write the equation with the least degree and integer coefficients that has the roots listed
3, 2 +-3i

What I think about the problem is that there are no specific rules to tackle it, but with careful analysis I have deduced the answer for the total dots in the 50th hexagon to be 7701 dots.

To find the total number of dots in the 50th hexagon, we can use the formula for finding the number of dots in the nth hexagon, where n is the number of the hexagon. The formula is:

Dots = 3n^2 + 3n + 1

Substituting n = 50, we get:

Dots = 3 * 50^2 + 3 * 50 + 1

= 7550 + 150 + 1

= 7701

So, there are 7701 dots in the 50th hexagon.

To think about the problem, we can observe that each additional hexagon added to the previous one will add 3 dots to the total count. This is because each new hexagon adds 3 sides to the previous hexagon, each side having one dot. And, each new hexagon will also add one additional dot to the center.

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Answer:

{3,4,5,.........,49,50}

Step-by-step explanation:

All these numbers are greater than 2, but less than 51.

By using the shell method to find the volume of the solid generated when R is revolved about the y-axis is V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx

The volume of a solid that is generated by rotating a region about a given axis is called the volume of revolution. One of the methods to find the volume of revolution is the shell method.

Let's consider the region R bounded by the curves y = 11−x, y = 0, x = 3, x = 9 and find its volume when it is revolved about the y-axis.

The first step is to sketch the region R in the xy-plane. The curves y = 11−x and y = 0 intersect at x = 11, y = 0. The region R is a trapezoid with height 11 and bases 3 and 9.

Next, we need to find the expression for the volume of a thin shell of thickness dx, whose axis is along the y-axis.

Let us consider a thin shell at x = x0. The height of the shell at x = x0 is given by 11−x0. The inner and outer radii of the shell are given by y = 11−x0 and y = 11−x0−dx respectively.

The volume of the shell is given by the formula:

=> V = 2π(y2−y1)x0 = 2π(11−x0)x0(11−x0−dx)

We can now integrate this expression over x0 to find the total volume of the solid.

The limits of integration are x0 = 3 and x0 = 9. The volume of the solid is given by:

V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx

Solving this definite integral will give us the volume of the solid.

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By assessing performance on memory and recognition tests, as well as the accuracy of answers to fill-in-the-blank and multiple choice questions, Roediger & Karpicke operationalized the dependent variable.

The dependent variable was operationalized by Roediger & Karpicke by evaluating how well subjects performed on memory and recognition tests. Participants responded to fill-in-the-blank and multiple choice questions to achieve this as well as the accuracy of answers to fill-in-the-blank and multiple choice questions, Roediger & Karpicke operationalized the dependent variable. The results of these tests were then utilized to gauge both the participants' recall recall and the accuracy of their responses. The replies were compared to the answer key and their correctness was scored in order to determine how accurate they were. This made it possible for the researchers to more precisely gauge how their independent factors affected the dependent variable.

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Answer:

To evaluate the function when x = -1, 0, and 4, we need to substitute those values into the equation and solve for y.

1. When x = -1,

y = -2(-1) - 4

y = 2 - 4

y = -2

2. When x = 0,

y = -2(0) - 4

y = -4

3. When x = 4,

y = -2(4) - 4

y = -8 - 4

y = -12

So, the function has the values of -2, -4, and -12 when x = -1, 0, and 4 respectively.

Answer: So the length of one side of the triangular-shaped walking path is 330 feet.

Step-by-step explanation:

The perimeter of the triangular-shaped walking path is 990 feet, and the length of one side is represented by x. We can write an equation to find x using the formula for the perimeter of a triangle:

P = a + b + c

Where P is the perimeter, and a, b, and c are the lengths of the sides of the triangle. Since one of the sides is represented by x, the equation can be written as:

990 = x + x + x

Simplifying the equation, we can find the value of x:

990 = 3x

Dividing both sides by 3, we get:

330 = x

So the length of one side of the triangular-shaped walking path is 330 feet.

At this rate, the amount of sauce and cheese which Paula would use to make 5 pizzas is: B. Paula will use 35 oz of sauce and 20 oz of cheese to make 5 pizzas.

In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following number of sauce:

4 pizzas = 28 sauce

5 pizzas = X sauce

Cross-multiplying, we have:

X sauce = 5/4 × 28

X sauce = 35 sauces.

