A catering service offers 8 appetizers, 11 main courses, and 4 desserts. A banquet chairperson is to select 5 appetizers, 9 main courses, and 2 desserts for a banquet. In how many ways can this be done?

Answer:

The polynomial is [tex]x^3+2x-3[/tex].

Step-by-step explanation:

The quotient stands for division, so when we are told that the quotient of [tex]x^5-3x^3-3x^2-10x+15[/tex] and a polynomial, we have to think of a division which result is [tex]x^2-5[/tex]. The goal of this exercise is to find the value of such polynomial that is divisor.

Solving for the divisor

We can write the quotient in a general way using proper naming as follows:

[tex]\cfrac{\text{dividend}}{\text{divisor}}=\text{result}[/tex]

Solving for the divisor we have

[tex]\text{dividend}=\text{divisor} \times\text{result}\\\cfrac{\text{dividend}}{\text{result}}=\text{divisor}[/tex]

So the goal is to work with that division to find the polynomial, that is

[tex]\cfrac{x^5-3x^3-3x^2-10x+15}{x^2-5}[/tex]

Long division

In order to set up for long division, we have to realize that the dividend or numerator has not the [tex]x^4[/tex] term, so we can fill it with [tex]0x^4[/tex]

So we will have

[tex]x^5+0x^4-3x^3-3x^2-10x+15[/tex]

Please check the attached image file to see the steps for the long division that will be explained here in text.

The first step is to divide always the first term of the dividend that is the [tex]x^5[/tex] by the first term of the polynomial we are dividing by, that is [tex]x^2[/tex], so we get

[tex]\cfrac{x^5}{x^2} =x^3[/tex]

We write that on top and then we multiply it times the polynomial we are dividing by that is

[tex]x^3(x^2-5) = x^5-5x^3[/tex]

We write that below the dividend and proceed subtracting each column, that will give us

[tex]2x^3-3x^2-10x+15[/tex]

So we can continue with the division, just looking at first terms we get

[tex]\cfrac{2x^3}{x^2}=2x[/tex]

Then we continue multiplying

[tex]2x(x^2-5) = 2x^3-10x[/tex]

And we write that below as can be seen on the attached image, so the subtraction of each column give us

[tex]-3x^2+15[/tex]

Finally we can work with the last division of first terms.

[tex]\cfrac{-3x^2}{x^2}=-3[/tex]

And we write that -3 on top, and we multiply

[tex]-3(x^2-5) = -3x^2+15[/tex]

And work with the last division and we get 0. Getting 0 is a way to verify that there is no remainder and that our work is correct for the quotient.

Lastly the expression on top is the original polynomial of the quotient, we can conclude that the polynomial is [tex]x^3+2x-3[/tex]

Answer: 20, 22, 24, 26

An arithmetic sequence

a1=20

d=2

98 seats

an arithamtic series

2,360 total seats

Step-by-step explanation:

r = 62 mph

t = 4.5 hours

d = 4.5*62 = 279 total miles

The question provided is a fifth-degree polynomial equation in mathematics, specifically algebra, which requires solving for variable x. Higher-degree polynomial equations like this may require numerical methods or synthetic division to solve. The solutions may include both real and complex numbers.

The given question is a polynomial equation that requires solving for the variable x. In mathematics, specifically in algebra, solving polynomial equations can sometimes be achieved through factoring, applying the rational root theorem, or using synthetic division. However, the provided equation 4x5 – 12x4 + x3 – 52x2 – 60x – 16 = 0 is a fifth-degree polynomial, which might not have a straightforward solution method such as factoring or simple root identification.

To solve higher-degree polynomials, one can use numerical methods, attempt to factor by grouping (if that results in a solvable factorization), or apply the synthetic division repeatedly to find possible real roots. If the equation can be factored down to quadratic factors, the quadratic formula ax² + bx + c = 0 could be applied to find the roots of those quadratic factors. It's important to note that a fifth-degree polynomial will have five roots according to the Fundamental Theorem of Algebra, which can be real or complex numbers.

Other examples provided in the question seem to be related to solving quadratic equations or conditions for quadratic expressions which are not directly applicable to the fifth-degree polynomial but showcase general algebraic problem-solving techniques.

