2.3.4 In a game between two equal teams; the home team wins with probability p > 1/2_ In a best of three playoff series; a team with the home advantage has a game at home, followed by a game away, followed by a home game if necessary The series is over as soon as one team wins two games. What is P[H], the probability that the team with the home advantage wins the series? Is the home advantage increased by playing a three-game series rather than a one-game playoff? That is, is it true that P[H] > p for all p > 1/2?

Answer:

140

Step-by-step explanation:

To solve this, we must reverse all the steps Adnan took to get the final number of 3.

If the last thing he did was take the square root, we need to square 3 to get the result. \(3x^{2} =9\), so the sum they are referring to in the prompt is 9.

Before that, it says he added 1, so we need to subtract 9-1=8 to get the previous number.

It says that he took the square root before that, so we need to square 8 to get \(8x^{2} =64\).

It says that he subtracted 6 to get this number, so we have to add 6 to get\(64+6=70\).

Since the first thing Adnan did was divide his number by 2, we must multiply 70 by 2 to get Adnan's original number: \(70*2=140.\)

Adnan's original number was 140.

Hope this helps! :)

The statement given is false. The reason for this is that the convergence of a function does not necessarily imply anything about the value of its derivative. To disprove the statement, we can consider the function f(x) = x^2, which converges for all x, but its third derivative f'''(x) = 0, which means that f'''(0) is also equal to 0. Hence, f′′′(0) is not equal to 2.

In general, it is important to note that the convergence of a function does not provide any information about the behavior of its derivatives. Moreover, a function may converge at some points and diverge at others, and this can be determined by analyzing the behavior of its terms or by using convergence tests. In this case, it is necessary to compute f′′′(0) directly using the definition of the derivative or by applying differentiation rules.

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Answer:

The answer is 5 pieces of art.

Step-by-step explanation:

5% of 100 = 5.

Hope this helps!

Answer:

20

Step-by-step explanation:

he has 100 pieces and he only had 5% of them at an art show so 100 divied by 20 equals 5.

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Answer:

\({:}\leadsto \)\(\sf {\dfrac {3}{7}}\)

\({:}\leadsto \)\(\sf {\dfrac {3×3}{7×3}}\)

\({:}\leadsto \)\(\sf {\dfrac {9}{2}}\)

\({:}\leadsto \)\(\sf {\dfrac {1}{3}}\)

\({:}\leadsto \)\(\sf {\dfrac {1×7}{3×7}}\)

\({:}\leadsto \)\(\sf {\dfrac {7}{21}}\)

\({:}\leadsto \)\(\sf {\dfrac {9}{21}}\iff {\dfrac {7}{21}}\)

\({:}\leadsto \)\(\sf {\dfrac{9}{21}} \gt {\dfrac {7}{21}}\)

\(\therefore\)\(\sf {\dfrac {3}{7}} \gt {\dfrac {7}{21}}\)

Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Area of polygon is 7.5 square unit.

What do you mean by polygon?

A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves.

                           The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). In order to create a closed figure, at least three line segments must be connected end to end.

The polygon with three vertices is,

The polygon is triangle with base b = 5 units and height h = 3 units.

Determine the area of polygon.

  A = 1/2 . b . h

      = 1/2 . 5 . 3

     = 15/2

      = 7.5

So area of figure is 7.5 square unit.

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Answer:

Step-by-step explanation:

2x+1=x-4

2x-x= -4-1

1x=-5

Given the information provided, we know that the average (mean) length of time people keep their cars before replacing is 9 years, and the standard deviation is 2 years.

We are asked to analyze a randomly selected person in this context.

To determine the probability or characteristics related to this randomly selected person, we need more specific information or a question to address.
Without additional details or a specific inquiry, we cannot provide a meaningful answer or analysis.

However, based on the average and standard deviation provided, we can make general statements about the distribution of car ownership duration within the population.

The average of 9 years suggests that, on average, people tend to keep their cars for around 9 years before replacing them.
The standard deviation of 2 years indicates that there is some variability in car ownership duration, with some individuals keeping their cars for longer or shorter periods.

