A chess master plays 15 games. In how many ways can these games result in 10 wins, 2 losses, and 3 draws?

the value of P(-2) is -2.

To find P(-2), we can use synthetic division and the Remainder Theorem.

We have the polynomial P(x) = x³ + 4x² - 8x - 6 and we want to evaluate it at a = -2.

1. Set up the synthetic division:

    -2 |  1   4   -8   -6

2. Bring down the coefficient of the highest degree term (1) to the bottom row:

    -2 |  1   4   -8   -6

        ------------------

        1

3. Multiply -2 by 1 and write the result below the next coefficient (4):

    -2 |  1   4   -8   -6

        ------------------

        1  -2

4. Add the two numbers in the second row (4 + (-2) = 2) and write the result below the next coefficient (-8):

    -2 |  1   4   -8   -6

        ------------------

        1  -2    2

5. Repeat the process by multiplying -2 by 2 and adding the result to -8:

    -2 |  1   4   -8   -6

        ------------------

        1  -2    2    4

6. Finally, add 4 to -6 (-6 + 4 = -2):

    -2 |  1   4   -8   -6

        ------------------

        1  -2    2    4

              -2

The bottom number, -2, is the remainder when dividing P(x) by (x + 2). According to the Remainder Theorem, this is also the value of P(-2).

Therefore, the value of P(-2) is -2.

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The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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The terms with "x" cancel out, and we're left with:

0 = 12

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.

Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:

Slices with only pepperoni: 6 slices

Slices with only mushrooms: 10 slices

Slices with both pepperoni and mushrooms: $x$ slices

Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices

We know that the total number of slices is 12, so we can write an equation:

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.

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Answer:

0.00003703703

Step-by-step explanation:

(3 to the power (-3))*(10 to the power (-3))

Answer:

i think the answer is A. 14 surfaces with glue on them

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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Answer:

$60

Step-by-step explanation:

First you must find how much he earns per hour. In order to do this, you must divide 36 by 3. This gets you 12. So, we know that Ed earns 12 dollars per hour. Now you just multiply this by 5 to get you answer (60).

Answer:

Ed will earn $60 for 5 hours of work

Step-by-step explanation:

36/3=12----Divide the money he makes($36 dollars) for the hours he works.(3 hours) To see how much he make an hour

12*5=60----Now that we know how much he makes a hour multiply this by however many hours you want.(5 hours) And you get 60.Just add your money symbol ($)

I hope this helped!

Answer:

as below

Step-by-step explanation:

\(\frac{2}{7}\) = \(\frac{6x}{4x + 17}\)

2(4x + 17) = 7(6x)

8x +34 = 42x

34 = 42x-8x

34 = 34x

\(\frac{34}{34}\) = x

1 =x   :)

We arrive at the standard form expression for the volume of the rectangular prism:

V = a(b^4c + b^3a^2) = ab^3(bc + a^2)

The volume of the rectangular prism is given by:

V = length × width × height

Substituting the given values, we get:

V = (b^2) × a × (ab + c)

Multiplying the terms inside the parentheses, we get:

V = a(b^3)(c + ab)

Expanding further, we get:

V = a(b^4c + b^3a^2)

Rearranging and grouping like terms, we arrive at the standard form expression for the volume of the rectangular prism:

V = a(b^4c + b^3a^2) = ab^3(bc + a^2)

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Answer:

64 degrees

Step-by-step explanation:

The measure of the exterior angle should be that same as the measures of the two remote interior angles. The remote interior angles are 37 & 27, so when you add them together, you get 64.

Hope this helps :-)

The required numbers are -2.33 and 1 are a distance of 5/3 unit from -2/3 on a number line.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

Here, we have,

We have been given that number line, the numbers that are 5/3 units away from the number -2/3 are the numbers that are 5/3 units to its right and left.

The numbers are given by -2/3 - 5/3 and -2/3 + 5/3.

