Given the polynomial function p(x)=12+4x-3x^(2)-x^(3), Find the leading coefficient

However, since she wants to visit each city once, she cannot go to the same city twice. The number of possible schedules is equal to the product of the number of choices for each day, i.e.,3 × 2 × 1 = 6

Laura wants to visit a few European cities in her upcoming vacations but can only manage three in a week, one city per day. She wants to plan her schedule to maximize her enjoyment, and she is wondering how many different schedules are possible.

As she wants to visit one city per day, she has to choose one of the cities she wants to visit from Monday to Wednesday. There are three different choices available for Monday, two for Tuesday, and one for Wednesday.

Therefore, the number of possible schedules is equal to the product of the number of choices for each day, i.e.,3 × 2 × 1 = 6

So there are six different schedules possible in which Laura can visit each city once. We can also list all possible schedules, assuming that A, B, and C are the three cities: ABCACBBACACBCB

However, since she wants to visit each city once, she cannot go to the same city twice.

Learn more about plan  here:

https://brainly.com/question/30091666

#SPJ11

The dimensions which would be needed to find the volume of the following prism as required are; base of the triangle, height of the triangle and height of the prism.

It follows from the task content that the dimensions needed to find the volume of the given prism is to be determined.

On this note, since the given prism is a triangular prism. Its volume is a function of the triangular base area and the height of the prism.

Consequently, since the base area of the triangle depends on the base and height of.the triangle;

The required dimensions to calculate the volume of the prism are; base of the triangle, height of the triangle and height of the prism.

Read more on volume of a triangular prism;

https://brainly.com/question/29663752

#SPJ1

Answer:

-11

Step-by-step explanation:

Insert the value of b:   |(-4 * -2) - 8| + |-1 - (-2)²| + 2(-2)³

Simplify & solve:          |8 - 8| + |-1 - 4| + 2 * -8

                                     |0| + |-5| + -16

                                     0 + 5 - 16

                                     -11

Answer:

$42.00

Step-by-step explanation:

So, something hasn't been subtracted from your bottom line. The bank is saying you only have $26.33. You think you have $68.33.

Let's look for the difference. This is one of those great times when the word in english and the word in math have the same meaning. Difference is telling us to subtract.

68.33 - 26.33

= 42.00

Check:

If you subtract the missing entry, $42.00 from your total,

68.33 - 42.00

you get $26.33, exactly the balance the bank says you have. Now your account is balanced!

Partial fraction decomposition is a method used to decompose a rational function into simpler fractions known as partial fractions.

In this problem, we are to solve for the partial fraction decomposition of the rational functions 5x + 1/[(x - 1)²(x² + 6)] and 1/[(x² - 1)(x² + 2)].

To solve for the partial fraction decomposition of 5x + 1/[(x - 1)²(x² + 6)],

we start by writing it in the form shown below.(5x + 1)/[(x - 1)²(x² + 6)] = A/(x - 1) + B/(x - 1)² + Cx + D/(x² + 6)

We then equate the coefficients of the numerator of the given rational function to that of the partial fractions. This gives us the equation:

5x + 1 = A(x - 1)(x² + 6) + B(x² + 6) + Cx(x - 1)² + D(x - 1)²

We solve for A, B, C, and D by substituting appropriate values of x and equating the coefficients of like powers of x in the above equation. We obtain A = 0, B = 5/7, C = 5/6, and D = 1/6.

The partial fraction decomposition of 5x + 1/[(x - 1)²(x² + 6)] is thus given by:(5x + 1)/[(x - 1)²(x² + 6)] = 0/(x - 1) + 5/7(x - 1)² + 5/6x + 1/6(x² + 6)

To solve for the partial fraction decomposition of 1/[(x² - 1)(x² + 2)], we start by writing it in the form shown below.

1/[(x² - 1)(x² + 2)] = A/(x - 1) + B/(x + 1) + C/(x² + 2) + D/(x² - 1)

We then equate the coefficients of the numerator of the given rational function to that of the partial fractions. This gives us the equation:

1 = A(x + 1)(x² + 2) + B(x - 1)(x² + 2) + C(x - 1)(x + 1) + D(x + 1)(x - 1)

We solve for A, B, C, and D by substituting appropriate values of x and equating the coefficients of like powers of x in the above equation.

We obtain A = 1/4, B = -1/4, C = -1/2, and D = 1/4.

