In how many ways can you select five people from a group of ten if the order of selection is important?

[tex]y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false[/tex]

[tex]y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false[/tex]

The expected payoff from rolling the die is 0 usd.

According to the given question.

A die is rolled.

So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}

⇒ Total number of outcomes = 6

Also, it is given that

If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.

As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as

P(E) = total number of favorable outcomes/ Total number of outcomes

So,

The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3

And, the probability thet die rolls 3, 4, 5, or 6

= 1/6 +  1/6 + 1/6 + 1/6

= 4/6

= 2/3

Therefore, the excepted payoff from rolling this die

= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]

[tex]= \frac{2}{3} - \frac{2}{3}[/tex]

= 0 usd

Hence, the expected payoff from rolling the die is 0 usd.

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Step-by-step explanation:

31) the answer is (98765x9) +3=888888

why if u look at the equation is descending and if u verify the cinjecture u will find out is correct

41)½+¼+⅛+1/16+1/32=1-1/32

just d same reason with (31)

The volume of a vase with a radius of 1 m and height of 7 m is 22000 L

An equation is an expression that shows the relationship between two or more variables and numbers.

Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section

Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:

Volume of vase = π * radius² * height

Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L

The volume of a vase with a radius of 1 m and height of 7 m is 22000 L

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the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.

= -2 +k*(5/n)

The study of geometry utilizing coordinate points is referred to as coordinate geometry (or analytic geometry). Finding the distance between two points, dividing lines in the m:n ratio, locating a line's midpoint, and computing the area of a triangle in the Cartesian plane can all be done using coordinate geometry.

The range for the definition of the function f(x) = x^2 + 4 is (-2, 2).

Between this interval, there are a total of 5 equal pieces.

Height of each rectangle's right endpoint equals if the interval is divided into n equal pieces. k=(5/n)

Therefore, the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.

= -2 + k*(5/n)

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The equation is neither geometric nor arithmetic

The function is given as

f(x) = 2x^2 + 6x - 9

As a general rule, arithmetic functions or sequences have a common difference while geometric functions or sequences have a common difference

Set x = 0, 1 and 2

f(0) = 2(0)^2 + 6(0) - 9 = -9

f(1) = 2(1)^2 + 6(1) - 9 = -1

f(2) = 2(2)^2 + 6(2) - 9 = 11

Calculate the common difference (d)

d = 11 --1 = -1--9

d = 12 = 8 ---- false equation i.e. no common difference

Calculate the common ratio (r)

r = 11/-1 = -1/-9

d = -11 = 1/9 ---- false equation i.e. no common ratio

The above function is not an arithmetic function.

This is so because it does not have a common difference

Also, the function is not a geometric function.

This is so because it does not have a common ratio

Hence, the true statement about the function is (c) the equation is neither geometric nor arithmetic

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21 + (36 + 0 + 19) Equals 76.

A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.

Equation to be used: 21 + (36 + 0 + 19)

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I understand that the you are looking for is :

Several properties are used to evaluate this expression. Identify the property used in each step.

21 + (36 + 0 + 19)

21 + (36 + 19):

21 + (19 + 36):

(21 + 19) + 36:

40 + 36

76

The function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x  + 16 = 9.

Given the function; f(x) = x² - 8x + 7

To rewrite by completing the square.

We simplify the function into a proper form to completing the square.

x² - 8x + 7 = 0

x² - 8x = -7

We create a trinomial square on the left side of the equation that is equal to the square of the half of b.

(b/2)² = (-4)²

Next, we add the term to both side of the equation.

x² - 8x + (-4)² = -7 + (-4)²

x² - 8x  + 16 = 9

Therefore, the function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x  + 16 = 9.

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The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

According to the statement

we have to explain the characteristics of the Geometric Sequence.

So, For this purpose

We know that the

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

From its definition it is clear that the

There is a common ratio between the terms.

And this point represent the characteristics of the Geometric Sequence not all other points.

Now, The option A is the correct rather than the other options.

