help im no good at this

Help Im No Good At This

Answers

Answer 1

Answer:

8.2 × 10⁻³

Step-by-step explanation:

1.64 × 10⁰      1.64 × 1         1.64

-------------- = -------------- = ---------- = 0.0082

2.0 × 10²        2 × 100        200

Scientific notation: 8.2 × 10⁻³

I hope this helps!


Related Questions

In the 2-man bobsled competiton in the olympics, the gold medalists were about 0.2 seconds faster than the silver medalists, and the silver medalists were about 0.14 seconds faster than the bronze medalists. Which gap in time was larger? By how much?

Answers

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

what is unitary method ?

The unit technique is a strategy for addressing issues that entails first figuring out the value of a specific unit, then dividing that value to figure out the needed value. Simply put, the unit method is employed to derive a single system value from a multiple that is supplied. For example, 40 pens might cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, computational equations, or algebra of matrices or operators.

given

time separation of gold medalists by silver medalists is equal to 0.14 minus 0.2, or 0.11.

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

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Can u please help.............

Answers

Answer:

152°

Step-by-step explanation:

2x + 48 = 3x - 4 (the measure of an exterior angle of a triangle = the sum of the measures of the two non-adjacent interior angles of the triangle)
=> 4 + 48 = 3x - 2x (on transposing)
=> 52 = x
Substituting the vale of x in the m∠JKM,
m∠JKM = 3x - 4 = 3(52) - 4 = 152°

Hope you understood!!

domain and range of f(x)=|x|

Answers

The domain and range of f(x) = |x| is

Domain: all real numbers

range: positive real numbers

What are absolute values?

The distance of a number from a number line's origin is referred to as the absolute value of that number. Its representation is |x|, which establishes the size of any integer 'x'.

Any integer's absolute value, regardless of its sign, will be one of the real numbers, whether it is positive or negative. The modulus of x, which is represented by two vertical lines |x|, is a mathematical concept.

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value.

Since absolute value can be zero the range is all positive numbers

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A ball was dropped from a height of 150 cm. The rebound factor of the ball is

0. 8. About how high, in centimeters, did the ball go after the third bounce?

A. 77

B. 96

C. 234

D. 293

Answers

the ball go after the third bounce is 77 centimeters  when A ball was dropped from a height of 150 cm. The rebound factor of the ball is

0. 8.

In math, height is defined as the vertical distance from the top to the object's base. Occasionally, it is labeled as 'altitude'. The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry

based on the given information

A ball was dropped from a height of 150 cm.

The rebound factor of the ball is 0.8

Evaluate the ball go after the third bounce is given by

150* 0.8 ^3= 77

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Is 9x² 24x 16 a perfect square trinomial?

Answers

9x² + 24x + 16, which is the full quadratic trinomial expressed as (3x +4)².

What is a trinomial expression?

A trinomial expression is an algebraic expression containing three distinct terms, hence the name "trinomial expression". An algebraic expression called a trinomial expression contains three nonzero terms. A trinomial expression is formed when three monomials are added or subtracted from each other. A quadratic trinomial has the form: ax² + bx + c, where a, b, and c are nonzero real values.

Given that

9x² + 24x + 16

= (3x)² + 2(12x) + 16

= (3x)² + 2(3x)(4) + 4²

This is similar to a² + 2ab + b² = (a + b)².

So you can write:

= (3x + 4)²

= (3x +4) (3x + 4)

So this is a complete quadratic trinomial.

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What’s is the prime factorization of |-21|

Answers

Prime factorization of |-21| is 3 & 7
The prime factorization is 3,7

How do you find the area of an acute triangle without height?

Answers

The area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

The area of an acute triangle without height can be calculated using Heron's Formula. Heron's Formula states that the area of a triangle is equal to the squareroot of s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.

To find the area, first calculate the semi-perimeter of the triangle. The semi-perimeter is equal to one-half the sum of the three sides. For example, if the lengths of the three sides of a triangle are 5, 7, and 8, the semi-perimeter is equal to 5 + 7 + 8 divided by 2, which is equal to 10.

Next, plug the values into Heron's Formula. Using the same triangle as an example, the area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

Finally, calculate the area of the triangle by taking the square root of 24, which is equal to 4.9. Therefore, the area of the triangle is 4.9 square units.

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A book is 6 inches wide and 9 inches tall.

A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 9 inches.