The partial fraction decomposition of 1/[(x² - 1)(x² + 2)] is thus given by:1/[(x² - 1)(x² + 2)] = 1/4(x - 1) - 1/4(x + 1) - 1/2(x² + 2) + 1/4(x² - 1)

Partial fraction decomposition is a useful method in evaluating integrals and solving differential equations. In partial fraction decomposition, we break down a rational function into simpler fractions known as partial fractions. These fractions have a denominator that can be written in a factorized form and their numerator can be either a constant or a polynomial whose degree is less than that of the denominator. To solve for the constants in partial fraction decomposition, we equate the coefficients of like powers of x in the numerator of the given rational function and the resulting partial fractions. We then obtain a system of linear equations that can be solved to obtain the values of the constants.

To know more about Partial fraction visit:

brainly.com/question/30763571

#SPJ11

The first trigonometric function in terms of the second for θ in the given quadrant. csc(θ),cot(θ);θ in Quadrant II is cot(θ).

Given, Quadrant IIIn Quadrant II, the values of sin(θ) and cos(θ) are positive while tan(θ) and cot(θ) are negative.csc(θ) = 1/sin(θ)This implies that csc(θ) is positive in Quadrant II as sin(θ) is positive.

Therefore, csc(θ) is positive in Quadrant II. Now, we need to find the cot(θ) function in terms of csc(θ).cot(θ) = cos(θ)/sin(θ).

Multiplying the numerator and denominator of the above fraction with csc(θ), we have:

cot(θ) = (cos(θ) × csc(θ)) / (sin(θ) × csc(θ))

cos(θ) / sin(θ) × 1/csc(θ)= cos(θ) × csc(θ) / sin(θ) × csc(θ)

csc(θ) × cos(θ) / sin(θ),

Now, cos(θ) / sin(θ) = - tan(θ).

Therefore, we can say:cot(θ) = csc(θ) × (- tan(θ)).

Therefore, the  answer to the given question is the first trigonometric function in terms of the second for θ in the given quadrant. csc(θ),cot(θ);θ in Quadrant II is cot(θ).

We can say that cot(θ) is the first trigonometric function in terms of the second for θ in Quadrant II when csc(θ) and cot(θ) are given.

To understand this, we need to understand the values of different trigonometric functions in Quadrant II. In Quadrant II, the values of sin(θ) and cos(θ) are positive while tan(θ) and cot(θ) are negative.

So, we can say that csc(θ) is positive in Quadrant II as sin(θ) is positive.

To find the cot(θ) function in terms of csc(θ), we use the formula cot(θ) = cos(θ)/sin(θ). We then multiply the numerator and denominator of the above fraction with csc(θ) to get the value of cot(θ) in terms of csc(θ).

We simplify the obtained expression and use the value of cos(θ)/sin(θ) = - tan(θ) to get cot(θ) in terms of csc(θ) and tan(θ).

Therefore, the first trigonometric function in terms of the second for θ in Quadrant II when csc(θ) and cot(θ) are given is cot(θ).

The first trigonometric function in terms of the second for θ in Quadrant II when csc(θ) and cot(θ) are given is cot(θ).

To know more about trigonometric function visit:

brainly.com/question/25618616

#SPJ11

The areas that needs correction has been attended to and they include the following:

4.)533.8 meters

5.)22686.5 m²

8.)19.06 m

To determine the radius of a circle, the diameter should be divided into two.

For the wheel, the radius is calculated as follows;

Diameter = 150/2

= 85 meters.

For 4.)

The circumference of the wheel with the given radius;

Formula = 2πr

= 2×3.14×85

= 533.8 meters

For 5.)

Area of the wheel = πr²

= 3.14×85×85 = 22686.5 m²

For 8.) The arc length between the two cars;

= circumference/number of compartment

= 533.8/28

= 19.06 m

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

Answer:

-8 -8

Step-by-step explanation:

Because it is the most reasonable

True The six sigma DMAIC approach is a problem solving methodology that involves Define, measurement , Analyze, Improve, and Control steps.

The six sigma DMAIC approach is a problem solving methodology that follows a defined sequence of steps to ensure that all potential causes of a problem are identified and addressed. It is a powerful tool for businesses to use when trying to improve their processes, products, and services. The DMAIC approach stands for Define, Measure, Analyze, Improve, and Control. The Define step involves understanding the problem and setting the goal. The Measure step involves gathering data and metrics on the process. The Analyze step involves analyzing the data to identify potential root causes. The Improve step involves developing and implementing solutions. The Control step involves monitoring the process to ensure that the solutions are effective. This approach is very effective and should be used whenever possible to ensure that all issues are addressed and the best possible solution is achieved.

Learn more about measurement here

https://brainly.com/question/4725561

#SPJ4

Answer: 72 options

Step-by-step explanation: please I need brainliest for next rank

Answer: The answer is the last one

Step-by-step explanation:

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

Which makes b5 j2 j4.

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

Which gets you to b5 x j6.

So the last one is the answer

Answer:

\(b^5 * j^6\)

Step-by-step explanation:

Well we can use the exponential identity: \(x^a*x^b=x^{a+b}\)

The base must be the same for this to work.