So, The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which statements describe characteristics of a geometric sequence? Check all that apply.

a.There is a common difference between terms

b.Each term is multiplied by the same number to arrive at the next term.

c.The sequence increases or decreases in a linear pattern

d.There is a common ratio between terms

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The required equation that represents the line of best fit is y = 2x + 4

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.

Using the following points (4, 12) and (2, 8)

The equation of the line will be in the form y = mx + b

where

m is the slope

b is the y-intercept

Determine the slope

Slope = y2-y1/x2-x1

Slope = 8-12/2-4
Sope = -4/-2
Slope = 2

Determine the y-intercept

Using the coordinate point (2, 8) and m = 2

8 = 2(2) + b

b = 8 - 4

b = 4

Hence the required equation that represents the line of best fit is y = 2x + 4

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The sum of the geometric series is 2199; option E.

S6 = a(rⁿ - 1) / r -1

= 1468(1/3^6 - 1) / (1/3 - 1)

= 1468(0.00137174211248 - 1) / -2/3

= 1468(-0.9986282578875) / -0.66666666666666

= -1,465.98628257885 / -0.66666666666666

= 2198.97942386829

Approximately,

S6 = 2199

Arithmetic series

Sn = n/2{2a + (n -1)d}

= 36/2 {2×27 + (36-1)-5/2}

= 18{54 + (35)-5/2}

= 18(54 + 175/2)

= 18(54 + 87.5)

= 18(141.5)

s36 = 2547

a36 = a + (n - 1) d

= 27 + (36 - 1)-5/2

= 27 + (35)-5/2

=27 + -175/2

= 27 - 87.5

= -60.5

S20 = n/2{2a + (n -1)d}

= 20/2{2×27 + (20-1)-5}

= 10(54 + (19)-5)

= 10{54 + (-95)}

= 10(54-95)

= 10(-41)

s20 = -410

Missing terms of the geometric sequence:

nth term = ar^n-1

448/135 = 63/80×r^(6-1)

448/135 = 63/80×r^5

r^5 = 448/135 ÷ 63/80

= 448/135 × 80/63

= 35,840/8,505

r = 5√35,840/5√8505

= 946.57/461.11

r = 2.05

Second term = a×r

= 63/80×2.05

= 1.614375

Third term = ar²

= 63/80×2.05²

= 63/80×4.2025

= 3.30946875

Fourth term = 63/80 × 2.05³

= 63/80×8.615125

= 6.7844109375

Therefore, none of these are correct

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A polygon is a figure that has a given number of sides.

A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.

a. 12.gon - An interior angle measures 150°

The polygon that has 12 sides is called the Dodecagon.

Given that the sum of the interior angles in a dodecagon is 1800, then  each interior angle is; 1,800/12

= 150°

b. 15-gon - An exterior angle measures 24°

The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is  24° then;

360/ 24° = 15 sides

c. 16-gon - The sum of the interior angles is 2,520°

The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 =  157.5°

d. 18-gon - An interior angle measures 160°

A polygon that contains 18 sides is called an octadecagon .

We have;

160 = (n−2) × 180° / n

160n = 180n - 360

360 = 20n

n = 18

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Missing parts;

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the properties to the regular polygons they describe.

An interior angle measures 150".

An exterior angle measures 24.

The sum of the interior angles is 2520°.

An interior angle measures 160".

The sum of the exterior angles is 180º.

The sum of the interior angles is 2160°.

15-gon

16-gon

12.gon

18-gon

Answer:

Step-by-step explanation:

If the side are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

Given that area of a shape of 37 [tex]mm^{2}[/tex] in which 60% is green.

We are required to find the area of green region if the side is increased by 45%.

Area is basically part of a surface covered by a shape.

When the side is increased by 45% then the area will increase by 45%*45%=20.25%.

Increased area =37*20.25%=7.4925

New area=37+7.4925

=44.4925

We have been given that 60% is the area of green.