If you have a specific question or scenario related to the randomly selected person, please provide more details, and I'll be happy to assist you further.
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The time of depreciation is 3.3 year

From the question, we have the following parameters:

Initial value = $27,300

Final value = $22,100

Rate of depreciation = 6.1% per year

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of years

A  = Initial value = 27300

A(n) = Final value = 22100

r = rate of decay = 6.1%

Substitute the known values in the above equation, so, we have the following representation

27300*(1 - 6.1%)ⁿ = 22100

Divide

(1 - 6.1%)ⁿ = 0.81

0.939ⁿ = 0.81

Take the logarithm

n = log(0.81)/log(0.939)

Evaluate

n = 3.3

Hence, the number of years is 3.3 year

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Answer:

To write a number in ordinary form, we need to move the decimal point according to the power of 10. For example, 1.46 × 10^-2 means that we move the decimal point two places to the left since the exponent is negative. Here are the steps:

1. Start with 1.46 × 10^-2

2. Move the decimal point two places to the left: 0.0146

3. Write the number without the power of 10: 0.0146

Therefore, 1.46 × 10^-2 in ordinary form is 0.0146.

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Answer:

The insurance will cost £ 12.75

Step-by-step explanation:

first off, let's notice the LCD of all denominators will be hmmmm 4, so let's use that to do away with the denominators

\(x-\cfrac{1}{4}=\cfrac{1}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( x-\cfrac{1}{4} \right)=4\left( \cfrac{1}{2} \right)}\implies 4x-1=2 \\\\\\ 4x=3\implies x=\cfrac{3}{4}\)

The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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The given expression, \(\(350y \cdot C \cdot \cos(u)\)\), involves variables \(\(y\), \(C\)\), and \(\(u\)\) and their respective operations and functions.

The expression \(\(350y \cdot C \cdot \cos(u)\)\) represents a mathematical equation involving multiplication and the cosine function. Let's break down each component:

1. \(\(350y\)\) represents the product of the constant value 350 and the variable \(y\).

2. \(\(C\)\) is a separate variable that is being multiplied by \(\(350y\)\).

3. \(\(\cos(u)\)\) represents the cosine of the variable \(\(u\)\).

The overall expression represents the product of these three terms: \(\(350y \cdot C \cdot \cos(u)\)\).

To evaluate this expression or derive any specific meaning from it, the values of the variables \(\(y\), \(C\)\), and \(\(u\)\) need to be known or assigned. Without specific values or context, it is not possible to provide a numerical or simplified result for the given expression.

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There were 14-floor seat tickets sold to their spring play.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let's assume x be floor seat tickets and y be balcony seats

As per the given formation, the equation would be as:

x + y = 800  ....(i)

110x + 8y = 7740 ...(ii)

Multiply by 8 into equation (i), and subtract into equation (ii),

110x + 8y - 8x - 8y = 7740 - 6400

102x = 1340

x = 1340/102

x = 13.7 ≈ 14

Therefore, there were 14-floor seat tickets sold.

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The ratio of the plant cell's length to its width is 2:1 (5.8 x 10^-6 m to 2.9 x 10^-6 m).

To calculate the ratio of the plant cell's length to its width, we first need to find the length and width of the cell. The given data states that the length of the cell is 5.8 x 10^-6 m and the width is 2.9 x 10^-6 m. To calculate the ratio, we divide the length by the width. In this example, we divide 5.8 x 10^-6 m by 2.9 x 10^-6 m, which equals 2. Thus, the ratio of the plant cell's length to its width is 2:1.

length / width = 5.8 x 10^-6 m / 2.9 x 10^-6 m = 2

length : width = 5.8 x 10^-6 m : 2.9 x 10^-6 m = 2:1

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Answer:

I think the answer is (a) triangle as if you slice the traingular prism with perpendicular to the base as if we slice it with cross sectionally

Hope it helps

Answer:

(-3,8)

Step-by-step explanation:

When reflecting over the y-axis, you are switching from positive to negative x-values. Since 3 was already positive, we change the integer and in this case, to negative, so it becomes -3. Since the y value remains the same we don’t change the 8. So (-3,8)

I hope this helps!

Please give thanks or brainliest if this helps!

