eight people are sitting around a circular table, each holding a fair coin. all eight people flip their coins and those who flip heads stand while those who flip tails remain seated. what is the probability that no two adjacent people will stand? (2015amc10a problem 22 or 2015amc12a problem 17) (a) 47 256 (b) 3 16 (c) 49 256 (d) 25 128 (e) 51 256

Answer:

2,525 FEET

Step-by-step explanation:

The solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.

First, we need to rewrite the function in standard quadratic form:

f(x) = 25x^2 - 81

To solve this quadratic function using the square root method, we want to isolate the x^2 term and divide both sides by the coefficient of x^2, which is 25:

25x^2 - 81 = 0

25x^2 = 81

x^2 = 81/25

Taking the square root of both sides, we get:

x = ±(9/5)

Therefore, the solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.

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Answer: (-3u + -3) -5

Step-by-step explanation:
Use distributive property

The terms and properties of operations that complete the statement and reasons for the equivalent expressions are;

3. Same

4.The properties of operations to write the equivalent expressions are; (-4), (-4) Distributive property

(-4), (-4), Associative property

(-4), (-3) Distributive property

5. When x = 2, and y = -5 -28·x + 12·y is -116 = -116

Equivalent expressions are expressions that have the same value for the values of the input variable.

3. The completed statement is presented as follows;

Equivalent expressions evaluate to the same value when a given set of values of x and y are substituted into both expressions.

4. The expressions in the question can be expanded to collect like terms as follows;

Expression; -28·x + 12·y

The common factor of 28 and 12 is 4, therefore, we get;

-28·x + 12·y = (4 × (-7))·x + (4 × 3)·y

To make the coefficient of the leading term positive, we get;

-28·x + 12·y = (-4 * 7)·x + (-4 * (-3))·y; Distributive property

Factoring the algebraic expression on the right, where the common factor is -4, we get;

(-4 * 7)·x + (-4 * (-3))·y = -4 × (7·x) + -4 × (-3·y);  Associative property

= -4 × ((7·x) + (-3·y));

Therefore; -28·x + 12·y = -4 × (7·x + -3·y); Distributive property

5. Evaluation of the left and right side of the expression, where; x = 2, and y = 5, we get;

-28 × 2 + 12 × -5 = -116

(-4) × ((7 × 2) + (-3 × -5)) = -4 × 29 = -116

The completed equations are therefore;

-28·x + 12·y = -4 × (7·x + -3·y)

-28 × 2 + 12 × (-5) = -4 × (7 × 2 + -3 × (-5))

-116 = -116

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Answer:

Step-by-step explanation:

In mathematics and statistics, a bar graph is commonly employed. Bar graphs, generally referred to as bar charts, are graphic illustrations of grouped data. A bar graph is a graph that displays all of the data in the form of rectangular bars with heights proportionate to the values they represent. The graph’s bars can be depicted vertically or horizontally. The bars provide a visual representation of quantities in various categories.

Graphical Representation is a way of analyzing numerical data. It exhibits the relation between data, ideas, information, and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

Line Graphs – A line graph or linear graph is used to display continuous data and it is useful for predicting future events over time.

Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.

Histograms – The graph that uses bars to represent the frequency of numerical data that are organized into intervals. Since all the intervals are equal and continuous, all the bars have the same width.

Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.

Frequency Table – The table shows the number of pieces of data that falls within the given interval.

Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered 100% and the categories occupied are represented with that specific percentage like 15%, 56%, etc.

Stem and Leaf Plot – In the stem and leaf plot, the data are organized from the least value to the greatest value. The digits of the least place values from the leaves and the next place value digit from the stems.

Box and Whisker Plot – The plot diagram summarises the data by dividing it into four parts. The box and whisker show the range (spread) and the middle ( median) of the data.

The angle measures in triangle RGH are:

[tex]< RGH = 60\\ < HRG = 99\\ < RHG = 41\\[/tex]

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation.

To solve for the value of x and the angle measures in triangle RGH, we can use the fact that the sum of the angles in any triangle is always 180 degrees.

Therefore, we can set up the equation:

[tex]< RGH + < HRG + < RHG = 180[/tex]

Substituting the given angle measures, we get:

[tex](6x+6) + (11x-3) + (5x+1) = 180\\[/tex]

Simplifying the equation, we get:

[tex]22x + 4 = 180\\x = 8\\[/tex]

Now that we know [tex]x = 8\\[/tex], we can substitute it back into the angle measures to find their values:

[tex]< RGH = (6x+6) = 54 + 6 = 60\\ < HRG = (11x-3) = 88 + 11 = 99\\ < RHG = (5x+1) = 41\\[/tex]

Therefore, the angle measures in triangle RGH are:

[tex]< RGH = 60\ degree\\ < HRG = 99\ degree\\ < RHG = 41\ degree\\[/tex]

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The answer of the given question based on the  exponential function is the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ.