The probability of the product being even when two six-sided dice are rolled is 3/4 or 0.75, since there is a 1/2 chance of rolling an even number on each die, and the only way to have an odd product is if both dice show odd numbers.

To solve this problem, we will find the probability that the product of two rolls of a six-sided die is even. The product of two numbers is even if at least one of the numbers is even. In the case of a six-sided die, there are 3 even sides (2, 4, 6) and 3 odd sides (1, 3, 5).

For the first roll, the probability of rolling an even number is 3 out of 6, or 1/2. The second roll is independent of the first, so the probability of rolling an even number again is also 1/2. To find the probability that at least one roll is even, we can use the complement rule which states that the probability of an event 'E' is 1 minus the probability of the event's complement. The only way not to get an even product is to roll two odd numbers.

The probability of rolling an odd number on the first toss is 3/6, and similarly 3/6 for the second toss. Therefore, the probability of both being odd is (3/6) × (3/6) which simplifies to 1/4. Hence, the probability of at least one die being even (and therefore the product being even) is 1 - 1/4 = 3/4.

The final answer is that the probability of getting an even product from two rolls of a six-sided die is 3/4 or 0.75.

Answer:

A perfect cube is a number that is the result of multiplying a whole number by itself three times. Check a number by finding the cube root. If the cube root is a whole number, then the number is a perfect cube.

Answer:

you been waiting for your answer since 2017 bru im so sorry LLMA O the answer is 840

Answer:

840

Step-by-step explanation:

30 + 62 + 8 = 100

100 x 12 = 1,200

70 people out of 100 do activities for at least three hours a week.

70 x 12 = 840

100 x 12 = 1,200

840/1,200 in the school are expected to play outdoor games for at least three hours every week.

oml you asked this question in 2017. THATS 5 YEARS AGO

sorry

Answer:

The required inequality that shown in the given graph is [tex]y\geq 2x-2[/tex].

Step-by-step explanation:

Consider the provided graph.

The y-intercept of the line is, (0,-2)

The x-intercept of the line is, (1,0)

To find the equation of line use the formula:

[tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute [tex](x_1,y_1)=(0,-2)\text{and}(x_2,y_2)=(1,0)[/tex]

[tex]y-(-2)=\frac{0-(-2)}{1-0}(x-0)[/tex]

[tex]y+2=\frac{(2)}{1}(x)[/tex]

[tex]y+2=2x[/tex]

[tex]y=2x-2[/tex]

Therefore the equation of line is [tex]y=2x-2[/tex].

The graph is solid line and shaded region is above the line. So, use the inequality sign "≥".

Thus, the required inequality that shown in the given graph is [tex]y\geq 2x-2[/tex].

L= 2+w

I cannot solve this, however, because you have not included the total perimeter/area

The length and width of a rectangle can be represented as x + 2 cm and x cm, respectively.

In this problem, we are given that the length of a rectangle is 2 centimeters more than the width. Let's say the width of the rectangle is x centimeters. Then, the length of the rectangle would be x + 2 centimeters.

So, the dimensions of the rectangle are: length = x + 2 cm and width = x cm.

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This question is based on the concept of Euler’s Formula. Therefore, there are 40 edges.

Given:

Faces: 25 Vertices: 17

We need to determined the number of edges by using the  Euler’s Formula (F + V = E + 2).

According to the question,

It is given that,

Faces: 25

Vertices: 17

By using Euler’s Formula ,

F + V = E + 2

Now put all the given values in the formula.

We get,

25 + 17 = E + 2

42 = E + 2

42 - 2 = E

E = 40

Therefore, there are 40 edges.

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To find the number of boys at Molly's daycare that are under 1 year old, we can use the given fractions to calculate the answer.

To find the number of boys at Molly's daycare that are under 1 year old, we first need to determine the total number of boys at the daycare. Since 1/8 of the children are boys, we can assume that 1/8 of the total number of children are boys. Let's say there are a total of x children at the daycare. If 1/8 of x represents the number of boys, we can write the equation (1/8) * x = number of boys. Now, we need to find the number of boys that are under 1 year old. Since 2/5 of the boys are under 1 year old, we can write the equation (2/5) * (1/8) * x = number of boys under 1 year old. Simplifying this equation gives us the answer: (1/20) * x = number of boys under 1 year old.

