The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−5
Find a possible formula for P(x).
P(x)=

If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

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Answer: 60 meters

Step-by-step explanation:

if the car travels 20 meters in 15 seconds

you want to take 45 and divide it by 15, giving you 3

now you want to multiply 20x3

which will get you 60 meters

Answer: 60 meters

Step-by-step explanation: you can divide 20 by 15 to get 3/4 and 3/4 times 45 is 60

oof sorry if its wrong or the explanation is too lazy

The equation of the line that passes through (2, −6) and is perpendicular to y = 2/3x + 4 is y = -3/2x - 3.

The equation of a line in point slope form is expressed as;

y - y₁ = -1/m(x-x₁)

Given the equation of a line y = 2/3x + 4, the slope is 2/3.

Substitute the slope and the point into the equation to have:

m = 2/3

(x₁, y₁) = (2, -6)

Substitute

y-(-6) = -3/2(x-2)

y+6 = -3/2(x-2)

2(y+6) = -3(x-2)

2y + 12 = -3x + 6

2y = -3x  + 6 - 12

2y = -3x - 6

y = -3/2x - 3

This gives the required equation of the line.

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Answer:

no

Step-by-step explanation:

it does not have any (0,0) value

Answer:

Step-by-step explanation:

hello friend !!!!!!!!!

There are infinite no. of rational no's between any two rational no's

hope this helps

plz mark as brainliest!!!!!!!

Answer:

volume = 3x6x2 = 36 cubic inches

Step-by-step explanation:

Answer:

That's easy, just take base times width times Hight. or in this case 6x2x3=

do this on a calculator. :)

Step-by-step explanation:

And anytime you are doing volume, it will always be cubed.

Line QT has a 5 unit length.

A line is a geometric object with an endless length and no breadth, depth, or curvature.

Lines are one-dimensional objects since they can exist in two, three, or higher-dimensional regions.

A line segment with two points indicating its endpoints is also referred to as a line in daily speech.

So, using the relationship between the sides of comparable triangles, we have the following.  ΔRST and  ΔRPQ:

   ST/RT = PQ/QR

   RQ = QT + RT

Then,

   ST/RT = PQ/QT + RT

Then, we obtain:

   QT + 5/RT = PQ/QT + RT

Given that QT is the natural number then, QT = 5 units.

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The rate function f(t) representing the per hour charge applied to your credit card at time t is $24.

To represent the per hour charge applied to your credit card at time t, we can define the rate function, f(t), as follows:

f(t) = 8 dollars/hour/computer

Since you are planning to use three computers (including yours and your two friends'), the rate function will be multiplied by 3:

f(t) = 3 * 8 dollars/hour/computer

f(t) = 24 dollars/hour/

Therefore, the rate function f(t) representing the per hour charge applied to your credit card at time t is $24.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

Step-by-step explanation:

No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

J = 2G + 5.96/2 will give you the distance Joe ran last week.

Three friends were training to run a race. Joe ran 8.5 miles. If Gavin ran 2.98 miles less than Joe, then;

G = J - 2.98 ...... 1

If Nate ran twice as far as Joe, then Nate distance will be:

N = 2J ....... 2

From equation 1

J = G + 2.98 .........  3

Substitute equation 3 into 2 to have;

N = 2(G + 2.98)

N = 2G + 5.96

J = N/2
J = 2G + 5.96/2

Hence the equation to find the distance that Joe ran last week is J = 2G + 5.96/2

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Answer:

  7000 boxes

Step-by-step explanation:

The number of boxes can be found by dividing the total quantity by the quantity in each box.

  (35000 kg)/(5 kg/box) = 7000 boxes

The farm can fill 7000 boxes with their produce of mangoes.

Using the concept of ratios, the constant of proportion between middle school and high school is 3/4

Proportionality is a fundamental concept in mathematics and physics. It is a relationship between two or more variables where a change in one causes a proportional change in the other. In other words, the ratio between the two remains constant. Proportionality is an important concept in mathematics because it is used to make predictions and solve problems. The constant of proportionality is the ratio between the two variables that remain constant in a proportional relationship.