An equation is a statement that two expressions are equal. It contains an equal sign (=) which separates the two expressions, and it can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

The general form of exponential function is:

f(x) = a(b)ˣ

where a is the initial value, b is the base, and x is the independent variable.

We can use the two given points to form a system of equations and solve for the values of a and b.

Using the point (0,4):

f(0) = a(b)⁰ = a = 4

Using the point (4,0.25):

f(4) = a(b)⁴ = 0.25

Now we can substitute a = 4 into the second equation and solve for b:

4(b)⁴ = 0.25

(b)⁴ = 0.25/4 = 1/16

b = (1/16)⁽¹/⁴⁾ = 0.5

Therefore, the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ

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The probability that team A wins the best-of-three series over team B is 3/16.

If team A is the underdog and has a probability of 1/4 of winning every game it plays against team B,

The probability that it wins the best-of-three series over team B :

Let us first begin by determining the probability of team A winning two games in a row. Since each game is independent, we can use multiplication to calculate the probability of winning two games in a row:

P(Team A wins 2 in a row) = P(Team A wins Game 1) x P(Team A wins Game 2)

Using the probability given in the problem, we can substitute:

P(Team A wins 2 in a row) = (1/4) x (1/4) = 1/16

Now we must determine the probability of team A winning two games in the series. There are three ways that Team A could win the series:

Winning the first two games;

Winning the second two games;

Winning the first and third games.

Assuming that each of these scenarios is equally probable, the probability of team A winning the series is the sum of the probabilities of these scenarios:

P(Team A wins series) :

= P(Team A wins first two games) + P(Team A wins second two games) + P(Team A wins first and third games)P(Team A wins series)

= (1/16) + (1/16) + (1/16)P(Team A wins series)

= 3/16

Therefore, the probability that team A wins the best-of-three series over team B is 3/16.

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Atoms of oxygen most different from atoms of nitrogen as they have different masses.

A subatomic particle known as an atom is made up of a nucleus composed of protons and neutrons, which is encircled by a swarm of electrons. The atom is the fundamental unit of the chemical elements, and the chemical elements are differentiated from one another by the count of protons present in their atoms. For instance, sodium is any atom that comprises 11 protons, and copper is any atom that includes 29 protons. The isotope of the element is characterized by the number of neutrons. Solid blue crystals can also be a form in which oxygen exists, with molecules that are diatomic.

Interestingly, Priestley was not immediately aware that he had discovered oxygen, and instead believed he had obtained a certain component of air. In a hermetic device, he observed the breakdown of mercury oxide and used a lens to direct sunlight onto the oxide.

In terms of the interaction between nitrogen and oxygen, these substances react in the presence of an electric current. Nitrogen is a stable molecule and does not readily react with other substances.

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The coordinates of the child after 75 seconds on a carousel that revolves once every minute counter-clockwise, assuming the child entered at point (1,0), are (-0.766, -0.643).

Since the carousel revolves once around in one minute, its angular velocity is 2π/60 radians per second or π/30 radians per second.

Let's find the angle that the child has covered in 75 seconds.

angle = (angular velocity) x (time) = (π/30) x 75 = 2.5π

After 2.5π radians, the child has completed 2.5 full revolutions and is back at the starting point. Therefore, the coordinates of the child at point (1, 0) are (-0.766, -0.643).

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Let us call the number of children "c" and the number of adults "a." Based on the facts provided, we can then construct two equations: c + a = 259 (equation 1) (equation 1).  

1.5c + 4a = 676 (2nd equation)

In equation 1, we may solve for one variable in terms of the other:

c = 259 - a

So, in equation 2, substitute this expression for "c":

1.5(259 - a) + 4a = 676

Distribute the 1.5:1:1:1:1:1:1:1:

388.5 - 1.5a + 4a = 676

Merge similar terms:

2.5a = 287.5

Multiply by 2.5:

a = 115

This translates to 115 adults being accepted. We can plug this number back into equation 1 to find "c":

c + 115 = 259

c = 144

As a result, 144 youngsters were hospitalised.

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Answer:

y = 2/3x +6  for x< -3.

y = 2/3x +1     for x> 3.

Step-by-step explanation:

Explanations are given in attachment!

The correct options for the average speed of both runners are:

B: Candace ran 4 meters per second

F: Candice ran at a faster rate

The formula for slope between two coordinates is:

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

For Antonio, we take two coordinates from the table to find the average speed.