So the required numbers would be:

⇒ -2/3 - 5/3 = -7/3 = -2.33

⇒ -2/3 + 5/3 = 3/3 = 1

Therefore, the required numbers are -2.33 and 1 are a distance of 5/3 unit from -2/3 on a number line.

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Lauren can spend up to $33.33 per day during spring break if she wants to have $2,700 left at the end of the break.

What is the linear equation?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y-intercept.

Lauren wants to spend some money each day during spring break such that she has $2,700 left at the end of the break.

Let x be the amount of money she can spend each day during spring break. Then, we can set up an equation based on the given information:

Amount of money spent during spring break = Total amount of money at the beginning of spring break - Total amount of money she wants to have at the end of spring break

Therefore, we have:

9x = 3000 - 2700

9x = 300

x = 33.33 (rounded to two decimal places)

Hence, Lauren can spend up to $33.33 per day during spring break if she wants to have $2,700 left at the end of the break.

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Answer:

\( \sqrt[12]{48} \)

es igual a 1,380 (decimal)

The union of the two events (oil industry investment is successful and municipal bond investment is successful) contains three sample points: (Oil Industry investment is successful, Municipal Bond investment is successful), (Oil Industry investment is unsuccessful, Municipal Bond investment is successful), (Oil Industry investment is successful, Municipal Bond investment is unsuccessful).

a. There are four sample points for this experiment: (oil industry investment is successful, municipal bond investment is successful), (oil industry investment is unsuccessful, municipal bond investment is successful), (oil industry investment is successful, municipal bond investment is unsuccessful), (oil industry investment is unsuccessful, municipal bond investment is unsuccessful).

b. The tree diagram for this experiment is shown below:

    Investment

       |

       |

   --------------

   |            |

Oil Industry    Municipal Bond

Sample Points:

• (Oil Industry investment is successful, Municipal Bond investment is successful)

• (Oil Industry investment is unsuccessful, Municipal Bond investment is successful)

• (Oil Industry investment is successful, Municipal Bond investment is unsuccessful)

• (Oil Industry investment is unsuccessful, Municipal Bond investment is unsuccessful)

c. The sample points in o (oil industry investment is successful) are:

• (Oil Industry investment is successful, Municipal Bond investment is successful)

• (Oil Industry investment is successful, Municipal Bond investment is unsuccessful)

The sample points in M (municipal bond investment is successful) are:

• (Oil Industry investment is successful, Municipal Bond investment is successful)

• (Oil Industry investment is unsuccessful, Municipal Bond investment is successful)

d. The sample points in the union of the events (o ∪ M ) are:

• (Oil Industry investment is successful, Municipal Bond investment is successful)

• (Oil Industry investment is unsuccessful, Municipal Bond investment is successful)

• (Oil Industry investment is successful, Municipal Bond investment is unsuccessful)

The union of the events can be expressed mathematically as:

o ∪ M = {(Oil Industry investment is successful, Municipal Bond investment is successful), (Oil Industry investment is unsuccessful, Municipal Bond investment is successful), (Oil Industry investment is successful, Municipal Bond investment is unsuccessful)}

To calculate the union of the two events, we can use the formula for the union of two sets:

A ∪ B = {x | x ∈ A ∨ x ∈ B}

In this case, A = o and B = M, so the union of the two events can be expressed as:

o ∪ M = {x | x ∈ o ∨ x ∈ M}

= {(Oil Industry investment is successful, Municipal Bond investment is successful), (Oil Industry investment is unsuccessful, Municipal Bond investment is successful), (Oil Industry investment is successful, Municipal Bond investment is unsuccessful)}

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Answer:

Cada bombón negro cuesta $3,125 y cada bombón blanco cuesta $6,75

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones. Es decir, resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema.

Si compro 2 bombones de chocolate negro y 5 de chocolate blanco, la suma da $40. Si compro 4 bombones de chocolate negro y 2 de chocolate blanco, gasto $26. Siendo:

Entonces el sistema de ecuaciones a resolver es:

\(\left \{ {{2*x+5*y=40} \atop {4*x+2*y=26}} \right.\)

El método de sustitución consiste en aislar en una ecuación una de las dos incógnitas para sustituirla en la otra ecuación.