By applying direct proportion to the given information, we have the following number of sauce:

4 pizzas = 16 cheese

5 pizzas = X cheese

Cross-multiplying, we have:

X cheese = 5/4 × 16

X cheese = 20 cheese.

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Answer: 920?

20 charachters euhfiwudhfiuwefhiuhrieuhwdfiuhriurh

If the 1/12 scale model of the rocket stood 48 inches high. The height of the actual rocket is 576 inches.

A ratio box can be defined as a tool that can be used to set up and solve proportion problems.

In order to use a ratio box to solve this problem, we can set up the following proportion:

Scale model height / Actual rocket height = 1/12

48 inches / actual rocket height = 1/12

To solve for the actual rocket height, we can cross-multiply and divide:

48 inches××12 = actual rocket height

Actual rocket height = 576 inches

Therefore the height of the actual rocket is 576 inches.

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The expected value of buying car insurance is $794.5.

Insurance is a contract between an individual or entity and an insurance company, in which the insurance company agrees to provide financial protection or reimbursement against losses in exchange for payment of premium. It is a form of risk management, mainly used to hedge against the risk of a contingent or uncertain loss.

The expected value of buying car insurance is the sum of the product of the value and the probability of each outcome. To calculate the expected value, we multiply the probability of having an accident by the average coverage paid ($2,500), and add it to the product of the probability of not having an accident multiplied by the insurance cost ($600).

So, expected value = (0.105 * $2,500) + (0.895 * $600) = $267.5 + $527 = $794.5

Therefore, the expected value of buying car insurance is $794.5.

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The total price the store charges to deliver $140 worth of groceries will be $4.20.

It should be noted that the certain grocery store charges a fee of 3% of the total bill to have groceries delivered. A percent is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic.

Therefore, the total price the store charges to deliver $140 worth of groceries will be:

= Percentage charged × Cost

= 3% × $140

= 0.03 × $140

= $4.20

The amount charged is $4.20.

The entire cost for the retailer to deliver $140 worth of goods is $4.20.

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The area of square of a given figure with a side 4w is 16w ^2

What is Area of square ?

Area of square could be defined as the square of its side.

Given ,

From the figure,

There is square with a side 4w and given all sides are equal

so , we have to find the area of square ,

area of square could be = side*side

given side =4w

By substituting the given value,

we get,

= 4w* 4w

= 16 w ^2

So, area of square = 16w^2

Therefore, The area of square of a given figure with a side 4w is 16w ^2

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The inequalities that the represents the graph is;  y < 1 and y  ≥ x

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, when the line is horizontal line is parallel to the x - axis, the equation is y equal to the number that the line crosses.

Now, Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Thus, the horizontal line has the inequality; y = 1 But since the shading is below, then we have; y < 1

Now, the solid line shows that the symbol used is ≤ or ≥.

In this case, the x-values and the corresponding y-values are the same and as such we have; y = x

However, since the shading is above, then we have;

y  ≥ x

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Answer:

  C, D

Step-by-step explanation:

You want to know possible rational roots of x⁴-6x³-19x² +84x+180.

The rational root theorem tells you any rational roots will be fractions of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

Here, the coefficient of x⁴, the leading coefficient, is 1. So any rational roots will be divisors of ±180. Those divisors are (plus or minus) ...

  1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The highlighted values are ones that are answer choices.

__

Additional comment

An estimate of the upper bound of the magnitude of the roots would be ...

  [tex]2\max(\sqrt[4]{180},\sqrt[3]{84},\sqrt{19},6)=12[/tex]

The rational root theorem allows roots larger than this.

The roots of this polynomial are actually {-3, -2, 5, 6}.

The m∠DFE in triangle DEF is 72°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, There is a triangle DEF in which segment EG intersects the side DF at point G.

Angle DEG and angle FEG are congruent and the length of the side DE and side EF is labeled as c.

Now, If m∠DEG = 18° ⇒ m∠FEG = 18° and side EF and DE are equal so their opposite angles will also be equal.

Let, The two opposite equal angles be 'x'.

Therefore,

x + x + (18 + 18) = 180°.

2x + 36 = 180°.

2x = 144°.

x = 72°.

So, The measure of angle DFE is 72°.

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In the trapezoid ABCD , when AB || DC and M, N are the midpoint of AD and BC then the value of AB , DC , and MN is equal to 26, 10, and 18 respectively.

