Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?

The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56

what is synthetic division ?

Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).

In the given question,

To use synthetic division to rewrite the fraction, we first set up the problem like this:

   -3 | 4    17    14    -3    0    2

       |     -12    -15    3   0

       +----------------------------------

          4     5    -1     0    0    2

The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.

We then proceed to perform synthetic division as follows:

Bring down the first coefficient, which is 4, and write it under the horizontal line.

Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.

Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.

Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.

Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.

Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.

Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.

The result of the synthetic division is:

4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56

Therefore, we have rewritten the fraction in the desired form:

4x⁵+17x⁴+14x³-3x²+2

---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)

         x+3

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Step-by-step explanation:

[tex]3 ln(2x) = 12[/tex]

[tex] ln(2x) = 4[/tex]

Let both sides be a power of a base e.

[tex]e {}^{ln(2x)} = e {}^{4} [/tex]

The e and ln would just cancel out so

[tex]2x = e {}^{4} [/tex]

[tex]x = \frac{ {e}^{4} }{2} [/tex]

The amount you will have in the account in 30 years is $22836.77

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Amount = P * (1 + r)^t

Where

P = Principal = 3000

r = Rate = 7%

t = time = 30

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

Amount = 3000 * (1 + 7%)^30

Evaluate

Amount = 22836.77

Hence, the amount is 22836.77

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The correct option is the last one, the mean will decrease.

For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:

mean = (x₁ + x₂ + ... + xₙ)/N

Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.

That will cause a decrease in the mean, because we are removing one of the larger values.

The correct option is the last one.

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Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

GIVE NICE GUY BRAINLINEST PLEASE

Step-by-step explanation:

[tex](x + 3)(x - 2) = 2x\\ {x}^{2} + x - 6= 2x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: or \: x = - 2[/tex]

Here is a tree diagram to represent the sample space of Jill tossing a coin three times:

      H               T

    /   \           /   \

   H     T         H     T

 /  \   /  \     /  \   /  \

H   T  H   T    H   T  H   T

The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.

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Answer:

Earned = 25 + 18h

Earned = 151

Step-by-step explanation:

The amount earned is the travel time plus the amount per hour times the hours

Earned = 25 + 18h

She works 7 hours

Earned = 25 + 18*7

Earned = 25 + 126

Earned = 151

The volume of the new object is approximately 439.3 cubic inches

To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:

The volume of a cylinder: = πr²h

where:

r = radius

h  = height

Note that the volume of a rectangular prism is :  = lwh

l = length

w = width

h = height

Assumption: In the above case, we will  assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.

Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.

So  V_prism = lwh

 = 16 × 16 × 8

= 2048 cubic inches

V_cylinder = πr²h

= π × 8² × 8

= 512 π cubic inches

Hence To get  the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:

V_new = V_prism - V_cylinder

= 2048 - 512π

= 2048  - 1608.70

= 439.3 cubic inches

Hence, the volume of the new object is about 439.3 cubic inches

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For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.

The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.

The given function is:

f(x) = 2 ÷ x²

We are asked to find the value of f(x) when x = 2.

Substituting x = 2, we get:

f(2) = 2 ÷ 2²

= 2 ÷ 4

= 1/2

= 0.5

Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:

f(x) = 2 ÷ x²

= 2 ÷ 4

= 1/2

Then, substituting x = 2, we get the same result:

f(2) = 1/2

f = 0.5

Hence, option (d) is correct.

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Answer:113

Step-by-step Explanation:

To create an equation to predict the number of seats in any row, we need to start by defining a few variables:

Let's call the number of seats in the first row "a".

Let's call the number of additional seats in each row after the first row "d".

Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:

d = 6

We also know that the first row has 11 seats, so we can set a equal to 11:

a = 11

To find the number of seats in any row, we can use the following formula:

number of seats in a given row = a + (n - 1) * d

Where "n" is the number of the row we are interested in.

