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write an equation to represent this function. use function notation.

The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is \(\frac{N!}{n!(N-n)!}\)

=\(\frac{10!}{2!(8)!}\)

=\(\frac{10 \times 9 \times \times 8!}{8! \times 2 !}\)

=45

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Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

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Step-by-step explanation:

you can clarify on that please

Answer:

\(5xy^4\)

Step-by-step explanation:

\(\frac{15x^3y^5}{3x^2y}\)

= \(\frac{3\cdot \:5x^3y^5}{3x^2y}\)

= \(\frac{5xy^5}{y}\)

= \(5xy^4\)

Answer:

I think ( b) is non proportional linear

Answer:

6.25 days

Step-by-step explanation:

The total amount of achers / per acher day

75/12=6.25

The possible first coordinate x with a slope of 3 is equal to -13/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points and slope on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

3 = (4 - 8)/(x + 3)

3x + 9 = -4

3x = -13

x = -13/3

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Answer:

6 3/4 feet

Step-by-step explanation:

Answer:

6 3/4 feet

Step-by-step explanation:

2 1/4 x 3 = 6 3/4

Answer:

The graph increases as it approaches -∞.

The graph decreases as it approaches ∞.

Step-by-step explanation:

f(x) = -x - 2x³ + 3x + 9

f(x) = -2x³ + 3x - x+ 9

f(x) = -2x³ + 2x+ 9

Look at the highest exponent(which is 3).

SInce the highest exponent is odd, that means that the graph approaches infinity in a different direction as per negative infinity. Since the highest exponent has a negative sign:

The graph is going UP as x-values get SMALLER ( To  -∞)

The graph is going DOWN as x-values get LARGER ( To  ∞)

Hence:

The graph increases as it approaches -∞.

The graph decreases as it approaches ∞.

Answer:

Since the degree is odd, the ends of the function will point in the opposite directions.

Odd

(a) False. The number 2 is an integer, and integers are a subset of rational numbers.

Therefore, if 2 is rational, then it is also an integer.(b) True.

The statement is not true. If we assume that is a rational number, it means that it can be expressed as a fraction of two integers, say , where and are integers and ≠ 0. However, this does not imply that 2 is also a rational number.

(b)  If we assume that π is an irrational number, it means that it cannot be expressed as a fraction of two integers. If we take the square root of π, denoted as , it is known that the square root of an irrational number is also irrational unless it is equal to 0.

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Answer:

to find x you will substract 81.9 and 32

81.9-32

the answer will be 49.9

Answer:

9×10

Step-by-step explanation:

Just know that any number in power of zero is equal to one

The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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Answer:

The angle TQS has a value of 23.5º.

Step-by-step explanation:

\(\angle RQS\) and \(\angle PQR\) are supplementary to each other, that is, the sum of angles equals 180º, and ray \(QT\) divides \(\angle RQS\) into two equal parts. We construct this system of linear equations after a careful reading of statement:

\(\angle RQS = (x+1)^{\circ}\) (Eq. 1)

\(\angle PQR = (3\cdot x - 5)^{\circ}\) (Eq. 2)

\(\angle RQS + \angle PQR = 180^{\circ}\) (Eq. 3)

\(\angle RQS = \angle RQT + \angle TQS\) (Eq. 4)

\(\angle RQT = \angle TQS\) (Eq. 5)

Now we proceed to solve the system algebraically:

(Eq. 1) and (Eq. 2) in (Eq. 3)

\((x+1)^{\circ} + (3\cdot x - 5)^{\circ} = 180^{\circ}\)

\((4\cdot x-4)^{\circ} = 180^{\circ}\)

\((4\cdot x)^{\circ} = 184^{\circ}\)

\(x = \frac{184}{4}\)

\(x = 46\)

In (Eq. 1):

\(\angle RQS = 47^{\circ}\)

(Eq. 5) in (Eq. 4):

\(\angle RQS = 2\cdot \angle TQS\)

\(\angle TQS = \frac{1}{2}\cdot \angle RQS\)

\(\angle TQS = \frac{1}{2}\cdot (47^{\circ})\)

\(\angle TQS = 23.5^{\circ}\)

The angle TQS has a value of 23.5º.

Answer:

6 cups of coffee

4 cups of hot chocolate

Step-by-step explanation:

x=number of cups of coffee

y=number of cups of hot chocolate

1.75x+1y=14.5

x+y=10    y=10-x

substitute for y

1.75x+10-x=14.5

0.75x=4.5

x=6

y=10-6=4

Answer:

B) 7/2

Step-by-step explanation:

Answer:

0 years: $0

5 years: $460

10 years: $520

15 years: $580

20 years: $640

Step-by-step explanation:

The measure of arc XZ is 115 degrees and  measure of arc XYZ is 245 degrees

The given circle has a centre W

The measure of central angle is 115 degrees

We have to find the measure of the arc XZ

The central angle is equal to measure of the arc

115 = measure of arc XZ

Arc XZ =115 degrees

We know that the circle has a measure of 360 degrees

So the remaining angle is 360-115 = 245 degrees

The measure of arc XYZ is 245 degrees

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Answer:I believe is $75

Step-by-step explanation:

If you see in the graph is between 50 and 100

50 divided by two is 25 which means

50+25=75

A potential problem that can arise from the continual remodeling of bone matrix is an imbalance between bone resorption and bone formation, leading to weakened or compromised bone structure.