A publisher wants to use a scale factor of 1.5 to enlarge a book. What will the area of the front of the book be after the book is enlarged? (5 points)

a
54 in2

b
81 in2

c
121.5 in2

d
78.75 in2

Answers

The area of the front of the book after it has been enlarged would be = 121.5 in². That is option C.

What is a rectangle?

A rectangle is defined as the type of quadrilateral which has two opposite sides that are equal and parallel and with four angles that are equal to 90°.

The length of the rectangular book= 6 inches

The width of the rectangular book = 9 inches

Using the scale factor of 1.5 the new length and width is thus:

length = 6 × 1.5 = 9 inches

9× 1.5 = 13.5

Therefore area of the book = l×W = 9 × 13.5 = 121.5 in².

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Select perpendicular lines from the given pair of lines :

Select one:

a.
y = − 3x + 7, y = 3x + 11


b.
y = 3x + 7, y = x / 3 + 11


c.
y = − 3x + 7, y = x / 3 + 11


d.
y = − 3x + 7, y = − x / 3 + 11

Answers

Answer:

The line pairs that are pendicular are shown in option c.

c.    y = − 3x + 7, y = x / 3 + 11

Step-by-step explanation:

Perpendicular lines have slopes that are the negative inverse of each other.  For example, a line with slope of 5 would have a line perpendicular to it if the second line has a slope of -(1/5)  [the negative inverse of +5].

Cmpare the slopes of each pair of linear equations:

a.  -3 and 3  The negative inverse of -3 would be (1/3), not 3.  These lines are not perpendicular.

b.  3 and (1/3).  The negative inverse of 3 would be -(1/3), not (1/3).  These lines are not perpendicular.

c.  -3 and (1/3).  The negative inverse of -3 would be (1/3).  These lines are perpendicular.

d.  -3 and (-1/3).  The negative inverse of - 3 would be (1/3).   These lines are not perpendicular.

The 19th and 15th terms of an AP are- 5 and -7 1/2, respectively. What is the sum of the first 20 terms.

Answers

The sum of the first 20 terms of the sequence is - 206.25

What is an Arithmetic Progression?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2

a + 18d = - 5

a + 14d = -7 1/2

---------------------

4d = -5 + 15/2

8d = -10 + 15

8d = 5

d = 5/8

a + 18(5/8) = -5

8a + 90 = -40

8a = -40 - 90

8a = -130

a = -130/8

The sum of the first 20 will be;

Sum = (20/2) (2(-130/8) + (20-1)(5/8))

Sum = 10 (-260/8 + 95/8)

Sum = 10 (-165/8)

Sum = - 206.25

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Is the following a direct variation? If yes, identify the constant of variation. If not, explain why.

− y = 3x

Answers

The equation given as -y = 3x is a direct variation. The constant of variation is - 1/3

What is a direct variation?

It shows the relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

A straightforward correlation between two variables is referred to as direct variation. In this case, the constant of variation will be k.

This will be Illustrated as:

y = kx

-1 = 3k

Divide

k = -1/3

The constant is - 1/3.

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A rectangle has an area of 16x + 24. What could the length and width of the rectangle be

Answers

The length and width of the rectangle will be 2 and 8x + 12

Area of rectangle = 16x + 24.

A rectangle is a four-sided geometric shape having opposite sides that are equal in length and four right angles. The length and width of the rectangle are its opposing sides.

A rectangle's area is found by multiplying its length and width together, so:

Area = length x width

Calculating the length and width of the rectangle -

Factoring out 2 from the equation -

Therefore -

2 (8x+12)

Since, the area is the length times width, thus -

2 x (8x+12)

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Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D

Answers

The best answer is t = 7. Option C

What is a quadratic equation?

A quadratic equation is simply defined as an equation that could be rearranged in standard form.

It is also described as an algebraic equation having the highest exponent of as 2.

It is so arranged such that;

x represents an unknown valueVariables, a, b, and c represent known numbersAlso, a is not equal to 0, a ≠ 0

It is important to note that the three methods of solving quadratic equation are;

FactorizationUsing the quadratic formulaUsing completing the square method

From the information given, we have that the form is;

x² = c

Given  t squared minus 49 = 0

First, represent mathematically

t² - 49 = 0

Now, collect like terms, we have;

t² = 49

Take square root of both sides

t = √49

t = 7

Hence, the equation is  t = 7

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Choose all of the equations that represent a parabola with the focus (3,9) and the vertex (3, 6).
A. 12y = x² - 6x+81
B. 24y=x²-12x + 72
C. 24y=x² - 6x + 225
D. (x-3)2 24 (-9)
E. (x-3)² = 12 (y – 6)
F. (x-9)² = 24 (y - 3)

