angle C is 35°.

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Jacob is cutting a tile in the shape of a parallelogram. two opposite angles have measures of (6n − 70)° and (2n 10)°. what are the two different angle measures of the parallelogram-shaped tile?

Answers

The measures of the two different angles are 70° and 110°.

What is angle in parallelogram ?

A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.

Thus from the given question, we have:

(6n − 70)° + (2n + 10)° =  180°

8n - 60 =  180° + 60

8n = 240

n = 240/8

n = 30°

So that,

i. (6n − 70)° = (6[30] − 70)°

                    = 180 - 70

                     = 110°

   

ii. (2n + 10)° = (2[30] + 10)°

                   = 60 + 10

                   = 70°

               

Therefore, the measures of the two different angles are 70° and 110°.

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Line m contains the points (4, 16) and (0, 8). At what point will line m intersect with line n if the equation of line n is -8x+4y=24 ?

A) (0, 0)
B) (-4, 0)
C) The lines don't intersect
D) The lines intersect at an infinite number of points

Answers

The correct option regarding the point at which the linear functions intersect is given by:

C) The lines don't intersect.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:

y = 2x + 8.

Line n, in slope-intercept format, is given by:

-8x + 4y = 24

4y = 8x + 24

y = 2x + 6

Hence:

2x + 8 = 2x + 6

0x = -2

Which is impossible, hence they do not intersect and option C is correct.

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Three neon lights are turned on at the same time. One blinks every 4 seconds, the second one blinks every 5 seconds, and the third blinks every 6 seconds. In 5 minutes, how many times will all three lights blink at the same time?

Answers

In order to find how many times they will blink at the same time we need to find the common multiple of 4 and 6 between 1 and 60.

The first bulb blinks after every 4 seconds, means it blinks in multiple of 4.

The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

The second bulb blinks after every 6 seconds, means it blinks in multiple of 6.

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

The common multiple of 4 and 6 = 12, 24, 36, 48, 60.

in sixty seconds they will blink 5 times at the same time.

If the mean on a test is 83 and the standard deviation is 6: What % has:

At least a 70% (passing with a C)

An 80 or above (a B)

Answers

Using the normal distribution, it is found that:

98.5% of students have at least a 70.69.15% of students have an 80 or above.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 83, \sigma = 6[/tex]

The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 83}{6}[/tex]

Z = -2.17

Z = -2.17 has a p-value of 0.015.

1 - 0.015 = 0.985 = 98.5% of students have at least a 70.

The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 83}{6}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.

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word problem for 2.35+-4.57

Answers

Answer:

=> -2.22

Step-by-step explanation:

=> 2.35 + ( -4.57)

=> 2.35 - 4.57

=> - 2.22

13. Check all the true statements.

Answers

Based on the triangle midsegment theorem, the true statements are:

DE║AC

2DE = AC

What is the Triangle Midsegment Theorem?

If a line segment joins two sides of triangle and divides them at their midpoint, the divided segments will be congruent, and thus, the line segment joining the two sides is a midsegment of the triangle. According to the triangle midsegment theorem, the midsegment will be parallel to the third side that is not divided and also would be 1/2 its length. That is, the third side is twice the midsegment of that triangle.

In the image given, considering triangle ABC, we can make the following conclusions based on the triangle midsegment theorem:

D and E are midpoints of sides AB and BC respectively because they are divided by segment DE equally.

The midsegment is DE.

DE would be parallel to the third side, line segment AC.

Length of AC would be twice the length of DE

In conclusion, the true statements based on the triangle midsegment theorem are:

DE║AC

2DE = AC

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HELPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

The answer is 314

Step-by-step explanation:

You need to do

3.14(pie) times the radius times the height divided by 3

Answer:

C. 314 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume of a cone is: 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h'

1/3 x 3.14 x [tex]5^{2}[/tex] x 12

1/3 x 3.14 x 25 x 12

1/3 x 3.14 x 300

100 x 3.14

V = 314

A regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. a regular octagon has an apothem with length 10 centimeters and a perimeter of 66.3 inches. what is the area of the octagon, rounded to the nearest square inch?

Answers

331.5 inches²  is the area of the octagon, rounded to the nearest square inch.

What is octagonal in shape?

In geometry, an octagon is a polygon that has 8 sides and 8 angles. All the sides are joined end to end to form the shape of the octagon. The sum of the interior angles of an octagon is equal to 180 degrees.

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 × apothem × perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Put the values in the formula

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²  

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Answer: C). 332 in.2

Step-by-step explanation:

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The average of three numbers, p, q and 27 is 28.The average of five numbers p, q, r, s and 27 is 31.Find the average of r and s.

Answers

Using the given information, the average of r and s is 35.5

Calculating Average

From the question, we are to determine the average of r and s

From the give information,

The average of p, q and 27 is 28.

That is,  

(p + q + 27)/3 = 28

p + q + 27 = 3×28

p + q + 27 = 84

p + q = 84 - 27

p + q = 57

Also,

The average of p, q, r, s and 27 is 31

That is,

(p + q + r + s + 27)/5 = 31
p + q + r + s + 27 = 5 × 31

p + q + r + s + 27 = 155

Thus,

57 + r + s + 27 = 155

r + s = 155 - 57 - 27

r + s = 71

The average of r and s is (r + s)/2

(r + s)/2 = 71/2

(r + s)/2 = 35.5

Hence, the average of r and s is 35.5

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how do you find the length of a rectangle if the diagonal is 10 inches long and the width is 8 inches

Answers

Answer:

Step-by-step explanation:

Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.

Books front a certain publisher contain an average of 1 misprint per page. What is the probability that on at least one page?

Answers

The probability for at least 1 page is 0.667 .

Probability is the department of arithmetic concerning numerical descriptions of the way likely an event is to occur, or how probable it is that a proposition is actual. The probability of an event is a number between 0 and 1, where, roughly speaking, zero shows the impossibility of the event, and 1 suggests truth.

Possibility = the wide variety of methods of achieving success. The whole wide variety of possible outcomes. As an example, the opportunity of flipping a coin and its being heads is ½ because there's 1 way of having a head and the total quantity of viable outcomes is 2 (a head or tail). We write P(heads) = ½.

The form opportunity is from old French probability (14 c.) and at once from Latin probabilities (nominative probabilitas) "credibility, possibility," from probabilistic (see likely). The mathematical sense of the time period is from 1718.

As there's an average of 1 misprint in line with the web page, the possibility of a minimum of 5 misprints is 1 - P(0, 1, 2, 3, or 4 misprints)

P(0) = e-1/0!

P(1) = e-1/1!

P(2) = e -1/2!

P(3) = e-1/3!

P(4) = e-1/4!  

P(0, 1, 2, 3, or 4 misprints) = e-1(1 + 1 + half of + 1/6 + 1/24) = 2 17/24 e-1 = .99634

Then, P(5 or more misprints) is 1 - .99634 = .00366

Then, the P(at the least 1 page in a 300-page ebook has at least 5 misprints) = 1 - P(0 pages have at least 5 misprints).

P(0 pages have at the least 5 misprints) = P(300 of 300 pages have 0, 1, 2, 3, or 4 misprints) =.99634 300

(you could view this as C(300, 300) p300 in case you desire) = 0.332881690573629

Then, P(1 or greater pages have at least 5 misprints) = 1 - 0.332881690573629 = 0.667118309426371

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