Using this formula, we can find the number of seats in row 18:

number of seats in row 18 = 11 + (18 - 1) * 6

= 11 + 102

= 113

Therefore, there are 113 seats in row 18.

Answer:

x = 5√2, x = 3√2

Step-by-step explanation:

Question 1:

Using the 30-60-90 triangle properties, YX = WX /√3.

YX = 5√3 /√3 = 5.

Using the 45-45-90 triangle properties, x = YX *√2.

x = 5 *√2 = 5√2.

Question 2:

Using the 45-45-90 triangle properties, BC = AB *√2.

BC = 6 *√2 = 6√2.

Using the 30-60-90 triangle properties, x = BC / 2.

x = 6√2 / 2 = 3√2.

Answer:

B

Step-by-step explanation:

the answer is B because I know it

The area in square yards of the athletic field at IDEA Brentwood would be 170. 24 yards ²

The shape of the athletic field at IDEA Brentwood is shown to be a rectangle with two semi - circles attached.

The area of the athletic field at IDEA Brentwood is the sum of the areas of these shapes.

Area of rectangle :

= 15 x 8

= 120 yards ²

The area of the two semi - circles would be:

= π x radius x radius

= π x ( 8 / 2 ) x ( 8 / 2 )

= 50. 24 yards ²

The area of the athletic field at IDEA Brentwood is :

= 50. 24 + 120

= 170. 24 yards ²

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Check the picture below.

Answer:

A

Step-by-step explanation:

She earns $15 per poinsettia.

If  landscaper worked 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday then  total of 18.08 hours worked.

To find the total number of hours worked, we need to add up the hours worked on each day.

On Monday, the landscaper worked for 8-1/2 hours, which is the same as 8.5 hours.

On Tuesday, the landscaper worked for 3-1/3 hours, which is the same as 3.33 hours

On Wednesday, the landscaper worked for 6-1/4 hours, which is the same as 6.25 hours.

To find the total hours worked, we add the hours worked on each day:

Total hours worked = 8.5 + 3.33 + 6.25

Total hours worked = 18.08

Therefore, the landscaper worked a total of 18.08 hours.

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The median number of newspapers sold is 202 newspaper. So, correct option is C.

To find the median, we need to arrange the given data in ascending or descending order.

The given data in ascending order: 71, 81, 113, 202, 242, 248, 269

Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.

Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.

The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.

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Complete question is:

A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242​

Find the median number of newspapers sold.

A. 175 newspapers

B. 113 newspapers

C. 202 newspapers

D. 242 newspapers

Answer:

-9

Step-by-step explanation: Definitely correct

Answer:

B) Wx is equal to WX.

When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.

The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.

An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.

The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.

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Answer:

Time = Distance / Speed

Time is taken from home to park = d / 10

Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:

Time = Distance / Speed

Time is taken from park to home = d / 8

According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.

Total time is taken = Time from home to park + Time from park to home

6/5 = d/10 + d/8

To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:

(6/5) * 40 = (d/10) * 40 + (d/8) * 40

48 = 4d + 5d

48 = 9d

d = 48/9

d = 16/3 km

Now, to find the time taken from the park to Abel's home, we substitute the distance value:

Time from park to home = (16/3) / 8

Time from park to home = (16/3) * (1/8)

Time from park to home = 16/24

Time from park to home = 2/3 hour

Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.

Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.

The value of the given functions are:

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have the functions are as follows:

f(x)=x - 8,

g(x)=5 + 9

To solve :

a. (f + g)(x),

b. (f-g)(x),

c. (f • g)(x), and

d. (f/g)(x)

Now,

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

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The given question is incomplete, complete question is:

For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9

Answer:

B) The other number is even.

The number of packing materials the Amelia will need = 2.4

From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.

Where;

Length = 10in

Width = 6 in

Height = 8 in

The volume = 10×6×8 = 480 in³

But one bag = 200in³

The amount of bag that the music box can contain = 480/200 = 2.4

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