The coordinates are: (8, 29) and (12, 41)

Thus:

Average speed = (41 - 29)/(12 - 4)

= 12/8 = 1.5 m/s

For candice, we take two coordinates which are:

(10, 42) and (15, 62)

Thus:

Average Speed = (62 - 42)/(15 - 10)

= 20/5

= 4 m/s

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By answering the presented question, we may conclude that Therefore, the 25th term of the arithmetic sequence is 53.

In mathematics, a sequence is an ordered list of items. Elements can be numbers, functions, or other mathematical objects. A series is commonly expressed by putting the phrases in parentheses and separating them with commas. A natural number series, for example, can be denoted as: (1, 2, 3, 4, 5, ...) Similarly, the even number series is labelled as follows: (2, 4, 6, 8, 10, ...) A series can be finite or infinite depending on whether it has a finite or infinite number of words.

To find the 25th term,

an = a1 + (n - 1)d

In this case, a1 = 5 and d = 2. Plugging these values into the formula, we get:

a25 = 5 + (25 - 1)2

a25 = 5 + 48

a25 = 53

Therefore, the 25th term of the arithmetic sequence is 53.

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Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

Time is the duratiοn between twο events. Speed is the measure οf hοw fast sοmething mοves οver a given distance. Distance is the amοunt οf space between twο pοints οr οbjects.

Tο find οut hοw much faster Michael swam the 50-meter freestyle than the 100-meter freestyle, we need tο calculate the difference between their speeds.

Let's first find οut Michael's speed in meters per secοnd fοr each race.

Fοr the 50-meter freestyle:

speed = distance / time = 50 meters / 23.04 secοnds ≈ 2.17 meters/secοnd

Fοr the 100-meter freestyle:

speed = distance / time = 100 meters / 47.77 secοnds ≈ 2.09 meters/secοnd

Nοw, tο find the difference in speed, we can subtract the speed οf the 100-meter freestyle frοm the speed οf the 50-meter freestyle:

2.17 meters/secοnd - 2.09 meters/secοnd ≈ 0.08 meters/secοnd

Therefοre, Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

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Step-by-step explanation:

(x+90°)=7x (vert opp angles)

x-7x=-90°

-6x/-6=-90°/-6

x=15

the required number of packages of bias binding for the tablecloth is 2.

As the rectangular tablecloth measures 73 in. by 46 in., the perimeter of the tablecloth can be calculated by the following formula:

Perimeter of the tablecloth = 2(Length + Width)= 2(73 + 46)= 2(119)= 238 inches

Therefore, the length of the bias binding required to sew around the tablecloth will be equal to the perimeter of the tablecloth. The length of the bias binding available in a single package is 13 feet, which is equal to 156 inches.Therefore, the number of packages required can be calculated as:

Number of packages of bias binding required= Length of bias binding required / Length of bias binding in a package= 238 / 156= 1.52

Therefore, 1.52 packages of bias binding will be needed for the tablecloth. However, we cannot purchase a fractional part of a package. Therefore, we need to round up the decimal to the nearest whole number. Hence, 2 packages of bias binding are required for the tablecloth.

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Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.

Adding the length of the first two rolls, we get:

50 meters + 22.86 meters = 72.86 meters

Then adding the length of the third roll to the sum above, we get:

72.86 meters + 18.288 meters = 91.148 meters

Therefore, Ally will have 91.148 meters of tape in all.

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Answer:

The value of b will be completed when b = 24

Step-by-step explanation:

f(x) can also be determined as y.

(-6, 2)

y = 2x²+bx+74

Plug it in.

2 = 2(-6) ² + b (-6) + 74

2 = 2(36) - 6b + 74

2 = 72 - 6b + 74

2 + 6b = 72 + 74

6b = 70 + 74

6b = 144

b = 24

Answer:

n+9 = 14

Step-by-step explanation:

Let's Sean friends in grade 7 be n.

Then In grade 8, 9 persons are there.

Equation: n+9 = 14.

n = 14-9 = 5.

The probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.

What is probability?

Assuming that the coins are fair, meaning they have an equal probability of landing heads or tails, the probability of getting a specific sequence of outcomes is found by multiplying the probabilities of each individual outcome.

In this case, the probability of getting a tail on the first flip is 1/2, the probability of getting a head on the second flip is also 1/2, and the probability of getting a tail on the third flip is 1/2. Multiplying these probabilities together, we get:

(1/2) x (1/2) x (1/2) = 1/8

Therefore, the probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.

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What is an angle?

It is the opening that forms the intersection of two lines.

The sum of two angles:

What is a rectangle?

A rectangle is a polygon with four sides, with the characteristic that its opposite sides are equal.

What is the measure of the angle formed by the diagonals of the rectangle ABCD?

The area of a rectangle can be determined by knowing its diagonals and the angle they form between them.

