Write a polynomial function in standard form
-6,0,0,2

The numbers of ways that the director fill these positions is  504 ways.

There are a few different ways to approach this problem, but one possible method is to use the combination formula.

To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.

So, the total number of ways the director can fill these positions is:

9 × 8 × 7

= 504 ways.

Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.

For this case n is 9, and r is 3, so the permutation would be:

(9!/(3!(9-3)!)

= (987)/(321)

= 504

Therefore, In both cases, the answer is 504 ways.

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Therefore, the measures of those two angles are 33° and 24°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

We know, the sum of the angles in a triangle is always 180 degrees.

126 + x + y = 180

x + y = 54

Given that the two angles are in a ratio of 11:16, the proportion:

x/y = 11/16

Solving for x and y, we get:

x = 11y/16

We substitute this equation into the equation x + y = 54 and we get:

11y/16 + y = 54

Solving for y we get y = 24. Then we can use the proportion to find x:

x = 11 * 24 / 16 = 33.

So the two angles are 33° and 24°.

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The length of tile A is 2.36068 inches.

The quantity of square units required to completely fill a square is known as the area of a square.

The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.

The measurement is made using square units, with square meters serving as the standard unit (m^2).

The square unit serves as the unit of area.

Let us recall that the area of a square is given by;

A = side^2

This is because, all the sides of a square are equal hence

When A = 5 square inches

5 = side^2

side = √5

side = 2.36068 inches

Therefore, The length of tile A is 2.36068 inches.

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It is impossible to solve a 3-sided triangle because triangles require 3 sides and 3 angles in order to be solved.

A triangle is a three-sided polygon, and the sum of its angles is always 180 degrees. In order to solve a triangle, you must know the length of all three sides and the measure of all three angles. If you know two sides and the angle between them (the angle opposite to one of the sides), you can use the Law of Sines to determine the other angle. If you know two angles and a side, you can use the Law of Cosines to determine the other two sides. With all three sides and angles known, you can use the Pythagorean Theorem to check your work. However, if you only have three sides, it is impossible to solve the triangle because you do not have enough information.

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The height of the person is approximately 0.426 meters or 42.6 cm.

We can use the concept of similar triangles to solve this problem. The height of the building and the length of its shadow form a right triangle, with the height as the opposite side and the shadow as the hypotenuse. The person and their shadow also form a similar right triangle, with the height of the person as the opposite side and the shadow as the hypotenuse.

We can set up the following proportion:

(Height of building)/(length of shadow) = (height of person)/(length of shadow)

48/30 = h/0.8

Solving for h, we get:

h = (48/30) * 0.8 = 0.533 * 0.8 = 0.426

Therefore, the height of the person is approximately 0.426 meters or 42.6 cm.

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The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.

What is a differential equation?

A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.

The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Given,

    [tex]\frac{dy}{dx} = xy^{4}[/tex]

a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]

In quadrant II, the values of x < 0 and the values of y >0.

So  [tex]\frac{d^{2} y}{dx^{2} }[/tex] =  [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.

Therefore the concavity is up for of all solution curves of the given differential equation.

b)

         [tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]

      Now it is given that initial condition is f(4) = -1

   So substituting x =4 and y = -1 is the above equation to find c, we get

        [tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]

Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.

  [tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]

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Answer:

Ron killed 8 times as many spiders as Harry: R = 8 * H

Step-by-step explanation:

This expression represents the situation in which Ron killed 8 times as many spiders as Harry.

An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:

The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.

A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.

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Linear equations are mathematical equations that involve one or more variables. These equations can be solved by following a few simple steps:

Linear equations can be used to solve a wide range of mathematical problems and are an essential part of any mathematics curriculum.

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By solving the equation 5t - 3 = 3t - 5 we get the equation is true when t = -1. So the solution is t = -1.

To solve the equation 5t - 3 = 3t - 5, you can use algebraic manipulation to isolate the variable on one side of the equation.

The first step is to get all the terms with the variable on one side of the equation and all the constant terms on the other side.

5t - 3 = 3t - 5

adding 3 to both sides:

5t = 3t - 2

subtracting 3t from both sides:

2t = -2

then divide both sides by 2:

t = -1

So the solution is t = -1, meaning that when t = -1, the equation is true.