Area of green region=44.4925*60/100

=26.6955 [tex]mm^{2}[/tex]

Hence if the sides are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

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Answer: [tex]\Large\boxed{First~Choice.~-28}[/tex]

Step-by-step explanation:

Given function expression

f(x) = -5x² - x + 20

Requirement of the question

Find the value of f(3)

Substitute the values into the function

f(x) = -5x² - x + 20

f(3) = -5(3)² - (3) + 20

Simplify the exponents

f(3) = -5(9) - 3 + 20

Simplify by multiplication

f(3) = -45 - 3 + 20

Simplify by subtraction and addition

f(3) = -48 + 20

[tex]\Large\boxed{f(3)=-28}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

C) 98

Step-by-step explanation:

Hope this helps! sry  if I'm wrong

The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.

An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.

The given equation is

15x + 120 = 5x + 1100

Take the like terms together,

15x - 5x = 1100 - 120

10x = 980

x = [tex]\frac{980}{10}[/tex]

x = 98.

Thus, the option C is correct stating that the value of x in the given equation is 98.

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The complete question is as follows:

Find the value of x in the equation:

15x + 120 = 5x + 1100.

A. 66

B. 122

C. 98

D. 76

SUBMIT.

The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

According to the statement

we have given that the some data of the marks of 18 students and we have to make the plot of that data.

So, For this purpose, we have given that the

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

And it is used to find the median and the lower value and the maximum value.

So, The median become:

median = n /2

median = 18/2

median = 9th term and

median value is 71.

And then the lower value of the data is a 53.

And the upper value of the data is a 89.

So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.

So, The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

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Six different sized rectangles that have an area of 64 square units:

1) 64 units x 1 unit
2) 32 units x 2 units

3) 16 units x 4 units

4) 40 units x 1.4 units

5) 20 units x 3.2 unit

6) 10 units x 6.4 units

For given question,

Let l be the length of the rectangle and w be the width of the rectangle.

We know that, the area of a rectangle is equal to

A = l × w

Here, A = 64 square units

So, we get an equation

l × w = 64                     ...............................(1)

let's assume different values of l to get the different values of w.

Case 1) For l = 64 units

substitute in the equation 1

⇒ 64 × w = 64

⇒ w = 64/64

⇒ w = 1 units

The dimensions of the rectangle are 64 units x 1 unit

See the draw in the attached figure 1

Case 2) For l = 32 units

substitute in the equation 1

⇒ 32 × w = 64

⇒ w = 64/32

⇒ w = 2 units

The dimensions of the rectangle are 32 units x 2 unit

See the draw in the attached figure 2

Case 3) For l = 16 units

substitute in the equation 1

⇒ 16 × w = 64

⇒ w = 64/16

⇒ w = 4 units

The dimensions of the rectangle are 16 units x 4 unit

See the draw in the attached figure 3

Case 4) For l = 40 units

substitute in the equation 1

⇒ 40 × w = 64

⇒ w = 64/40

⇒ w = 1.4 units

The dimensions of the rectangle are 40 units x 1.4 unit

See the draw in the attached figure 4

Case 5) For l = 20 units

substitute in the equation 1

⇒ 20 × w = 64

⇒ w = 64/20

⇒ w = 3.2 units

The dimensions of the rectangle are 20 units x 3.2 unit

See the draw in the attached figure 5

Case 6) For l = 10 units

substitute in the equation 1

⇒ 10 × w = 64

⇒ w = 64/10

⇒ w = 6.4 units

The dimensions of the rectangle are 10 units x 6.4 unit

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we conclude that the correct option is A, the slope is:

"the average number of pounds per foot tall"

The linear equation:

y = 48.3*x - 127

Relates the height, x, and the weight, y of an adult.

Then the slope, which is 48.3, should have units of mass over height.

Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.

Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:

"the average number of pounds per foot tall"

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Answer:

$5 each teenager

Step-by-step explanation:

divide 75 by 15

The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

According to the statement

we have given that the  Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.

And we have to find the equation for this.

So, for given purpose,

we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

And from the given values the equation formed that the

In the equation the charges per mile is added to the original charges is equal to the total charges per day.