19.   13(x+5)=91

20.   (-8)×x-15=30

21.   p=23w

22.   S=P+2

23.   7

24.   -13

25.   -8

26.   13

27.   -10

28.   -72

29.   -6

30.   3

Fathi will need 12 sheets of paper to print a 48 page PDF document by printing two pages on each side of the paper. The total page count is halved twice, once for each side of a sheet and again for each pages printed per side.

Fathi has a PDF document that is 48 pages long and he wants to print it in a way that saves paper. This involves printing two pages on each side of a sheet of paper and then using both sides of the sheet. To find out how many sheets he will need, we can start by halving the total page count because printing two pages on each side means we effectively halve the number of pages. So, 48÷2 equals 24 'effective' pages. Then, because he's printing on both sides of each sheet, we halve that number again, giving us 24÷2 equal 12 sheets of paper. So Fathi will need 12 sheets of paper to print his 48-page document.

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Answer:

Option D.

Step-by-step explanation:

In the graph attached if we consider a point X. We find that the given point or figure is reflected over the y - axis first.

It means x gets a mirror image in second quadrant when reflected over y-axis (equidistant form y-axis) and the coordinates of X' becomes(-3, 2).

Now this point X'(-3, 2) is translated down by 5 units to form a new point Y in third quadrant with the new coordinates (-3, -3)

Y- coordinates of Y = Y coordinates of X' - (-3)

                                = 2 - (-3) = 5 units down.

Therefore, Option D.is the correct option.

The equivalent expression of the expression -21.8 - (-18.3) will be -3.5.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using operations like addition, subtraction, multiplication, and division.

The mathematical expression is given as;

⇒ - 21.8 - (- 18.3)

Now, Solve the expression as;

The mathematical expression is

⇒ - 21.8 - (- 18.3)

= -21.8 + 18.3        

(Since, Two negative sign give positive sign after combine.)

After subtract the numbers we get;

= - 3.5

So, The equivalent expression is;

⇒ - 21.8 - (- 18.3) = - 3.5

Thus, The equivalent expression of the expression -21.8 - (-18.3) will be -3.5.

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Answer:

brainlist plzz

Step-by-step explanation:

The fixed amount is a price you pay before using equipment. So, it is the price you pay at the 0-th day: 25$.

Then, after one you pay 15 more dollars (25+15=40), and after another day you pay 15 extra dollars again (40+15=55).

So, we can see that the pattern is that you start from $25 (fixed price), and then you pay $15 per day (renting price per day)

Answer:

The answer is 25

Step-by-step explanation:

i did the quiz :)

Final answer:

The prime factorization of 57 is 3 × 19, and the prime factorization of 54 is 2 × 3 × 3 × 3.

Explanation:

The prime factorization of 57 is 3 × 19. To find the prime factorization of 57, we start by dividing the number by the smallest prime number, which is 2. We continue dividing until we cannot divide any further. In this case, 57 is not divisible by 2. Next, we try dividing by the next smallest prime number, which is 3. 57 divided by 3 equals 19, which is a prime number. Therefore, the prime factorization of 57 is 3 × 19.

The prime factorization of 54 is 2 × 3 × 3 × 3. To find the prime factorization of 54, we use the same process. We start by dividing the number by 2, then 3, and so on, until we cannot divide any further. 54 divided by 2 equals 27. 27 divided by 3 equals 9, and 9 divided by 3 equals 3. 3 is a prime number, so we stop here. Therefore, the prime factorization of 54 is 2 × 3 × 3 × 3.

To produce a pie chart reflecting 2/3, the pie must be divided into 3 equal parts, representing the whole. Two of these sections are then filled in or marked, representing the 2 in the fraction 2/3 or roughly 66.7% of the total pie chart.

To create a pie chart representation of the fraction 2/3, you need to think of the pie as representing the whole or 1. From there, we split the pie into 3 equal parts (since your denominator is 3), then, you will shade in 2 of those parts (as your numerator is 2). That shaded area of the pie chart represents 2/3.

It's essential to remember that each slice of the pie in a pie graph represents a share of the total or percentage. Thus, if you consider your pie to be 100%, then each one-third piece would be roughly 33.3%, and two of these would give you approximately 66.7%, which is the decimal equivalent of 2/3.

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