A = D² Sen(γ)/2

Being;

Being;

A = (7)(6)

A =  42cm²

Apply the Pythagorean theorem to determine D.

D² = AB² + AD²

replace;

D² = (7)² + (6)²

D² = 49  + 36

D² = 82

Substitute in A;

 42=82 Sen(γ)/2

Solve for γ;

 84=82 Sen(γ)


γ = Sen⁻¹(84/82)

γ =

To solve this problem, we can set up a system of equations to represent the given information. Let R be the number of red tiles and B be the number of blue tiles. We are trying to find the value of R, the number of red tiles.

The first piece of information we are given is that the ratio of red to blue tiles is 3:5. This can be written as:

[tex]\dfrac{\text{R}}{\text{B}} =\dfrac{3}{5}[/tex]

The second piece of information we are given is that there are 12 more blue tiles than red tiles in the box.

This can be written as:

[tex]\text{B = R}+12[/tex]

We can solve this system of equations by substituting the second equation into the first equation and solving for R.

Substituting [tex]\text{B = R}+12[/tex] into the first equation, we get:

[tex]\dfrac{\text{R}}{\text{R}}+12 =\dfrac{3}{5}[/tex]

We can then simplify this equation to get:

[tex]\text{R} = 15[/tex]

Thus, there are 15 red tiles in the box.

The probability that Karen’s second card will be a black card is 26/51.

Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are.

Let R represent the red cards and B represent the black cards.

We are given that a standard deck of playing cards consists of 52 cards. There are 26 black and 26 red cards in a playing deck.

The probability of the first card being red:

P(First R) = [tex]26/52[/tex]

The probability of the Karen’s second card being black:

P(First R) = [tex]26/51[/tex]

Full question "Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen’s second card will be a black card?"

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Answer:

The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

Step-by-step explanation:

Numbers in order:

4,5,6,6,7,8,9,9,10,10,12,12,14,15

List into two equal parts:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Find middle numbers:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Lower quartile: 6

Upper quartile: 12

Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

It should be noted that the quotient of the division is 9r^2 + 2r - 5 and the remainder is -5

In this case, to solve this polynomial division, we can use either long division or synthetic division. Here, we'll use long division:

   9r^2 + 2r - 5

        ___________________________

r - 7  | 9r^3 - 73r^2 + 64r + 37

        - 9r^3 + 63r^2

        --------------------

                 - 10r^2 + 64r

                 + 10r^2 - 70r

                 ----------------

                          -6r + 37

                          -6r + 42

                          --------

                                -5

Therefore, the quotient is 9r² + 2r - 5 and the remainder is -5. Therefore: (9r³-73r² +64r +37)÷(r-7) = 9r^2 + 2r - 5 + (-5)/(r-7).

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Answer:

Step-by-step explanation:inconclusive

Answer:

1 cm

Step-by-step explanation:

To answer this question we use Pythagoras theorem. This is a² + b² = c², where a is the length, b is the width and c is the hypotenuse (diagonal).

As we are already given the diagonal, we have to rearrange the formula to apply to our question...

Now solve...

This means that our width is 1!

Hope this helps, have a lovely day! :)

The professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.

To calculate the sample size needed for a confidence interval with a maximum width of 1.7 hours, we need to use the formula:

n = ((z * σ) / E)^2

where:

n is the sample size we need to find

z is the z-score corresponding to the desired confidence level (97% in this case)

σ is the population standard deviation (14.9 hours in this case)

E is the maximum margin of error we want in our confidence interval (1.7 hours in this case)

The z-score corresponding to a 97% confidence level is 1.8808 (which can be found using a z-table or calculator).

Substituting these values into the formula, we get:

n = ((1.8808 * 14.9) / 1.7)^2

n = 246.644

Rounding up to the nearest whole number, we get:

n = 247

Therefore, the professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.

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The ordered pairs in the quadrants are option A and option D:

A. A= (2, 1)

D. C = (-1, -2)

The quadrant is the area that is bounded by the point where the X and Y axes connect. The cartesian plane's two axes, the X and Y axes, intersect at a 90° angle, forming four zones surrounding the intersection that are known as quadrants.

The points are given as:

A = (2, 1)

B = (1, 2)

C = (-1, -2)

D = (-1, -2)

Now, point A is in 1st quadrant so both the points will be positive.

So, A = (2, 1) is an ordered pair.

Now, B is in 2nd quadrant, so x coordinate will be negative and y coordinate will be positive.

B = (1,2) is hence not an ordered pair.

Now, C is in 3rd quadrant, so both the points will be negative.

C = (-1, -2) is an ordered pair.

Similarly, D is in 4th quadrant and x coordinate will be positive and y coordinate will be negative.

D = (-1, -2) is not an ordered pair.

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