In trapezoid ABCD,

AB || DC

AB = 7x + 5

DC = 4x -2

MN = 5x + 3

Using midpoint segment of two parallel lines in a trapezoid we have,

( AB + DC ) / 2 = MN

Substitute the value of AB, DC, and MN we get,

⇒ ( 7x + 5 + 4x -2 )/ 2 = 5x + 3

⇒11x + 3 = 10x + 6

⇒x = 3

⇒ AB = 7(3) + 5

         = 26

DC = 4(3) -2

      = 10

MN = 5(3) + 3

      = 18

Therefore, the value of AB, DC, and MN in the trapezoid ABCD is equal to 26, 10, and 18 respectively.

The above question is incomplete, the complete question is :

The drawing shows trapezoid ABCD with AB||DC; also, M and N are midpoints of AD and BC, respectively. Given: AB=7x+5, DC=4x−2, and MN=5x+3 find the value of AB, DC, and MN for the calculated value of  x.

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Answer:  0.9

Step-by-step explanation:

The probability is 1 - 0.1

                             = 0.9

If "r" is an odd function, "s" is an even function , then the function "s(x) × s(x)" will be an (a) Even Function .

A function is considered as Even Function if it satisfies : f(x) = f(-x) for all x in its domain, and

A function is considered as Odd Function if it satisfies : f(x) = -f(-x) for all x in its domain.

The product of two even functions is even, because if f(x) and g(x) are both even, then

⇒ (f(x) × g(x)) = (f(-x)) × (g(-x)) = f(-x) × g(-x) = f(x)g(x),

So, f(x)g(x) is also even.

In this case, since the function "s" is an even function, So , "s(x) × s(x)" is also Even .

The given question is incomplete , the complete question is

Assume that "r" is an odd function, "s" is an even function, and both "r" and "s" are defined on the entire real line R. Are the following functions even or odd?

Is "s(x) × s(x)" even or odd ?

(a) even function

(b) odd function

(c) neither

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Answer:

The interest rate for this investment is 15%. This can be calculated by dividing the annual interest of $54 by the initial investment of $360, which gives a result of 0.15 or 15%.

The interest rate is 15%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount invested = $360

Interest amount = $54

Now,

The interest rate.

= 54/360 x 100

=  15%

Thus,

5% is the interest rate.

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The vertex form of the parabola y = 4 · x² - 4 · x + 3 is the equation y - 2 = 4 · (x - 1 / 2)².

In this problem we find the case of the equation of a parabola in standard form, whose vertex form has to be found. These forms are described below:

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

This can be done by completing the square, an application by algebra properties. First, write the equation of a parabola in standard form:

y = 4 · x² - 4 · x + 3

Second, use algebra properties until vertex form is found:

y - 3 = 4 · (x² - x)

y - 3 + 4 · (1 / 4) = 4 · (x² - x + 1 / 4)

y - 2 = 4 · (x - 1 / 2)²

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If Ralph jut received hi june flah card bill. He did not pay hi may bill in full, o hi june bill how a previous balance & a finance charge. Ralph’ finance charge is:  $0.588.

First, calculate the monthly periodic rate (MPR) from the annual percentage rate (APR):

MPR = APR / 12

MPR = 1.5% / 12 = 0.125%

Next, calculate the finance charge by multiplying the average daily balance by the MPR:

Finance charge = Average daily balance * MPR

Finance charge = $470 * 0.125% = $0.588

Therefore  Ralph's finance charge for June should be $0.588.

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No, f is not continuous at x=-3. To show this, let's take the limit from both sides.

From the left side, the limit of f(x) as x approaches -3 is 5. From the right side, the limit of f(x) as x approaches -3 is 3. Since the two limits are not equal (5≠3), then f is not continuous at x=-3.No, f is not continuous at x=-3. This is because the limit of f(x) as x approaches -3 does not equal f(-3). The limit of f(x) can be calculated using the formula lim x->-3 f(x) = lim x->-3 (x^2 + 9). Calculating this limit, we get lim x->-3 f(x) = lim x->-3 (x^2 + 9) = 9. However, f(-3) = (-3)^2 + 9 = 0, which does not match the limit.

Mathematically, this can be shown using the following:

limx→−3 f(x) = 5 ≠ 3 = limx→−3+ f(x)

Since the two limits are not equal, then f is not continuous at x=-3.