So, The equation become

$25m + 0.35m = $42.50

And by this equation we represent the all given conditions related charges.

So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

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The total amount he puts towards emergency savings is $74

The correct option is C.

His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459

Now

that we are aware, his weekly deposits total $459 in total.

His total remuneration is $498 due to an error in his addition of the numbers.

The amount he has each week will be determined by deducting his deposits from his paycheck:

498-459 = 39

He contributes two equal payments of $20 and $15 to his emergency fund.

His entire contribution to emergency savings is = 20 + 15 = 35.

Only need to add the additional $39

To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:

39+35 = 74

the total per week that he can put towards emergency savings = $74

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I understand that the question you are looking for is:

Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?

a. $40

b. $60

c. $74

d. $55

Answer: C. $74

Step-by-step explanation:  C. $74.00

The shape of a bst approaches that of a perfectly balanced binary tree, (log2n) is the time complexity for a balanced binary search tree in case of insertions and search.

In computing, binary bushes are mainly used for looking and sorting as they offer a way to save statistics hierarchically. a few common operations that may be conducted on binary trees encompass insertion, deletion, and traversal.

A binary tree has a special situation that each node could have a most of two youngsters. A binary tree has the benefits of each an ordered array and a linked listing as search is as brief as in a taken care of array and insertion or deletion operation are as fast as in related listing.

In pc science, a binary tree is a tree information shape in which every node has at maximum two youngsters, that are known as the left baby and the proper toddler.

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For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

[tex]f_x=8x[/tex]

[tex]f_y=4y[/tex]

[tex]g_x=3[/tex]

[tex]g_y=3[/tex]

Setting up the Lagrange multiplier equations:

[tex]f_x=\lambda g_x[/tex]

⇒ 8x = 3λ                                        .....................(1)

[tex]f_y=\lambda g_y[/tex]

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944                            ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

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After reflected over  the triangle the point a become A = (-1,-6). The option c is correct.

According to the statement

we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.

So, For this purpose

we know that the when the triangle is at the x axis then the point A is A=(1,6).

But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other  words whole of the triangle shift to the negative side of the graph. That's why the point become negative.

So, The option c is correct. After reflected over  the triangle the point a become A = (-1,-6)

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The area of the shaded sector is 144π units squared.

To find the area of the shaded sector:

Given - The central angle of the sector is, θ [tex]=\frac{8\pi }{9} rad[/tex].

The radius of the circle is, [tex]R=18 units[/tex].

We know that the area of a sector of a circle of radius 'R' and central angle θ is given as:

[tex]A=\frac{1}{2} R^{2}[/tex]θ

Insert, θ [tex]=\frac{8\pi }{9} ,R=18[/tex] and obtain:

[tex]A=\frac{1}{2} *18^{2} *\frac{8\pi }{9} \\A=\frac{(324*4)}{9} \pi \\A=(36*4)\pi \\A=144\pi units^{2}[/tex]

Therefore, the area of the shaded sector is 144π units squared.

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The complete question is given below:

The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared

Answer: [tex]g(x)=2^{x-3}[/tex]

Step-by-step explanation:

The graph of y=g(x) is the graph of y=f(x) shifted 3 units right.

The value of expression 9/9/3-6/10-6/10 is 9/5.

Given an expression 9/9/3-6/10-6/10.

We are required to simplify the expression 9/9/3-6/0-6/10.

Expression is combination of numbers,fraction, coefficients, determinants,indeterminants, symbols.It is mostly not found in equal to form. It also includes algebraic operations also.

Expressions: 9/9/3-6/10-6/10

This is present in fraction which is combination of two numbers one is numerator and denominator. The numbers above division sign are known as numerator and the numbers below division sign are known as denominator.

Invert the fraction which is given in denominator.

=(9*3)/9-6/10-6/10

=27/9-6/10-6/10

Taking LCM now.

=(270-54-54)/90

=(270-108)/90

=162/90

=9/5

Hence the value of expression 9/9/3-6/10-6/10 is 9/5.

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