--The question is not clear, answering to the question below--

"How do you solve the equation 5t - 3 = 3t - 5?"

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Answer: 5 x 4/5

Step-by-step explanation:

In each column there is 4/5 shaded . There are 5 columns .

So , 5 x 4/5

Answer:

A) 5 × 4/5

Step-by-step explanation:

The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.

There are 5 columns.

Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):

A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]

Answer:

6.3

3

3.6

14

1.6

23.9

498

62

29

Step-by-step explanation:

0.9+5.4=6.3

6-3=3

13.6-10=3.6

7.032+2.485+4.59=14.107

57.403−55.78=1.623

13.5+7.8+2.6=23.

1,473−975=498

38+15+9=62

16+13=

Answer:

1. 0.92 rounds to 0.90 and 5.37 rounds to 5.40 (0.9 + 5.4 = 6.3)

2. 6.3 rounds to 6 and 2.8 rounds to 3 (6 - 3 = 3)

3. 13.56 rounds to 13.60 and 10.02 rounds to 10 (13.6 - 10 = 3.6)

4. 7.032 + 2.485 + 4.59 = 14.107

5. 57.403 - 55.78 = 1.623

6. 13.46 rounds to 13.50, 7.84 rounds to 7.80 and 2.59 rounds to 2.60 (13.5 + 7.8 + 2.6 = 23.9)

7. 1,472.63 rounds to 1,473 and 975.28 rounds to 975(1,473 - 975 = 498)

8. 38.24 rounds to 38, 14.53 rounds to 15 and 8.93 rounds to 9(38 + 15 + 9 = 62)

9. 16.4 rounds to 16 and 12.8 rounds to 13(16 + 13 = 29)

(some may be wrong but i did my best)

Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.

The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.

Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.

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Answer:

I have no idea tbh I need help with this too

Step-by-step explanation:

PLEASE HELP!!!!!!!!!!!!!!!

For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .

The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .

The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;

On differentiating both sides of the curve with respect to "x"  ,

we get ;

the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;

Now for the  x- intercepts , the value [tex]y = 0 ,[/tex]

On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,

we get ;

[tex]x^{2} +x(0)+0^{2} =27[/tex]

On simplifying further ,

we get ;

[tex]x=\pm 3\sqrt{3}[/tex] ;

So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;

to find the slopes , we substitute the values in the slope equation .

On substituting the values in the slope equation ,

we get ;

[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex]  and

[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].

we see that the slope at both the intercepts is same ,

Therefore , the lines tangents of the curve at the x intercepts are parallel .

The given question is incomplete , the complete question is

Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .

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The solution to the system of equations is x = 3 and y = 4.

this question is related to system of equations ,

the equations are,

x + y = 7         .......[1]

x + 2y = 11  

x= 11 - 2y

now, place the value of x in equation 1,

(11 - 2y) + y = 7

11 - 2y +y = 7

11 - y = 7

- y = 7 - 11

- y = - 4

y = 4

now to find the value of x, place the value of y in equation 1

x + 4 = 7

x = 7 - 4

x = 3.

so, the value of x and y is 3 and 4.

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Answer:

Step-by-step explanation:

To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).

Given that the discount is 3% and we want to find the price after the discount, that means:

1 - (3/100) = 1 - 0.03 = 0.97

So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.

For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7

10*0.97 = 9.7

The number of coordinates needed to specify the position and orientation of a rigid body in an n-dimensional space is n.

A rigid body is an object that maintains its shape and size while in motion. In order to specify the position and orientation of a rigid body in an n-dimensional space, we need to know its coordinates in each of the n dimensions. The coordinates describe the location of the body in the space and the orientation of the body relative to the space's coordinate system. Thus, n coordinates are required to fully specify the position and orientation of a rigid body in an n-dimensional space.

However, it is important to note that if the rigid body is placed in a space that's non-Euclidean, other parameters could be necessary to fully describe the rigid body position and orientation.

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The closing side of the triangle serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.

A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed geometrically, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or phenomenon known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.

given

As stated in the issue, we must determine the resultant vector by adding vectors A and B.

The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.

Option C is the proper response, thus.

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The probability that Sabreena is going to lose is given as 0.5833

Probability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.

A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.

