The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).

Answer:because angles in a triangle add up to 180 degrees.

Step-by-step explanation:

A=40

C=30

So 180-40-30=110

Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

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The area of the attached figure is 32 square mm

The similar question is added as an attachment

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

A square a triangle and a parallelogram

The shapes can be combined to

a triangle and a parallelogram

So, we have

Area = Sum of individual areas

Using the dimensions of the shapes as a guide, we have the following:

Area = 0.5 * 2 * 8 + 4 * 6

This gives

Area = 32

Hence, the area is 32 square mm

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Answer:

Step-by-step explanation:

213232131123123123123123

1. To find the class width, we first need to find the range of the data, which is the difference between the maximum and minimum values: 68 - 10 = 58. Then, we divide the range by the number of classes to get the class width: 58 / 7 = 8.29. However, we will round up to the nearest whole number, so the class width is 9.

2. The lower class limits are 10, 19, 28, 37, 46, 55, and 64, since we add the class width to the lower limit of each previous class to find the lower limit of the next class.

3. The upper class limits are 18, 27, 36, 45, 54, 63, and 68, since we add the class width to the lower limit of each class to find the upper limit of that class.

The supportive statement is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

We know a trapezoid is isosceles if the two nonparallel sides are equal.

Therefore, In KWRT, [tex]\overline{WK}[/tex] ≅ [tex]\overline{TR}[/tex] and [tex]\overline{KR} || \overline{TW}[/tex].

The missing statement to support all other statements would be,

m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Box plot, because the median can easily be determined from the large set of data.

What exactly is a median?

The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.

Now,

As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.

and it can handle a large set of data.

Hence,

            Box plot, because the median can easily be determined from the large set of data.

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Answer:box plots

Step-by-step explanation:

i did it

The number of positive integers that satisfy the conditions is 4

The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,

To satisfy positive integers that will have sum of four with a 1, a 2 or a 3

The integers are

13

31

112

211

therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3

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The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.

39 students uses bus for transportation.

12 students uses bike for transportation.

25 students walk for transportation.

24 students uses car for transportation.

Total number of students = 39 + 12 + 25 + 24 = 100

Total sector angle of a circle = 360°

Sector angle for bus = (39 / 100) × 360 = 140.4°

Sector angle for bike = (12 / 100) × 360 = 43.2°

Sector angle for walk = (25 / 100) × 360 = 90°

Sector angle for car = (24 / 100) × 360 = 86.4°

Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

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Answer:

15

Step-by-step explanation:

9/21 aproximatly = 0.42 then x35 = 15

Answer: 0.32 or 32%

Step-by-step explanation: 8/25

Answer:

Step-by-step explanation:

The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).

Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.

Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.

Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.

Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.

Answer:

76°

Just know that angles on the parallel sides always add up to 180°

1/(x+1)(x-2) is the simplified form of the expression

Given the expression below

x+2/4x²+5x+1 · 4x+1/x²-4

Factorise the quadratic expressions

4x²+5x+1 = 4x²+4x + x+1

4x²+5x+1 = 4x(x+1)+1(x+1)

4x²+5x+1 = (4x+1)(x+1)

For the expression x²-4

x²-4 = (x+2)(x-2)

Substitute

x+2/4x²+5x+1 · 4x+1/x²-4 = x+2/(4x+1)(x+1) · 4x+1/(x+2)(x-2)

x+2/4x²+5x+1 · 4x+1/x²-4 = 1/x+1 · 1/x-2

x+2/4x²+5x+1 · 4x+1/x²-4  = 1/(x+1)(x-2)

Hence the simplified form of the expression is 1/(x+1)(x-2)

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Answer:

Step-by-step explanation:

Given the information that the polynomial function 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, we can use this information to find a possible formula for P(x).

A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x - root) is a factor of the polynomial function n times.

So, based on the given information, we know that P(x) must be divisible by the factors (x - 1)^2, (x - 0)^2, and (x + 5), and that the leading coefficient must be 1.

Putting it all together, a possible formula for P(x) is:

P(x) = (x - 1)^2 (x - 0)^2 (x + 5) = (x^2 - 2x + 1)(x^2)(x + 5) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5

So, the possible formula for P(x) is P(x) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5.

Answer:   [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Explanation:

If k is a root of P(x), then x-k is a factor. The multiplicity is the exponent for that factor.

For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}-1)^2[/tex]

The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

However, we change that "8" to a "1" since the leading coefficient is 1 here.

