Find the area of the circle pictured above.
Round your answer to the nearest tenth

The probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

Take  [tex]A_{k}[/tex]  - the event that odd number appeared on the k-th throw,  B  - every even number appeared at least once.

Let’s find  P(B|[tex]A_{k}[/tex]) . Note that this probability is 0 for  k∈{1,2,3}  as you need  k≥4  to place all distinct even numbers before the odd one.

Now for  k≥4  we need to use the formula of inclusions and exclusions:  P(B¯|[tex]A_{k}[/tex])=P(C2+C4+C6|[tex]A_{k}[/tex])=

=P(C2|[tex]A_{k}[/tex])+P(C4|[tex]A_{k}[/tex])+P(C6|[tex]A_{k}[/tex])−P(C2C4|[tex]A_{k}[/tex])−P(C2C6|[tex]A_{k}[/tex])−P(C4C6|[tex]A_{k}[/tex])  where  Ci  is the event that the dice i is missing.

These probabilities are:

P(Ci/[tex]A_{k}[/tex])=[tex](\frac{2}{3} )^{k-1}[/tex]

P(CiCj|[tex]A_{k}[/tex])=[tex](\frac{1}{3} )^{k-1}[/tex]

So

P(B|[tex]A_{k}[/tex])=1–P(B¯|[tex]A_{k}[/tex])=1−3⋅[tex](\frac{2}{3} )^{k-1}[/tex]+3[tex](\frac{2}{3} )^{k-1}[/tex].= 1 − [tex]\frac{9}{2}[/tex].[tex](\frac{2}{3} )^{k}[/tex]+9[tex](\frac{1}{3} )^{k}[/tex]

Now as  P([tex]A_{k}[/tex])= [tex]\frac{1}{2^{k} }[/tex]we conclude that

P(B) = ∞∑k=4P(B/[tex]A_{k}[/tex])P([tex]A_{k}[/tex])=  ∞∑k=4([tex](\frac{1}{2} )^{k}[/tex]−[tex]\frac{9}{2}[/tex][tex](\frac{1}{3} )^{k}[/tex]+9.[tex](\frac{1}{6} )^{k}[/tex])=

=[tex]\frac{\frac{1}{16} }{\frac{1}{2} }[/tex]−[tex]\frac{\frac{1}{18} }{\frac{2}{3} }[/tex]+[tex]\frac{\frac{1}{144} }{\frac{5}{6} }[/tex] = [tex]\frac{1}{8}[/tex] -[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{120}[/tex] =[tex]\frac{6}{120}[/tex] = [tex]\frac{1}{20}[/tex]

the probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

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Answer:

7x 3,012=7(__3000__+__12_) = 21084

After using FOIL, the final answer will be

x2 + 3x + 2

What is the FOIL method?
The typical way of multiplying two binomials is known as the FOIL method since FOIL is a shorthand for it. The acronym FOIL stands for the following four terms that describe the item: (Each binomial "initial" term is multiplied together.) The FOIL method is a memory aid for the procedures involved in multiplying two binomials. The result of multiplying the first term, outer term, inner term, and last term is the product of two binomials: (a+b)(c+d)=ac+ad+bc+bd.

Solution explained:

A/Q we have

(x+2)(x-1)

= x * x + x + 2x + 2    (After expanding and applying distributive property)

= x2 + x + 2x + 2

= x2 + 3x + 2

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Answer:

Since angle 8 is 95 degrees, we will have to either subtract or use the rules to solve this!

Lets find angle 1 first!

Since opposite angles are the same, angle 1 will be 95 degrees!

Angle 2 will wave subtracting used to find it!

180 - 95 = 85

Angle 2: 85 degrees

Angle 3 is the same as angle 2 so 85 degrees!

Angle 4 is the same as angle 8 and 1 so 95 degrees!

Angle 5 is the same as 8, 4, and 1 so 95 degrees!

Angle 6 is the same as angle 3 and 2 degrees!

Angle 7 will be 85 by subtraction!

Angle 8 is given and it is 95!

Have an amazing day!!

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The height of the cylinder whose surface area and radius are as given in the task content is; 67 ft.