Answer:

(-3,8)

Step-by-step explanation:

product of two perpendicular line slopes must equals - 1 ;

As you know the coefficient of x is the slope of the line

Thus if we suppose that line has a slope of m , we have :

m × 2 = - 1

m = - 1 / 2

__________________________________

y = ax + b

y = - 1 / 2 x + b

The line passes through the point ( - 2 , - 2 ) thus :

- 2 = - 1 /2 × ( - 2 ) + b

- 2 = 1 + b

b = - 3

__________________________________

y = - 1/2 x - 3

Which mean the option c is the correct answer.

Answer:

y = -1/2(x) - 4

Step-by-step explanation:

\(y=-\frac{1}{2}(x)-4\)

Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

x divided by 4

Step-by-step explanation:

4 bags

O O

O O

strawberries would go in each

so lets say like 24 strawberries

24 (x) / 4 = 6

so six strawberries a bag

hope this helps like put a picture in your head

Answer:

x=  

6

43

​

Step-by-step explanation:

pasos  

4

3

​

x−5=  

8

3

Agrega 5 a ambos lados.

4

3

​

x=  

8

3

​

+5

Convertir 5 a la fracción  

8

40

​

.

4

3

​

x=  

8

3

​

+  

8

40

​

Como  

8

3

​

 y  

8

40

​

 tienen el mismo denominador, sume sus numeradores para sumarlos.

4

3

​

x=  

8

3+40

​

Suma 3 y 40 para obtener 43.

4

3

​

x=  

8

43

​

Multiplica los dos lados por  

3

4

​

, el recíproco de  

4

3

​

.

x=  

8

43

​

×(  

3

4

​

)

Multiplica  

8

43

​

 por  

3

4

​

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

x=  

8×3

43×4

​

Realiza las multiplicaciones en la fracción  

8×3

43×4

​

.

x=  

24

172

​

Reduzca la fracción  

24

172

​

 a su mínima expresión extrayendo y anulando 4.

x=  

6

43

​

To use a centimeter ruler to measure a matchstick, place the ruler parallel to the matchstick, aligning the zero mark with one end. Identify the nearest centimeter mark and estimate the millimeter measurement by looking at the divisions between centimeters and smaller increments for more precision.

To begin, ensure the centimeter ruler is in good condition and properly calibrated. Lay the matchstick on a flat surface, making sure it is straight. Position the ruler next to the matchstick, aligning the zero mark with one end while keeping it parallel to the matchstick. Observe the other end of the matchstick and identify the nearest centimeter mark on the ruler to the left of the end point. This represents the whole centimeter measurement. Next, look at the lines or ticks between the whole centimeter marks. Each centimeter is divided into 10 millimeter intervals. Estimate the length of the matchstick by identifying the millimeter line that aligns with the end of the matchstick. For more precise measurements, use the smaller divisions on the ruler. Each millimeter is further divided into smaller increments called tenths of a millimeter. Estimate the length by identifying the smallest increment that aligns with the end of the matchstick. Record the measurement by noting the number of centimeters, followed by the number of millimeters (and tenths of millimeters, if necessary). Handle the matchstick carefully to avoid any damage or inaccuracies in the measurement..

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Answer:

The answer would be 0 because it passes through

Step-by-step explanation:

Answer: See the diagram below

Explanation:

To go from P to A we follow these two steps (in any order)

After arriving at point A, move another "right 3, up 2" to arrive at point A'.

Then move back to point P. The goal is to travel to point B. Follow these motions in any order:

Repeat this motion to go from B to B'

Move back to point P. Move down 2 units to arrive at point C. Move another 2 units to arrive at point C.

This is all shown in the diagram below. Triangle A'B'C' has been enlarged by a scale factor of 2. It means that the sides of ABC have been doubled to get the corresponding sides of A'B'C'.

In other words,

Also,

These last three equations show that the distance from P to the new points (A',B',C') has been doubled compared to the original three points (A,B,C). Let me know if you have any questions.

Answer:

buy things

Step-by-step explanation:

Answer:

0.6×2.5

6.0×2.5

6.5×2.5

Step-by-step explanation:

This is in order from least to greatest