Answers

 (x-3)² = 12 (y – 6)  is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.

what is parabola ?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. The topic of conic sections includes parabola as a key component, and all related parabola topics are discussed. a plane curve produced by a point shifting such that its separation from a fixed point equals its separation from a fixed line: junction of a plane parallel to an element of a right circular cone with the cone. : a bowl-shaped object (such as an antenna or microphone reflector)

given

focus (3,9) and the vertex (3, 6)

general equation of parabola = (x - h)2 = 4a (y - k)

a = |y2 - y1| = | 9 - 6 |

a = 3

so

(x - 3 )[tex]^{2}[/tex] = 4 * 3 ( y - 6 )

= [tex](x-3)^{2} = 12 ( y - 6 )[/tex]

 (x-3)² = 12 (y – 6)  is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.

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Pat is making rectangular placemats each with area 1200cm2 she wants to braid trim around the edges how much trim does pat need for the placemat

Answers

Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat to braid trim around the edges.

To find out how much trim Pat needs for each placemat, we need to first find the perimeter of the rectangle.

The area of the rectangle is given as 1200 [tex]cm^2[/tex].

The perimeter of the rectangle is the sum of all four sides of the rectangle. If the length and breadth of the rectangle are L and B respectively, then the perimeter P can be calculated using the formula:

P = 2(L+B)

Now, let's find the length and breadth of the rectangle using the area formula,

Area = LB = 1200 [tex]cm^2[/tex]

so LB = 1200 [tex]cm^2[/tex]

Now we can substitute the value of L and B in the perimeter formula

P = 2(L+B) = 2(sqrt(1200)+sqrt(1200))

As the area of the rectangle is given as 1200[tex]cm^2[/tex] , the length and breadth can be calculated as [tex]\sqrt{1200}[/tex]cm.

So the perimeter of the rectangle is

P = 2*([tex]\sqrt{1200}[/tex] + [tex]\sqrt{1200}[/tex])

  = 2*2[tex]\sqrt{1200}[/tex]

  = 4[tex]\sqrt{1200}[/tex]cm

To find the total length of trim Pat needs for the placemat, we need to multiply the perimeter by the number of edges that need a trim. Since the edges are around the rectangular placemat, so it will be 4 edges.

So, the total length of trim Pat needs for the placemat is

P4 = 4[tex]\sqrt{1200}[/tex]*4 = 16[tex]\sqrt{1200}[/tex]cm

So Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat.

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Please help me with my hw

Answers

Answer:

9m^8 n^2

Step-by-step explanation:

Open up the parenthesis and simplify to find your answer.

The table shows pairs of values for the linear function f(x) = 3x -2. Which conjencture about linear functions in general is best supported by the table?

Answers

The information in a table shows that f(x) = 3(2)x  exponential function. An exponential function has the formula y = abx, wherein y and x are variables.

Describe the exponential function.

An exponential function is a mathematical function with the following formula: f (x) = 1 x. where an is a fixed sum that serves as the function's basis and x is a variable. The most frequent exponential-function base is the transcendent number e, or around 2.71828. Your function must be exponential if it has the equation y = a b x, or where are constant, a Zero and b > 0 and b 1. You always used functions to the power of 2 while solving quadratic equations. An exponential function's exponent is a variable.

Here,

given:

Using the table's (0, 3):

3 = ab° , a = 3

(2) and (12):

=>12 = ab²

=>12 = 3b²

=>b² = 4

=>b = 2

=>f(x) = 3(2)ˣ

The information in a table shows that the exponential function, f(x), equals 3(2)x.

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A fish swims at an altitude of -20. 2 meters. A bird flies at an altitude of 38. 1 meters. Which animal is closer to sea level?

Answers

The fish is closer to sea level. Sea level is defined as the mean sea level, which is a fixed point of reference for measuring altitude.

The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.  To explain further, sea level altitude is a point of reference that is used to measure the altitude of other objects. Sea level altitude is defined as the mean sea level which is a fixed point.

Therefore, when trying to determine which animal is closer to sea level, it is important to look at the altitude of both the fish and the bird. The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.

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Maria had lunch at a restaurant. If the bill was $12.25 and Maria wants to leave a 20% tip, what is a reasonable estimate for the amount she should leave for tip?