It follows from the task content that the height of the cylinder as described by the surface area and radius above be determined.

On this note, recall that the surface area of a cylinder is given by the formula;

Surface area = 2πrh

Therefore;

6732.16 = 2 × 3.14 × 16 × h

h = 6732.16/100.48

h = 67.

Consequently, the height of the cylinder which is as described is; 67 ft.

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The expressions represent the service fee charge on her account balance is 4x+3.

Given that,

Every time money is withdrawn from an ATM run by a different bank, Marley's Bank levies a $3 service fee. Marley needs to make four ATM withdrawals from a different bank while she is abroad.

We have to find which expressions represent the service fee charge on her account balance.

The expression we can write as,

4x+3

Because 4 times he has taken from ATM money and adding the service fee $3.

Therefore, The expressions represent the service fee charge on her account balance is 4x+3.

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Answer:

r = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

([tex]\sqrt{x}[/tex] )² = x

substitute the given values of w and h into the equation

r = [tex]\sqrt{w^2-h^2}[/tex]

  = [tex]\sqrt{(9\sqrt{2})^2-(5\sqrt{6})^2 }[/tex]

  = [tex]\sqrt{162-150}[/tex]

  = [tex]\sqrt{12}[/tex]

  = [tex]\sqrt{4(3)}[/tex]

  = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

  = 2[tex]\sqrt{3}[/tex]

Using the concepts of equilateral triangle, we got that  2.113 is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles.

Firstly we find the side length of equilateral triangle , G is the midpoint of side FE.

Let GE=x, since G is the midpoint due to that DE=GB.

So, using basic trigonometry=DG^GB=x√3.

Thus DB=2x√3.

Since DB is the diagonal of ABCD, it has length 10√2 Then we can set up the equation 2x√3=10√2. So the side length of the triangle is

2x=(10√2)/√3.

Now look at the diagonal AC it is made up of twice the diagonal of the small square plus the side length of the triangle. Let the side length of the small square be y:

Let the side length of the small square be y:

AC=y√2 + [(10√2)/√3]+y√2=10√2.

Solving  for y:

=>y√2+y√2 + (10√2√3)/3=10√2

=>y√2+y√2 + (10√6)/3=10√2

=> [3y√2+3y√2 + (10√6)] /3=10√2

=>6y√2+10√6=30√2

=>6y√2 = 30√2-10√6

=>y√2 = (30√2-10√6)/6

=>y = (30√2-10√6)/6√2

=>y = (60-20√3)/12

=>y= 5(3−√3)3  or 2.113

Hence, inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles is to be 2.113.

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The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

We need to write a linear equation to represent the number of pages

Lourdes has left the number of pages to read after x days

Lourdes reads 30 pages each day

Lourdes will read for x days

The number of pages Lourdes will read in x day = 30 x

The left pages will be the difference between the total pages of the

book and the pages Lourdes read.

After 9 days Lourdes completes 3/5 of the total number of pages.

So the  number of pages Lourdes reads after 9 days = 30×9 = 270 pages.

Let The total number of pages in the book = y

Therefore 3/5 × y = 270.

So y = 270 × (5/3) = 450 pages.

The total number of pages in the book = 450 pages.

Lourdes will read 30 x in x days

The number of pages left = 450 - 30 x

Assume that z represents the number of pages Lourdes has left to read after x days

z = 450 - 30 x

The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

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Answer:

Step-by-step explanation:

f/4 = 3

Answer:

18%

Step-by-step explanation:

[tex]x = y*\frac{60}{100} =y*0.6=0.6y\\x=0.6y[/tex]

[tex]y = z*\frac{30}{100} =z*0.3=0.3z\\y=0.3z[/tex]

x is what percent of z?

Since x = 0.6y and y = 0.3z:

[tex]\%=\frac{x}{z} *100\\\\\%=\frac{0.6y}{z}*100\\ \\\%=\frac{0.6(0.3z)}{z} *100\\\\\%=\frac{0.18z}{z} *100\\\\\%=0.18*100\\\\\%=18[/tex]

In the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and

m ∠N = 76°.

As given in the question,

In the given triangle LMN,

Measure of side LM = 18in.