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False. A positive correlation occurs when as one variable increases, the other one also increases.

It does not specify the direction of the change. On the other hand, a negative correlation occurs when one variable decreases as the other one increases. In other words, the variables are inversely related. In a positive correlation, the variables move in the same direction, while in a negative correlation, they move in opposite directions. It's important to note that correlation does not imply causation.

A positive correlation is a statistical relationship between two variables, where an increase in one variable is associated with an increase in the other variable, and a decrease in one variable is associated with a decrease in the other.

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On solving the provided question, we can say that the answers of the quadrilateral are as follows 1.True; 2.False and 3.True

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

the answers of the quadrilateral are as follows

1.True

2.False

3.True

4.True

5.False

6.False

7.True

8.True

9.True

10.False

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Answer:20.01%

Step-by-step explanation:Divide the tip left by the cost of the meal and multiply by 100 to get 20.01%

Answer: 20%

Step-by-step explanation:

   We will find what percent 2.60 is of 12.99. First, we will divide. Then, we will multiply it by 100 to make a percent.

      (2.6 / 12.99) * 100 = 20.0153 ≈ 20.02%

   She left a 20.02% tip.

The equivalent expression to 7/8+3/8x-3/4y-1/2 is given as follows:

3x/8 - 3y/4 + 3/8.

Equivalent expressions are expressions that have the same result when they are simplified.

The expression for this problem is defined as follows:

7/8+3/8x-3/4y-1/2.

The expression is simplified combining the like terms.

The like terms are given as follows:

Combining(adding) the like terms, the simplified expression is given as follows:

3x/8 - 3y/4 + 3/8.

As none of the options are this one, I suppose that there was a typing mistake either in the expression or in the options.

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Answer:

The son is 56, and the father is 112.

Step-by-step explanation:

Formula:

1/2x+84=2x

Answer:

father=40

son=20

Step-by-step explanation:

We can start by using the information given to set up a system of equations.

First, we know that the father's age is twice the son's age, so we can write the equation:

father's age = 2 * son's age

Next, we know that half the son's age plus 84 equals twice the father's age, so we can write the equation:

(1/2) * son's age + 84 = 2 * father's age

Now we can substitute the first equation into the second equation to get:

(1/2) * son's age + 84 = 2 * (2 * son's age)

Solving for x

(1/2) * x + 84 = 4x

x=20

father = 2*20 = 40

son = 20

The price p which the first coupon code give him a better deal is less than $99.93. The inequality he can use is the first coupon code will give Samir a better deal.

We can find the value of "p" by solving the inequality.

        (1 - 0.05) * p + 0 < (1 - 0.20) * p + 14.99

This inequality compares the total cost (price minus discount plus shipping) of using the first coupon code on the left-hand side and the total cost of using the second coupon code on the right-hand side. If the left-hand side is less than the right-hand side, then the first coupon code gives a better deal.

Solving for p, Samir can find the minimum price at which the first coupon code is a better deal.

        0.95 * p + 0 < 0.80 * p + 14.99

        0.95 * p < 0.80 * p + 14.99

       0.15 * p < 14.99

        p < 99.93

So, if the price "p" is less than 99.93, the first coupon code will give Samir a better deal.

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The energy of the light is less than the work function of Lithium (2.11 eV < 2.90 eV), the light will not have enough energy to remove electrons from the material.

To find this we have the work function of Lithium is 2.90 eV, which is a measure of the minimum energy required to remove an electron from the surface of the material. The energy of light is proportional to its frequency (E = hf) or its wavelength (E = hc/λ), where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.

Given the wavelength of light as 1850 nm, we can calculate its energy as follows:

E = hc/λ = (6.63 x [tex]10^{-34}[/tex]Js) (3 x [tex]10^8[/tex] m/s) / (1850 x [tex]10^{-9[/tex]m)

= 3.38 x [tex]10^{-19[/tex] J

Since 1 eV = 1.6 x [tex]10^{-19[/tex] J, the energy of the light can be converted to eV as follows:

E (eV) = 3.38 x [tex]10^{-19[/tex] J / (1.6 x [tex]10^{-19[/tex] J/eV) = 2.11 eV

Since the energy of the light is less than the work function of Lithium (2.11 eV < 2.90 eV), the light will not have enough energy to remove electrons from the material.

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