To determine the constant of proportionality in this relationship, we can write an equation in the form

y = kx

Or we can easily use ratio to find the constant of proportion

Number of girls in middle school = 6

Number of girls in high school = 8

The ratio = 6/8 = 3 / 4 = Option B

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there are still 10 fish.

if the point M is at the midpoint of AB, then the length of AM is 21 units

The side lengths are given as:

AM = 3x + 3

AB = 8x - 6

From the question, we understand that:

The point M is at the midpoint of AB

This means that:

AB = 2 * AM

Substitute the known values in the above equation

8x - 6= 2 * (3x + 3)

Evaluate the product

8x - 6 = 6x + 6

Evaluate the like terms

2x = 12

Divide by 2

x = 6

Substitute x = 6 in AM = 3x + 3

AM = 3 * 6 + 3

Evaluate

AM = 21

Hence, the length of AM is 21 units

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Complete question

Point m is the midpoint of ab . am=3x+3, and ab=8x−6. what is the length of am ?

(a) The volume of the prism is 144 cubic units. (b) Area of shaded base is 16 square units. Volume of prism is 144 cubic units. Both methods give the same result for the volume of the prism.

A rectangular prism is a three-dimensional geometric figure that consists of six rectangular faces that meet at right angles. It is also known as a rectangular cuboid or a rectangular parallelepiped. The rectangular prism is a special case of a parallelepiped, where all six faces are rectangles.

The rectangular prism has three pairs of parallel faces, each pair being congruent to each other. The length, width, and height of a rectangular prism are its three dimensions, and they are usually denoted as l, w, and h respectively.

(a) The expression to find the volume of the prism is:

Volume of prism = length x width x height

Substituting the given values, we get:

Volume of prism = 8 x 2 x 9 = 144 cubic units

(b) The shaded base of the prism is a rectangle with dimensions 8 by 2. Therefore, the area of the shaded base is:

Area of shaded base = length x width = 8 x 2 = 16 square units

We can also find the volume of the prism by multiplying the area of the shaded base by the height of the prism. The expression to find the volume of the prism using the area of the shaded base is:

Volume of prism = area of shaded base x height

Substituting the values, we get:

Volume of prism = 16 x 9 = 144 cubic units

As expected, both methods give the same result for the volume of the prism.

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A symmetrical distribution of exam scores in a college course indicates that the student's scores are evenly distributed across the entire range of scores. This suggests that about an equal number of students had relatively high and relatively low scores.

Correct answer will be b) About an equal number of students had relatively high and relatively low scores.

And that there is no single group that overwhelmingly outperformed or underperformed the others. Furthermore, it indicates that there were a substantial number of students who achieved high scores, as well as a substantial number who achieved low scores.

This type of even distribution of scores is often seen when students are equally prepared, and when the exam is designed to be neither too difficult nor too simple.

In conclusion, a symmetrical distribution of exam scores suggests that the students were similarly prepared and that the exam was appropriately challenging.

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To evaluate the line integral ∮C (2x - y^4)dx + (5y + 3x - 6)dy, where C is the boundary of a triangle with vertices, we can use Green's theorem.

Green's theorem states that for a vector field F = (P, Q) and a simple, positively oriented, piecewise-smooth curve C, the line integral ∮C Pdx + Qdy is equal to the double integral over the region D enclosed by C of (dQ/dx - dP/dy) dA.

Let's calculate the double integral first. The region D is the triangle enclosed by the vertices (0, 0), (2, 0), and (0, 3).

To apply Green's theorem, we need to compute the partial derivatives of the vector field components P and Q with respect to x and y, respectively:

∂P/∂x = 2

∂Q/∂y = 5

Now, let's calculate the double integral using the Green's theorem formula:

∬D (dQ/dx - dP/dy) dA = ∬D (5 - 2) dA = ∬D 3 dA

The integral of a constant over a region is simply the constant multiplied by the area of the region. The region D is a triangle with base 2 and height 3, so its area is (1/2) * base * height = (1/2) * 2 * 3 = 3.