Measure of angle MLN is equal to 28°

It is given that side LM ≅ LN

LM = 18 in.

LN = 18in.

In a triangle  LMN ,

In a triangle opposite sides are congruent to each other then angle opposite to them also congruent to each other.

LM ≅LN

⇒m ∠N = m ∠M

In a ΔLMN,

Let x° be the measure of angle M and N each.

m ∠M + m ∠N + m ∠L = 180°

⇒ x° + x° + 28° = 180°

⇒ 2x° = 180° -28°

⇒2x° = 152°

⇒ x = 76°

Therefore, in the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and m ∠N = 76°.

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Answer:

no

Step-by-step explanation:

the conditional p-> r is the basically both of the beginning 2 conditionals combined

Answer:

-7

Step-by-step explanation:

A= 4

B= -2

((4-2) × 4 + (4+2))/-2

14/-2

-7

In the special right triangle, x has a value of √3/2

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.

Using Pythagoras theorem;

[tex](\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }[/tex]

The value of x in the triangle is √3/2

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Answer: 9 quarters, 7 dimes, & 16 nickels

Step-by-step explanation:

We set number of dimes as d:

So, set up the equation to solve:

[tex]0.10d+0.25(d+2)+0.05(2d+2)=3.75\\\\0.10d+0.25d+0.5+0.1d+0.1=3.75\\\\0.45d=3.75-0.5-0.1=3.15\\\\d=7[/tex]

So now that we know there're seven dimes, we can plug them in our initial equations to find the number of quarters and nickels:

Answer:

0.2

Step-by-step explanation:

1/5 is equvalent with 10/5=0.2

The values of the variables s and c are 13 and 17, respectively.

We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.

s + 2c = 47

5s + 8c = 201

We will substitute the value of s from the first equation into the second equation.

s = 47 - 2c

5s + 8c = 201

5(47 - 2c) + 8c = 201

235 - 10c + 8c = 201

235 - 2c = 201

2c = 235 - 201

2c = 34

c = 17

We will substitute the value of c into the first equation to find the value of s.

s = 47 -2c

s = 47 - 2(17)

s = 47 - 34

s = 13

Hence, the values of s and c are 13 and 17, respectively.

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Answer:

16.80

Step-by-step explanation:

The ratio is 1:5.60. Where 1 is the amount of friends and 5.60 is the amount owed. Since there are 3 friends, multiply 5.60 by 3.

Answer: 16.8

Step-by-step explanation: basically multiply 5.60 by 3 (5.60 x 3 = 16.8) or add 5.60 3 times (5.60 + 5.60 + 5.60 = 16.8)

Answer:

Step-by-step explanation:

answer is:  x=9/2

Using the percentage of money the group gave out to the youth program, the amount of money the group raised is 6200 dollars.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

The group gives 50% of the money they raised to youth programs. This year the team gave $3,100 to youth programs.

Therefore, the amount of money the group raised can be calculated as follows:

let

x = amount of money raised by the group

Hence,

50% of x = 3100

50 / 100 × x = 3100

50x / 100 = 3100

cross multiply

50x = 3100 × 100

50x = 310000

divide both sides by 50

50x / 50 = 310000 / 50

x = 6200

Therefore, the group raised 6200 dollars this year.

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Answer:

It approximately dropped 0.027777 per hour.

Step-by-step explanation:

First, we calculate the decrease.

Decrease = 11/40 = 0.275

Then,  we calculate the time interval.

From 10 pm to 7:54 hours will be 9.54 hours

Time interval= (9 + 54/60) hours

Time interval=9.9 hours

Finally, we calculate how much it dropped each hour

0.275/9.9 ≈ 0.027777

So it approximately dropped 0.027777 per hour.

Answer:

7:54 A.M to 10 P.M is = 14 hrs and 6 mins

60 mins = 1 hour

therefore 6 mins = 0.1 hour

14 hrs plus 0.1 hrs = 14.1 hours

if 14.1 hrs = 11/40

1 HR = x

cross multiply

14.1x = 11/40

divide both sides by 14.1

14.1x / 14.1 = 11/40 / 14.1

Answer:

seven and two thirtieths

Step-by-step explanation:

3 2/5 + 3 4/6 find an equal value between 5 and 6

3 12/30 + 3 20/30

12+20=32

32/30=1 2/30

3+3+1=7

7 2/30

A polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.