That's how we get to

[tex]P(\text{x}) = 1\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Optionally if you were to expand everything out, combine like terms, and simplify then you'd get

[tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4- 9\text{x}^3+5\text{x}^2[/tex]

I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.

You can use a graphing tool like Desmos or GeoGebra to verify the answer.

The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420

This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:

(12+2w)(16+2w) = 420

Expanding and simplifying, we get:

4w² + 56w - 204 = 0

Dividing by 4, we get:

w² + 14w - 51 = 0

Factoring, we get:

(w+17)(w-3) = 0

Since the width of the path cannot be negative, the only valid solution is w = 3.

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Complete question is in the image attached

Answer:

To solve this problem, we need to use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = future value of the account

P = present value (the contributions)

r = interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

First, we need to find the future value of the account (A) after 10 years of withdrawals at $10,000 per quarter. This means there will be 40 quarters in total ($10,000 * 40 = $400,000).

Next, we need to find the present value of the account (P) after 15 years of contributions.

Let's call the quarterly contributions "x".

We can set up the equation as follows:

$400,000 = x * (1 + 0.08/4)^(4 * 15) - $10,000 * (1 + 0.08/4)^(4 * 10)

We can now solve for x using a financial calculator or by using a programming language to perform the calculation. The result of this calculation is that Mike's quarterly contributions should be $2,597.29 in order to accomplish his goal.

Answer:

151.37

Step-by-step explanation:

Answer:

151.372868 but rounded is 151.37

Step-by-step explanation:

1863.4/12.31=151.372868 rounded is 151.37

The percentage of students who are doing their homework regularly is 75%.

A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.

To find the percentage of students who are doing their homework regularly,

We find the total students and this is 75 + 5 = 80 students

The percentage is 60/80 * 100

= 75%

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Answer:

The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.

Step-by-step explanation:

Given:

[tex]8x+2y=44\\5x+2y=35[/tex]

We can combine the system of equations into a single equation:

[tex]13x+4y=79[/tex]

From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.

We can continue solving the system of equations by writing y in terms of x.

[tex]8x+2y=44\\2y=44-8x\\y=22-4x[/tex]

now substitute this into the single equation:

[tex]13x+4y=79\\13x+4(22-4x)=79\\13x+88-16x=79\\-3x+88=79\\-3x=-9\\x=3[/tex]

Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.

[tex]y=22-4x\\y=22-4(3)\\y=22-12\\y=10[/tex]

The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].

It will take 5.189 hours to get doubled the size of Sample.

A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

Growth rate = 5.8%

The continuous exponential growth model for populations is given by:

P(t)= [tex]P_0 e^{rt[/tex]

So, r= 5.8%

r = 0.058

Now, the time taken to double the sample then P(t) = 2P(0).

So, P(t)= [tex]P_0 e^{0.058t[/tex]

2P(0) = [tex]P_0 e^{0.058t[/tex]

[tex]e^{0.058t[/tex] = 2

Taking log on both side

log [tex]e^{0.058t[/tex] = log 2

0.058 t = 0.301

t= 0.301/ 0.058

t = 5.189

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If the shortest leg of the small triangle is 4 in and the hypotenuse is 12 in and the shortest leg of the large triangle 8 in, then the length of the hypotenuse of the large triangle is 24 inches.

We know that two triangles are proportional if their corresponding sides are in proportion to each other. That is, the ratio of the lengths of the corresponding sides is the same for both triangles.

Let's denote the length of the hypotenuse of the large triangle by "h". We can set up a proportion using the given information:

shortest leg of small triangle / hypotenuse of small triangle = shortest leg of large triangle / hypotenuse of large triangle

Plugging in the values we get:

4/12 = 8/h

Simplifying the equation we get:

h = (12*8)/4 = 24

To explain the solution, we used the fact that similar triangles have proportional sides. We then used the given information about the lengths of the sides of the small and large triangles to set up a proportion and solve for the unknown length of the hypotenuse of the large triangle.

The key to this problem was recognizing the relationship between similar triangles and using that relationship to set up and solve a proportion.

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Answer:

Step-by-step explanation:

The answer is d. f(x) = 3 (x-4) (x+2).

The relationship between precalculus and calculus has been explained and both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity etc.

