Write an equation describing the relationship of the given variables

The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr

Combination formula will be:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.

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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.

Combinations indicate the choosing of items from a predetermined list of items.

The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}

The quantity is given by n. and x is equal to how many objects are taken at once.

Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.

The expression for the number of possible distributions of such textbooks among the students is

⇒ ⁵C₂

⇒ 10

Hence, there are ten ways to distribute those textbooks could be among the students.

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Answer:

n = 13

Step-by-step explanation:

For this, you need to square all of the numbers and then add them together. Most of the time, you can put them into a calculator but I will work it out below.

Squaring means multiplying a number by itself, so we get:

3² + 4² +12² =n²

Turns into:

(3*3) + (4*4) +(12*12) = n²

Then work out the multiplication:

9 + 16 + 144 = n²

Add everything together

169 = n²

Now take the square root of each side:

[tex]\sqrt{169} =\sqrt{n^{2}}[/tex]

This comes out to be:

± 13 = n

The question asks for the positive number, so you answer is:

n = 13

First solution

(x-3)=11

x=11+3

Second solution

-(x-3)-11

multiply by -1 both sides

x-3=-11

x=-11+3

therefore

answer is

-8,14

We will have the following:

Answer: Here the correct option is 2) 58, 16, 00, 96, 95, 38, 39, 94, 04, 32

Step-by-step explanation:

Sphere solid is generated when the semicircle is rotated about the line.

Given,

The semi circle is rotated about the line.

To find the what solid is generated?

Now, According to the question:

We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.

Hence, Sphere solid is generated when the semicircle is rotated about the line.

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So, here we have that there are 175+63 = 238 birds in total.

We want to know the ratio of ducks to the total number of birds flying overhead. There are 175 ducks for a total of 238, so the ratio is:

175:238

Answer: (3,11)

Step-by-step explanation:

Answer:

The approximate cost during the years 1987 was $7527

Explanation:

The midpoint formula is:

For two given points.

In this case, we can see in the graph the points (1983, 5021) and (1991, 10033)

Then, using the midpoint formula:

Thus, the approximation for the year 1987 is $7527

Considering the given function, it is found that 3000 books were sold after eight months.

The function in this problem is defined as follows:

f(x) = 1000(∛x) + 1000

In which f(x) represents the number of books sold after x months.

After eight months, we have that x = 8, hence the number of books is calculated as follows:

f(8) = 1000(∛8) + 1000

The lone instance of x in the function was replaced by eight to find the numeric value.

The cube root of eight is calculated as follows:

8 = 2 x 2 x 2 = 2³

Hence:

∛8 = 2

Thus the numeric value of the expression is:

f(8) = 1000(∛8) + 1000 = 1000 x 2 + 1000 = 2000 + 1000 = 3000 books.

The graph of the situation is given by the image at the end of the answer, at a domain of x >= 0, as the number of months cannot assume negative values.

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The weekly cost C of producing x units in a manufacturing process is given by

The number of units x produced in t hours is given by

(a) The composite function C(x(t)) is given by

The function C(x(t)) gives us the cost of production for t hours.

(b) The number of units produced in 4 hours is given by

200 units will be produced in 4 hours.

(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000

As you can see, the value of t is 4.75 hours when the cost is $15,000.

Therefore, 4.75 hours must elapse until the cost increases to $15,000.

Answer:

slope = 3/7

Step-by-step explanation:

Locations of points: (-4 , 1) and (3 , 4)

slope = rise / run

between two plotted points this means that:

slope = change in y / change in x

slope = (4 - 1) / (3 - (-4))

slope = (4 - 1) / (3 + 4)

slope = 3/7

The range is the set of y-values of the points given.

The points given are:

{(3, 4), (7,-2), (11, -8)}

The range would be:

4, -2, and -8

Range = {4,-2,-8}

Option C

Answer:

The slope is o.   The line will be vertical and the equation of the line is y = -5

Step-by-step explanation:

Answer:

$33.75

Step-by-step explanation:

22.9% of $43.75 = $10.0

43.75 - 10.0 = $33.75

Hope that helps

Answer:

$35.60

Step-by-step explanation:

I cross multiplied related numbers:

[tex]\frac{43.75}{x}[/tex]=[tex]\frac{122.9}{100}[/tex] cross multiply

4375=122.9x, divide both sides by 122.9

35.598=x round to hundredths

35.60

Answer:

option A

Step-by-step explanation:

put x= 4 in condition 4<=x<8

as it satisfied condition

and put x= 2.1 in condition 2<x<4

Answer:

Sue travels 8 miles per hour.

Step-by-step explanation:

The solution for the given equivalent equation f(2x) is 10.

What is equation?

In mathematics, the term equation can be defined as the two algebraic expression which are equal to each other. This method is used to calculate the values of the parameters in the problems.

According to the question, the given equivalent equation is as follows:

Equivalent equation: f(2x) = 3x + 3 = x + 13

By using the addition-subtraction property, to generate the equivalent equations.

3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5

Now, f(2x) = 2x = 10

Hence, the solution for the given equivalent equation is 10.

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The correct equation is: f(2x) = 3x + 3 = x + 13

Answer:

7n-18

Step-by-step explanation:

The working out is attached. Hope it helps!

The degree of the second term in the polynomial;

is 19

The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Triangle XWY is transformed to produce triangle URL.

Now,

The images arise from transformation should remain the same with respect to the size or shape.

So, we get;

The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

Thus, The correct transformations are;

1. Reflection, then a translation

2. Rotation, then a reflection ​

3. Translation, then a rotation.

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The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.

What do you mean by sum?

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the two numbers be X and Y.

There are two condition given in the question through which we can form a system of equation containing two equations.

First condition: The sum of the numbers is 50.

Therefore,

X + Y = 50

Second Condition: Three times the first is 5 more than twice the second

Therefore,

3X = 2Y + 5

We get the system of equation:

X + Y = 50

3X = 2Y + 5

Solving this system of equation

3X - 5 = 2(50 - X)

3X - 5 = 100 - 2X

X = 105/5

X = 21

Putting the value of X in one of the equation:

Y = 50 - X

Y = 50 - 21

Y = 29

Therefore, two numbers are 21 and 29

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Answer:

Step-by-step explanation:

It should be option D

The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].

We have to complete the given sentence;

The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is ....................  .

we first complete the given sentence then we explain the sentence.

The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

Firstly about Quadratic Polynomial

When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.

Now about Constant Term

A number that is constant and does not have any variables in an algebraic expression is a constant term.

Now about Leading Coefficient

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.

Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].

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Find the scale factor by dividing the real length by the map length. Since Sonoma's house is 5 miles away from Paige's house but they appear 7cm appart in the map, then the scale factor is:

The associative property of multiplication states that you can choose any pair of numbers to multiply first when there are more than two numbers being multiplied. This doesn't change the final result:

a . b . c = (a . b) . c = a . (b . c)

So, we see an example of such property in the first option:

7 . (3 . 5) = (7 . 3) . 5

Let's check this is indeed true:

7 . (3 . 5) = 7 . 15 = 105

(7 . 3) . 5 = 21 * 5 = 105

Therefore, the first option is correct.

Notice that the second option uses the distributive property of multiplication over addition:

a . (b + c) = a . b + a . c

The third uses the commutative property of multiplication:

a . b = b . a

The fourth is wrong since zero multiplied by any number is zero, not one:

0 . a = 0, for all values of a.

Answer

ST = 14

According to the diagram

UV = VW

ST = UT

UT = VT - UV

UV = 14 and VT = 29

UT = 29 - 14

UT = 15

SInce UT = ST, Therefore, ST = 14