In the given question we have to find a polynomial function with real coefficient that has the given zeros -1, 8,3, -21.

The given zeros are -1, 8,3 - 21.

Let the variable is x.

So the factor from the given zeros are

(x-1), (x+8), (x+3), (x-21)

To find the polynomial we multiply the factors to each other.

=(x-1)(x+8)(x+3)(x-21)

We firstly multiply the factor with the pair of two using the distributive property.

={x(x-1)+8(x-1)}{x(x+3)-21(x+3)}

=(x^2-x+8x-8)(x^2+3x-21x+63)

Simplifying

=(x^2+7x-8)(x^2-18x+63)

=x^2(x^2+7x-8)-18x(x^2+7x-8)+63(x^2+7x-8)

=(x^4+7x^3-8x^2)-(18x^3+126x^2-144x)+(63x^2+441x-504)

=x^4+7x^3-8x^2-18x^3-126x^2+144x+63x^2+441x-504

=x^4−11x^3−197x^2−297x+504

Hence, a polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.

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The value of x on the given sides of the rectangles is 4.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, The area of the shaded region is 39.

As the smaller rectangle is inside the whole larger rectangle,

∴The area of the smaller rectangle subtracted from the area of the whole larger rectangle is the area of the shaded region.

So, (2x - 1)(x + 3) - (x - 2)(x + 1) = 39.

2x² + 6x - x - 3 - x² - x + 2x + 2 = 39.

x² + 6x - 1 = 39.

x² + 6x - 40 = 0.

x² + 10x - 4x - 40 = 0.

x(x + 10) - 4(x + `10) = 0.

(x + 10)(x - 4) = 0.

(x + 10) = 0 Or (x - 4) = 0.

x = - 10 Or x = 4.

Now if we put x = - 10 the lengths will be negative which is inappropriate.

So, the value of x that satisfies is 4.

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The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

The total amount that they have to spend on parking and admission = $89.50

The parking cost = $7.75

The ticket cost including tax = $27.25

Consider the number of people who can go to amusement park as p

Then the equation will be

7.75 + 27.25p = 89.50

Subtract both side of the equation by 7.75

27.25p + 7.75 - 7.75 = 89.50 - 7.75

27.25p = 81.75

Divide both side of the equation by 27.25

27.25p / 27.25 = 81.75 / 27.25

p = 3

Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

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The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.

It is given that the arithmetic sequence is

5, x, y, 32

We know that for any arithmetic sequence the term aₙ is

aₙ = a + (n - 1)d

where,

a = first term

n = order of the value in the sequence

Since x is the second term

x = 5 + (2 - 1)d

or, x = 5 + d

Similarly,

y = 5 + 2d

32 = 5 + 3d

or, 3d = 27

or, d = 9

Hence, x = 14

y = 5 + 18

= 23

Hence, the common difference is 9

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Second option is correct 0.04772.

The probability of a weight between 420 kilos and the mean of 400

kilos = 0.4772

Mean of a normal probability distribution is μ = 400 kilos

And standard deviation σ = 10 kilos

Let x be the variable in kilos.

X is between 400 kilos and 420 kilos

P( 400 < X < 420 ) = P ( 400 -  μ < X -  μ < 420 -  μ)

= P ( (400-μ)/σ < (X-μ)/σ < (420-μ)/σ )

= P ( (400 - 400) /10 < Z < (420 - 400)/10 )

= P ( 0 < Z < 2 )

= 0.4777 from the table appendix B1.

The link for the appendix table B1 :

www.webassign.net%2Faswsbe13%2Fappendix-b.pdf&usg=AOvVaw3QlkaDTdGZ1Z01YZPYCL6h

The probability of a weight between 420 kilos and the mean of 400

kilos = 0.4772

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Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

3/8*4/3

The 3 can be cancel out

you can also cancel out 8 and 4

leaving you with 1/2