Therefore, the double integral becomes:

∬D 3 dA = 3 * 3 = 9

Hence, the line integral ∮C (2x - y^4)dx + (5y + 3x - 6)dy, where C is the boundary of the triangle with vertices (0, 0), (2, 0), and (0, 3), is equal to 9.

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Step-by-step explanation:

complement means together they have 90°.

supplement means together they have 180°.

180 - x = 5(90 - x) = 450 - 5x

4x = 270

x = 270/4 = 67.5°

After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.

To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.

Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.

The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.

To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.

Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.

To find the value of s, we take the square root of both sides. So, s = √(7√3).

Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

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The production function is used to examine the relationship between inputs and outputs.

The production function is a fundamental concept in economics that represents the relationship between inputs and outputs in the production process. It helps us understand how much output can be produced with a given set of inputs.

In the production process, inputs such as labor, capital, raw materials, and technology are combined to produce goods or services. The production function captures the quantitative relationship between these inputs and the resulting output. It provides a framework to analyze how changes in input levels affect the output level.

The production function typically takes the form of a mathematical equation or a graphical representation. It shows how the quantity of output depends on the quantities of various inputs used in the production process.

By studying the production function, economists can analyze factors such as efficiency, productivity, and technological progress. It helps firms make decisions regarding the optimal combination of inputs to maximize output or minimize costs. Additionally, it allows policymakers to assess the impact of policies on production and economic growth.

Therefore, the production function primarily focuses on examining the relationship between inputs and outputs, rather than supply and demand, producers and consumers, or price and cost.

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Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.

Each element of a non-empty set A has a function connecting it to at least one element of a second non-empty set B. A function f between two sets, A and B, is said to have a "domain" and a "co-domain" in mathematics. For any value of an or b, F = (a,b)| holds true.

Which piece will the function include?

Given that,  

f(x) = [ x + 3] which is an absolute value function.

Therefore,

| x+3 | > 0

By removing the modulus,

x+3 > 0

x > - 3

Hence x + 3, x > -3 is the piece which will be included in the given function:

f(x) = [ x + 3].

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Таким образом, (X-2)(3x-1) = 0 можно переписать в виде двух уравнений:

X-2=0 или 3x-1=0

Решение для

X=2

Solving for x in the second equation, we get:

3x=1

x=1/3

Therefore, the possible values of X are X=2 and x=1/3.

Mean household income and median household income are two different measures of the income distribution in a population.

Mean household income is calculated by adding all of the earnings in a population and then dividing the total by the number of households. Very high or low salaries can distort the average in any direction, influencing this statistic.

In contrast, median household income is the income level that divides the top half of households from the bottom half. When all household earnings are organised from lowest to highest, it is the middle value. The median is less vulnerable to outliers or extreme numbers, making it a more robust estimate of income distribution central tendency.

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If the employee's initial salary is $52,800.00, the employee's salary be after 7 years 64937.13

Future value is the value of an asset or cash at a specified date in the future, based on the expected growth rate of the investment. The future value amount is the amount of money that an investment or asset is expected to be worth at a future date, assuming that the investment earns a specified rate of return or interest over time.

we would solve this by

52,800 * (1 + 3%)^7

= 52,800 x 1.03^7

=  52,800 x 1.22987

= 64937.13

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Thus, there are two ways to get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction.

To get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction, we can break down the problem into smaller steps.

First, we need to get from (0,0) to (1,1). This can only be done with one step, either going right or up.

Then, we need to get from (1,1) to (7,4). We can do this by taking six steps to the right and three steps up. However, we need to make sure that we always pass through (1,1).

One way to ensure this is to take three steps to the right, then one step up to (2,2), and then three more steps to the right and two steps up to (7,4).

Therefore, there are two ways to get from (0,0) to (7,4) passing point through (1,1) and only taking steps in a positive direction:

1. One step to the right and then three steps to the right, one step up, three more steps to the right, and two steps up.
2. One step up and then two steps to the right, three steps to the right and one step up to (2,2), and then three more steps to the right and two steps up to (7,4).

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First, let's graph the complex number:

The trigonometric form will be given by:

The angle θ here is 225° (5π/4), the r-value will be

Now we have the trigonometric representation:

Therefore the correct answer is the letter D.