If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7

In this case, the odds of Sabreena winning are 5:7,

so the probability of winning is 5/(5+7)

the probability of not winning is 1 -  5/12

The probability of not winning is approximately 0.5833

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On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Answer:

To find the number of hours you work, you need to set up an equation using the information given. Let's say that the number of hours you work is x. The equation would be:

17(x/2) = 42.50

The parentheses around x/2 indicate that the division should be done before the multiplication. So, x/2 = 2.5. Multiplying both sides of the equation by 2 gives us:

x = 5

So, you work 5 hours.

Step-by-step explanation:

So, we know that you earn $17 per 2 hours. We also know that we earned $42.50. Now, we just need to find the hours! We can do this by using a cross multiply.

$17 is directly correlated to 2 hours of work. Therefore, to find the hourly wage we should divide it by 2:

   $8.5 = 1 hour

$42.50 = x hours?

Now cross multiply:

$8.5x = $42.50

x = 5 hours

Therefore, your answer is 5 hours!

Hope this helps!

Answer:

Yes

Step-by-step explanation:

y = x has the inverse x = y

Hassan can paint maximum 11 bookcases with 10 gallons of paint.

A fraction represents a numerical value, which defines the parts of a whole.

Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction.

Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.

Given,

Hassan has 10 gallons of paints.

1 bookcase requires 7/8 gallons of paint

Let Hassan paints x bookcases.

According to the question

7/8x = 10

7x = 80

x = 80/7

x = 11.43

But no. of bookcases should be in whole.

Number of bookcases painted with 10 gallons of paint = 11.

Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint

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Answer:

2/15

Step-by-step explanation:

make x= 0.13

multiply it by  10^1 .  

10x = − 1.33

subtract x from 10x

10x−x =

1.33 - 0.13

9x =  1.2  

divide both sides by 9 to get x as a fraction

x =  1.2/9  =  

12/90  =  

2/15

httpssocraticorgquestionshowdoyouconvert0133beingrepeatedtoafraction#242780

A bar over a digit in a decimal number, such as 0.133 with a bar over the 3, indicates that the number is a repeating decimal. In this case, 0.133 is a repeating decimal and the digit 3 is repeating infinitely.

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In Week 1,

Salesman C got larger paycheck than Salesman A and Salesman B.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.

Given,

Commission of salesman A per sale = $65

Commission of salesman B per sale = $40

Commission of salesman C per sale = $0

Salary of salesman A per week = $0

Salary of salesman B per week = $300

Salary of salesman C per week = $900

No. of sales × commission + salary = total earning

In week 1.

Earning of A

11 × $65 + $0 = $715

Earning of B

14 × $40 + $300 = $860

Earning of C

16 ×$0 + $900 = $900

In week 2.

Earning of A

14 × $65 + $0 = $910

Earning of B

15 × $40 + $300 = $900

Earning of C

12 ×$0 + $900 = $900

In week 3.

Earning of A

16 × $65 + $0 = $1040

Earning of B

13 × $40 + $300 = $820

Earning of C

111 ×$0 + $900 = $900

By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.

In week 2 and week 3 his paycheck is smaller than both of the other salesman.

Hence, Salesman C  received larger paycheck than both of the other salesmen in Week 1.

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The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]

The given equations are

                        [tex]6x+y=20\\x-4y=-5[/tex]

We need to find the value of [tex]x[/tex] and [tex]y[/tex]

First let's take equation [tex]2[/tex]  and we can simplify it

                                 [tex]x-4y=-5\\x=-5+4y[/tex]

Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is

                     [tex]6x+y=20\\6(-5+4y)+y=20[/tex]

We can open the bracket and simplify

                       [tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]

Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]

                       [tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]

The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.

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The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).

Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:

y = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:

y = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)

f(x) = (x + 7) · (x - 3) · (x - r)

Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.

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Answer:

∠ SQT = 63°

Step-by-step explanation:

since QS bisects ∠ RQT , then

∠ RQS = ∠ SQT = 7x + 7

then

∠ RQS + ∠ SQT = ∠ RQT , that is

7x + 7 + 7x + 7 = 9x + 54

14x + 14 = 9x + 54 ( subtract 9x from both sides )

5x + 14 = 54 ( subtract 14 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Then

∠ SQT = 7x + 7 = 7(8) + 7 = 56 + 7 = 63°