So let's combine like bases: \((b^2*b^3)*(j^2*j^4)\)

We can simplify b^2 * b^3 using this identity to get: b^(2+3) = b^5

This gives us the equation: \(b^5*(j^2*j^4)\)

But to take a deeper look as to why this identity holds, let's represent b^2 and b^3 by what it really means: \((b * b) * (b * b * b)\), so this is really just: \(b * b * b * b * b\) which can be simplified as an exponent: \(b^5\), hopefully this helps you understand intuitively why this identity makes sense.

So using this identity, we can simplify j^2 * j^4 to j^6

This gives us the equation: \(b^5 * j^6\)

Answer:

14

Step-by-step explanation:

2.5(r - 4) + 5 = 30

multiply out left side:

2.5r - 10 + 5 = 30

add 5 from both sides:

2.5r - 10 + 5 + 5 = 30 + 5

2.5r = 35

divide bot sides by 2.5:

2.5r/2.5 = 35/2.5

r = 14

Answer:

9c4

factoring the monomial

(3c2)(-3c2)

Answer:

B

Step-by-step explanation:

Values of y are decreasing where x is in the range (-4;02)

Answer:

Write the dividend under the bar and the divisor to the left. Each is written in descending order of powers of

x

. If any power of

x

is missing, then include it with a

0

coefficient. For example, if you were dividing by

x

2

−

1

, then you would express the divisor as

x

2

+

0

x

−

1

.

Choose the first term of the quotient to cause leading terms to match. In our example, we choose

x

2

, since

(

x

−

1

)

⋅

x

2

=

x

3

−

x

2

matches the leading

x

3

term of the dividend.

Write the product of this term and the divisor below the dividend and subtract to give a remainder (

2

x

2

).

Bring down the next term (

−

x

) from the divisor alongside it.

Choose the next term (

2

x

) of the quotient to match the leading term of this remainder, etc.

Stop when there is nothing more to bring down from the dividend and the running remainder has lower degree than the divisor.

In our example, the division is exact. We are left with no remainder.

Step-by-step explanation:

i did the test

185 said they like dogs, 170 said they like cats, 86 said they liked both cats and dogs, and 74 said they don't like cats or dogs. The number of people who were surveyed is 515.

The number of people who were surveyed can be found by adding the number of people who liked dogs, the number of people who liked cats, the number of people who liked both, and the number of people who did not like either. So, the total number of people surveyed can be found as follows:

Total number of people who like dogs = 185

Total number of people who like cats = 170

Total number of people who like both = 86

Total number of people who do not like cats or dogs = 74

The total number of people surveyed = Number of people who like dogs + Number of people who like cats + Number of people who like both + Number of people who do not like cats or dogs

= 185 + 170 + 86 + 74= 515

You can learn more about the survey at: brainly.com/question/31624121

#SPJ11

The complex numbers will be 3-i and I and the coordinates will be (-1,-3) or C point on the coordinate plane.

Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.

Here,

A=(1,3)

B=(-3,1)

C=(-1,-3)

D=(3,-1)

=(3-i)/i

=-1-3i

The coordinates will be (-1,-3) that is C point on the coordinate plane and the complex numbers be 3-i and i.

To know more about coordinate plane,

https://brainly.com/question/19498351

#SPJ4

Answer:

Step-by-step explanation:

opposite angles are congruent

Answer:

140

Step-by-step explanation:

200-60 = 140

Answer:

c

Step-by-step explanation:

Substitute the values in the problem to get, (200) = 2(60) + 2W. Solve for W to get 200 = 120 + 2W. Subtract 120 on both sides to get 80 = 2W. Divide by 2 on both sides to get 40 = W or a width of 40 feet.

hope that helped you.

Yes, there are conditions in which it can be acceptable to allow skewed variables into a research study. Skewed variables are variables that do not follow a symmetrical distribution and have a longer tail on one side.

In research, it is important to consider the appropriateness of including skewed variables based on the specific research question, study design, and analysis techniques. Here are a few conditions under which it might be acceptable:

1. Natural occurrence: If the variable being studied naturally exhibits a skewed distribution in the population, it may be necessary and acceptable to include it. For example, income data often exhibit right-skewness due to a few high-income outliers, but studying income inequality or socioeconomic disparities would require considering this variable.

2. Theoretical justification: If there is a strong theoretical rationale or prior research suggesting that the variable is expected to be skewed, it can be included in the study. This is particularly relevant when studying phenomena that inherently have asymmetric distributions, such as reaction times, human behavior, or certain psychological constructs.