Please explain how you got the answer

Answers

Answer: $2.45

Step-by-step explanation:

An easy way to find the correct tip is to learn what 20% of 12.25 is

Let's convert the percentage to a decimal by moving the decimal point two spaces to the left. Now we have .2

.2 X 12.25 = 2.45

2.45 is 20% of 12.25

PLEASE HELP ME I DONT UNDERSTAND GIVING 100 POINTS

Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year

Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)

Is this equation okay to use for the height of the trees in this problem?

There is one equation that is incorrect.... determine which one? why is it incorrectly?

Creat two new equations written in point slope form

Answers

Answer:

(e) is the incorrect equationy -9 = 3/4(x -8)y -15 = 3/4(x -16)

Step-by-step explanation:

Given a tree is 3 ft tall when planted and grows at 3/4 ft per year, you want to identify the point-slope equation that does NOT fit this description, and you want two (2) more point-slope equations that DO fit this description.

Point-slope equation

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Points

The point representing the initial height of the tree is (x, y) = (years, feet) = (0, 3). If the rate of growth is 3/4 ft per year, then the equation can be written ...

  y -3 = 3/4(x -0) . . . . . . . . . matches choice (a)

All of the given equations have m = 3/4, so to find the incorrect equation, we need to find the point that is not on the line described by the above equation. We can do this by identifying the point (h, k) in each equation.

The attachment shows the point values used in each of the other equations (b) through (e). We find they all fall on the line except the point (15, 15) used in equation (e).

The incorrect equation is equation (e) y -15 = 3/4(x -15).

Additional equations

We can write additional equations by finding additional points that are on the line. For the purpose, it is convenient to choose x-values that are multiples of 4. Already, equations use x = 0, 4, 12, 15. We can choose x=8 and x=16 for the equations we write. The graph shows the corresponding y-values are 9 and 15, respectively. Then two additional equations could be ...

  y -9 = 3/4(x -8)

  y -15 = 3/4(x -16)

__

Additional comment

There are several ways to find the equation that doesn't belong. Another way, apart from plotting the points on a graph, is to rewrite each equation into the same form. Slope-intercept form is fairly convenient for this.

(a) y -3 = 3/4(x -0)   ⇒   y = 3/4x +3

(d) y -12 = 3/4(x -12)   ⇒   y = 3/4x -9 +12 = 3/4x +3

(e) y -15 = 3/4(x -15)   ⇒   y = 3/4x -11.25 +15 = 3/4x +3.75 (incorrect)

You can see that 3/4x (and y) will be an integer only if x is a multiple of 4. We like integers, so it is convenient to choose x as a multiple of 4.

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Find the values of x and y in parallelogram PQRS.

PT=​y, TR=4x+​1, QT=2​y, TS=5x+8

Answers

The values of x and y in parallelogram PQRS are x =2 and y = 9

How to determine the values of x and y in parallelogram PQRS

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

The parallelogram

On the parallelogram, we have the following readings

PT=​y, TR=4x+​1, QT=2​y, TS=5x+8

Rewrite them as

PT= ​ y

TR = 4x + ​1

QT = 2​y

TS = 5x + 8

Because the point T is the midpoint of the parallelogram, we have

PT = TR

QT = TS

Substitute the known values in the above equation, so, we have the following representation

y = 4x + 1

2y = 5x + 8

This means that

8x + 2 = 5x + 8

Evaluate the like terms

3x = 6

So, we have

x = 2

Substitute x = 2 in y = 4x + 1

y = 4 x 2 + 1

So, we have

y = 9

Hence, the values are 2 and 9

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How many solutions does y 2x 5 and 8x 4y =- 20 have?

Answers

A system of linear equations: y + 2x = -5 and 8x + 4y = -20  has infinitely many solutions.

The 3 possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

The given linear system is:

y + 2x = -5           ....... (equation 1)

8x + 4y = -20     ..........(equation 2)

Rearrange equation 1 to:

2x + y = -5

Multiply both sides by 4:

8x + y4 = -20

Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.

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How to find the height of an isosceles triangle given 3 sides?

Answers

The height of an isosceles triangle can be found by using the Pythagorean Theorem to calculate the length of the hypotenuse, subtracting the lengths of the other two sides, and taking the square root of the difference.

To find the height of an isosceles triangle given three sides, you can use the Pythagorean Theorem. Begin by calculating the length of the hypotenuse (the longest side of the triangle). To do this, square the lengths of the two other sides and add them together. Then, take the square root of that sum. This is the length of the hypotenuse. Next, subtract the lengths of the other two sides from the hypotenuse and take the square root of the difference. The result is the length of the altitude, which is also the height of the triangle.