Precalculus is the study of mathematics or the course that includes algebra, trigonometry etc. to make a student for study the calculus . The precalculus covers the topics likes complex numbers, composite numbers, trigonometric functions, vectors, matrices, probability etc.

Calculus is the study of mathematics that deals with the rate of changes. Applications of the calculus are finding the slope of the curve, finding the area of region, calculation of x intercept and y intercept etc.

Both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity, acceleration, area, volume etc.

Therefore, the relationship between precalculus and calculus has been explained

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The number of weekly downloads can be modeled using an exponential function h(x) = 548 × 1.04ˣ.

What is exponential function?

An exponential function is a mathematical function in which the value of the output is proportional to the value of a fixed number (known as the base) raised to the power of the input value. The general form of an exponential function is:

                                      y = abˣ

where a and b are constants, x is the input value, and y is the output value. The constant a controls the vertical scaling of the function, while the constant b controls the rate of growth or decay. If b is greater than 1, the function grows rapidly as x increases. If 0 < b < 1, the function decays as x increases. If b is equal to 1, the function is a linear function.

Exponential functions are widely used in many fields, including finance, biology, physics, and engineering, to model growth and decay processes.

The number of weekly downloads can be modeled using an exponential function.

                             h(x) = 548 * 1.04ˣ

where x is the number of weeks after the release date, h(x) is the estimated number of weekly downloads, and 1.04 is the growth factor (1 + the expected weekly increase of 4%).

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The two provided payments of $17,000 and $3,300 due in 1 year and 2 years, respectively, would be replaced by two equal payments of $2,287.87 made in 6 months and 5 years.

To solve this problem, we need to find two equal payments that would replace the two given payments, given the time and interest rate. We can use the present value formula to calculate these payments:

PV = C / (1 + r)^n

Where

PV is the present value,  

C is the future value of the payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the first payment of $17,000 due in 1 year, its present value in 6 months can be calculated as:

PV1 = 17,000 / (1 + 0.08/4)^(2*2) = $14,785.28

For the second payment of $3,300 due in 2 years, its present value in 5 years can be calculated as:

PV2 = 3,300 / (1 + 0.08/4)^(4*2) = $2,424.67

To find the equal payments that would replace these two payments, we can use the annuity formula:

PMT = PV / [(1 - (1 + r)^(-n)) / r]

Where

PMT is the equal payment,

PV is the present value,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the two payments to be made in 6 months and 5 years, respectively, the total number of compounding periods is

4*2.5 = 10.

The equal payment can be calculated as follows:

PMT = (PV1 + PV2) / [(1 - (1 + 0.08/4)^(-10)) / (0.08/4)] = $2,287.87

Therefore, two equal payments of $2,287.87 made in 6 months and 5 years would replace the two given payments of $17,000 and $3,300 due in 1 year and 2 years, respectively.

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Answer:

Step-by-step explanation:

The floor-to-ceiling clearance is 7 ft 5 in, which is equal to 7 * 12 + 5 = 89 inches.

We need to construct 8 shelves, each of which is 1 inch thick, so the total thickness of the shelves is 8 * 1 = 8 inches.

We also need to leave an equal space between each shelf and the next, the top shelf and the ceiling, and the bottom shelf and the floor. So, there will be 7 equal spaces in total (6 between shelves and 1 between the bottom shelf and the floor).

Therefore, the space between each shelf and the next will be (89 - 8) / 7 = 11 inches.

Here's a step by step solution:

Calculate the total height of the room in inches: 7 ft 5 in = 7 * 12 + 5 = 89 inches.

Calculate the total thickness of all the shelves: 8 shelves * 1 inch/shelf = 8 inches.

Deduct the thickness of the shelves from the height of the room to find the total space available: 89 inches - 8 inches = 81 inches.

Divide the total space available by the number of spaces (7) to find the space between each shelf and the next: 81 inches / 7 = 11 inches.

Horizontal lines have a slope of zero, since the "rise" is; zero.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.

If the slope has a value of zero, the line is horizontal, neither increases nor decreases.

Therefore,

Horizontal lines always have an equation of the form; y = a

Vertical lines always have an equation of the form; x = b

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Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.

Step-by-step explanation:

To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.

Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:

FV = $40,000 * (1 + 0.04)^12 = $47,564

So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n - 1 / r), where A is the annual payment and r is the interest rate.

Plugging in the values, we get:

FV = $3,000 * (1 + 0.05)^12 - 1 / 0.05 = $41,592

So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.