3. Robust analysis techniques: If appropriate statistical techniques exist to handle skewed variables, it may be acceptable to include them. For instance, non-parametric tests or transformations (e.g., logarithmic or square root transformations) can be used to address skewness and still obtain meaningful results.

4. Subgroup analysis: If the skewness is driven by a particular subgroup within the data, researchers might consider conducting subgroup analysis or stratifying the data based on the skewed variable. This approach allows for exploring potential effects or relationships within specific subgroups while accounting for the skewness.

5. Sensitivity analysis: Researchers can also perform sensitivity analyses to assess the robustness of their findings to the inclusion or exclusion of skewed variables. This helps evaluate whether the results are sensitive to the specific distributional characteristics of the variable.

In summary, allowing skewed variables in a research study can be acceptable under certain conditions, such as when the variable naturally exhibits skewness, is theoretically justified, appropriate analysis techniques exist, or subgroup analysis is conducted. It is crucial to carefully consider the research question, study design, and analysis plan to ensure that the inclusion of skewed variables does not compromise the validity and interpretability of the findings.

To know more about skewed variables refer here:

https://brainly.com/question/28330505

#SPJ11

The expression that is equivalent to the given expression, 4t - 12 + 3 - 5t, is -t - 9 or -(t + 9)

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is

4t - 12 + 3 - 5t

To determine the expression that is equivalent to the given expression, we will simplify the expression.

Simplifying the expression

4t - 12 + 3 - 5t

Simplify the middle terms

4t - 9 -5t

Collect like terms

4t - 5t - 9

-t - 9

-(t + 9)

Hence, the expression is -t - 9 or -(t + 9)

Learn more on Determining equivalent expressions here: https://brainly.com/question/28058543

#SPJ1

The iterated integral in polar coordinates will be:

∬R fdA = ∫c^d ∫a^b f(r,θ) r dr dθ.

Since the problem does not provide a specific description or image of the region R, I am unable to determine the values of a, b, c, and d. However, I can explain the general process of setting up an iterated integral in polar coordinates.

In polar coordinates, the differential area element is given by dA = r dr dθ, where r represents the radial distance and θ represents the angle.

To write the double integral in polar coordinates, you need to determine the limits of integration for r and θ.

The integral limits for r will depend on the boundaries of the region R in the radial direction. These limits can be expressed as a ≤ r ≤ b.

The integral limits for θ will depend on the boundaries of the region R in the angular direction. These limits can be expressed as c ≤ θ ≤ d.

Please provide a more specific description or image of the region R in order to determine the values of a, b, c, and d, as well as the differential element dA.

Know more about iterated integral here:

https://brainly.com/question/27396591

#SPJ11

For the region R below, write ∬R​fdA as an iterated integral in polar coordinates. With a= ___ , b=___, c=______ and d= ______. ∬R​fdA=∫ab​∫cd​fdA, where dA= ____ d___ d____

The surface area of the cone is 305.30 inches squared.

The height of the cone is 7 inches and the diameter of the cone is 8 inches. Therefore, let's find the surface area of the cone as follows:

surface area of the cone = πr(r + l)

where

Hence,

r = 8 / 2 = 4 inches

l² = 7² + 4²

l = √49 + 16

l = √65

l = 8.0622577483

l = 8.06 inches

Therefore,

surface area of the cone = 3.14 × 8.06(4 + 8.06)

surface area of the cone = 25.3154893297(12.06)

surface area of the cone = 305.304801316

surface area of the cone = 305.30 inches squared

learn more on cone here: https://brainly.com/question/12175769

#SPJ1

Find the circumference of the circle:

Circumference = 2 x r x pi

Circumference = 2 x 200 x 3.14

Circumference = 1,256 feet.

4 inches/ 12 inches per foot = 0.333 ft.

Divide the circumference by the spacing:

1255/0.333 = 3,768

You will need 3,768 flowers

Hello

Answer:

-9j+5

Step-by-step explanation:

=-4j-1-5j+6

=-4j-5j+6-1

=-9j+5

Answer:

A, B, C, D

Step-by-step explanation:

Quadrilaterals are shapes that have a total of four sides. Rectangles, parallelograms, squares, and rhombuses all have a total of four sides. Therefore, they are quadrilaterals.

Rectangle, Parallelogram, Square and Rhombus are Quadrilaterals.

We know,

A quadrilateral is a polygon with four sides. It is a geometric shape that is characterized by having four straight sides and four vertices. The interior angles of a quadrilateral add up to 360 degrees.

As, Rectangle have four sides then it is a quadrilateral.

As, Parallelogram have four sides then it is a quadrilateral.

As, Square have four sides then it is a quadrilateral.

As, Rhombus have four sides then it is a quadrilateral.

Learn more about Quadrilaterals here:

https://brainly.com/question/29934291

#SPJ6