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7. Plumber A charges $60 an hour. Plumber B charges $40 to visit your home plus $55 for each

hour. For how many hours will the total cost for each plumber be the same? How much will that

cost be? If a customer thinks they will need a plumber for 5 hours, which plumber should the

customer hire? Explain.

Answers

The total cost will be $480.

What is an Equations?

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a sentence, it is not an equation. It will be viewed as a phrase.

There should be two equations

For Plumber A = 60x

For Plumber B = 40 + 55x

Now in order to consider the cost to be the same we equate these two equations

60x = 40 + 55x

5x = 40

x = 8 hours

And, the total cost for plumber B is

= 40 + 55(8)

= 480

Hence, The total cost will be $480.

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What is the coefficient of X²Y in the product 7x² 5y X² 3y )? *?

Answers

The coefficient of the expression X²Y in the product 7x² 5y X² 3y is 35.

7x² 5y X² 3y

= 7x² X² (5y 3y)

= 7x² X² (2y)

= 7x² X² 2y

= 14x² 2y

= 28xy

= 35

The given expression is 7x² 5y X² 3y. This can be rearranged as 7x² X² (5y 3y). This is equal to 7x² X² (2y). This can further be rearranged as 7x² X² 2y. This is equal to 14x² 2y. This can be further rearranged as 28xy. This is equal to 35. Therefore, the coefficient of X²Y in the product 7x² 5y X² 3y is 35.

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35. Solve the following, giving your answer as a fraction in its lowest terms 5 3/4 ÷ 1 1/2​

Answers

The fraction after solving and simplifying the mixed fraction 5 3/4 ÷ 1 1/2​ is 23 / 6.

What is the mixed fraction?

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.

Given:

5 3/4 ÷ 1 1/2​

Solve the mixed fraction into improper fractions as shown below,

5 × 4 + 3 / 4 ÷ 1 × 2 + 1 / 2

20 + 3 / 4 ÷ 2 + 1 / 2

23 / 4 ÷ 3 / 2

23 / 4 × 2 / 3

23 × 2 / 4 × 3

On simplifying,  

23 × 1 / 2 × 3

23 / 6

Thus, the value is 23 / 6.

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The table lists recommended amounts of food to order for party guests. And are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering​ purposes, they will count each of these​ "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with ​drop-in guests?

Answers

To calculate the amount of food to order for the graduation party with drop-in guests, you should multiply the number of "full" guests, which is 40 + x/2, by the recommended amounts listed in the table.

To calculate the amount of food to order for the graduation party, you need to take into account the number of guests and the recommended amounts listed on the table. Since the party is for 40 guests and there will also be "drop-in" guests, you need to convert these guests into an equivalent number of "full" guests. To do this, you can divide the number of drop-in guests by 2.

So if there are x drop-in guests, the number of "full" guests will be 40 + x/2.

Now you can use this number of "full" guests to calculate how much of each food item to order. For example, if the table recommends 1/4 lb of meat per guest, you would order (40 + x/2) × 1/4 lb = 10 + x/8 lb of meat.

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Why is 3 a polynomial?

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A variable has a degree of zero and no exponent. Each constant polynomial has a degree of zero.

A polynomial is what?

A polynomial only uses addition, subtraction, multiplication, and non-negative integer exponentiation of the variables as its operations. In mathematics, the term "indeterminate" is frequently used to describe variables. A polynomial is an equation that combines variables, constants, and exponents while using addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

A variable has no exponent, the degree is 0. The degree of each constant polynomial is zero .

Since 3 can be expressed as  [tex]3 X 0[/tex] and is a constant polynomial, it has a degree of [tex]0[/tex].

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Identify an irrational number between 7 and 8

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We know that the square root of 2 is irrational. We also know its greater than 1, but less than 2, so lets add 6 to the square root of 2, which we know is greater than 7, but less than 8

One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.

(Assume that the computers do not back up at the start of the 24-hour period.)

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Answer:

Since the two computers back up at different intervals, we can find the least common multiple of the two intervals to determine how often they back up at the same time. The least common multiple of 5 and 2 is 10. Therefore, the two computers will back up at the same time every 10 minutes. In 24 hours, there are 60 minutes/hour * 24 hours = 1440 minutes. Dividing this by the interval of 10 minutes gives 1440 minutes / 10 minutes/backup = 144 backups. Therefore, the two computers will back up at the same time 144 times in 24 hours.

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