Entonces, aislando la variable x de la primer ecuación:

\(x=\frac{40-5*y}{2}\)

Sustituyendo en la segunda ecuación:

\(4*\frac{40-5*y}{2}+2*y=26\)

Resolviendo:

\(\frac{4}{2}* (40-5*y)+2*y=26\)

2* (40-5*y)+2*y=26

2*40- 2*5*y+2*y=26

80- 10*y+2*y=26

- 10*y+2*y=26 -80

-8*y= -54

y= (-54)÷ (-8)

y= 6,75

Reemplazando en la expresión \(x=\frac{40-5*y}{2}\), se obtiene:

\(x=\frac{40-5*6,75}{2}\)

\(x=\frac{40-33,75}{2}\)

\(x=\frac{6,25}{2}\)

x= 3,125

Entonces, cada bombón negro cuesta $3,125 y cada bombón blanco cuesta $6,75

Answer:

These relationships are realted because the variable is multiplied by ten to get the function.

9cm: 90mm

12 1/4cm: 122.5mm

50cm: 500mm

88.49cm: 884.9mm

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Answer:

38.3 hours

Step-by-step explanation:

Given data

We have been given the function that describes his pay, which is

y=6.50h

Where h is the number of hours

now we have the amount y= 249

substitute

249=6.50*h

make the subject of the formula

249/6.5=h

h=38.3

Hence he needs to work for at least 38.3 hours

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer:

D

Step-by-step explanation:

The 6 represents the initial value of 6000.  The cases are going down 5,000 a month.

Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The supplied input should simply be replaced in the function definition for that precise interval.

An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.

Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.

When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.

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Answer:

regular pentadecagon

Step-by-step explanation:

it has 15 sides

that is what matches the exterior angled sum property - 360degree

let me explain it

1 side = 180 - 156 = 24

360/24 = 15

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The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."

Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.

The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.

Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.

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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.

The distance between the car and Johnstown is decreasing at a rate of 33 miles per hour.

After travelling 63 miles, the distance between the car and Johnstown is changing at a rate of 33 miles per hour, and the distance between the car and Johnstown is 100 miles

To calculate the distance between the car and Johnstown after travelling 63 miles, we need to first find the starting distance.

The car starts off 163 miles directly north from the city of Johnstown, so the starting distance is 163 miles.

We then need to subtract the distance travelled from this starting distance. Since the car is travelling at a rate of 33 miles per hour, it has travelled 63 miles in the given time.

Therefore, the distance between the car and Johnstown is 100 miles

(163 - 63 = 100).

Finally, we need to calculate the rate of change of this distance. Since the car is travelling at a rate of 33 miles per hour, the rate of change of the distance between the car and Johnstown is also 33 miles per hour.

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Answer:

c\leq 96

Step-by-step explanation:

plz crown

Answer:

32.375 or 32 with a remainder of 3

Step-by-step explanation:

The expression that represent the new price is p(0.5 + 1).

Lora bought a house for a price of p dollars. After 1 year the value of the house increased by 50%.

Therefore, the expression that can be used to represent the new value of the house can be represented as follows:

Hence,

increased price = 50% of p

increased price = 50 / 100 p

increased price = 0.5p

Hence, the expression that represent the new price is as follows;

expression for the new price = 0.5p + p

expression for the new price = p(0.5 + 1)

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The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.

We have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.

1 cm = 0.394 inches

126 cm = 126 × 0.394 inches

126 cm = 49.644 inches

So the picture has length 16 inches and width 49.644 inches

area of picture = 16 inches × 49.644 inches

area of picture = 794.304 square inches

1 inch = 0.0833 feet

794.304 square inches = 794.304 × 0.0833 square feet

794.304 square inches = 66.166 square feet.

In conclusion, the picture has an area of 66.166 square feet.

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