The continual remodeling of bone matrix is a dynamic process in which old bone tissue is resorbed by specialized cells called osteoclasts, and new bone tissue is formed by osteoblasts. This remodeling process allows for the renewal and repair of bone, as well as the adaptation of bone structure to changing mechanical demands.

However, if there is an imbalance between bone resorption and bone formation, it can lead to potential problems. Excessive bone resorption without adequate bone formation can result in a net loss of bone mass, leading to conditions such as osteoporosis, where bones become weak and brittle. On the other hand, excessive bone formation without sufficient bone resorption can lead to abnormal bone growth and density, which may contribute to conditions like osteopetrosis.

Maintaining a balance between bone resorption and bone formation is crucial for healthy bone remodeling. Factors such as hormonal imbalances, nutritional deficiencies, certain medications, and aging can disrupt this balance, leading to potential problems with bone health and structure. Regular monitoring and appropriate interventions are important in managing and preventing these issues.

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Step-by-step explanation:

x = Moe's money

y = Loki's money

z = Nick's money

1/5 x = 1/4 y = 1/3 z (Moe gave 1/5, Loki 1/4, Nick 1/3, but all donations to Ott are the same amount of money).

that also means

y = 4/5 x

z = 3/5 x

in total the group has

x + 4/5 x + 3/5 x = 5/5 x + 4/5 x + 3/5 x = 12/5 x

Ott got 3× 1/5 x (since everybody gave the same amount of money, so it is in sum 3 times of what Moe gave).

so, Ott now has 3/5 x , out of a total of 12/5 x.

his fractional part is therefore

3/5 / 12/5 = 3/5 × 5/12 = 3/12 = 1/4.

he has 1/4 of the group's total money.

Answer:

Step-by-step explanation:

When you multiply radicals together, the only rule that needs to be followed is that the index is the same on both. These are both square roots (so the index is a 2 on each radical) so we can multiply the radicals together to get 5√66.  That does not simplify at all and is irrational (since the decimal goes on without repeating)

The diagonal matrix A' for T relative to the basis \(\(B'\)\) is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find the diagonal matrix A' for the linear transformation T relative to the basis B', we need to perform a change of basis using the given matrix A and basis B'.

Let's denote the standard basis as \(\(B = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}\).\)

To perform the change of basis, we need to find the matrix P such that P[B'] = B.

We can write the vectors in B' as column vectors:

\(\[B' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find \(P\), we solve the equation P[B'] = B for P:

\(\[P \cdot B' = B\]\\\\\P = B \cdot (B')^{-1}\]\)

Calculating the inverse of \(\(B'\)\):

\(\[B'^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now we can calculate \(\(P\)\):

\(\[P = B \cdot B'^{-1} = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right] = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now, the diagonal matrix A' for T relative to the basis B' can be calculated as:

\(\[A' = P^{-1} \cdot A \cdot P\]\)

Calculating\(\(P^{-1}\):\)

\(\[P^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Substituting the values into the equation for \(\(A'\)\):

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Performing the matrix multiplication:

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Calculating the matrix multiplication, we get:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Therefore, the diagonal matrix A' for T relative to the basis B' is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

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Answer:

518

Step-by-step explanation:

P = 2

Q = 8

p3 + 64q

Multiply "p" (which is 2) with 3

Multiply "q" (which is 8) with 8

Add the two numbers you get

And you have you answer

I hope this helps. :)

Answer:

b = 9

Step-by-step explanation:

24b - 10b = 126

so because 24b and 10b are the same you can minus them giving

14b = 126

now we have 14b's but we only want 1

so we divide by both sides

b = 9

Answer:

See below

Step-by-step explanation:

How to solve equations algebraically

To solve equations algebraically, your main goal is to get the variable on one side of the equal sign while getting the constant on the other side of the equal sign.

Its important to remember that

How to move variables and constants to the other side:

We can change the position of a variable/constant regarding which side of the sign it is on by using inverse operations. For example if we have 2x = 7 + x. We would want to get the x on the other side, we can do this by doing the inverse of adding an x which would be subtracting an x. So we would subtract x , but whatever we do to one side we must to do the other, so we would subtract x from both sides resulting us in getting 2x -  x = 7 + x - x which simplifies to x = 7.

Remember these are the operations inverses

We have

( There are some other ones but these are the three main ones )

What are like terms?

Like terms are terms with the same variable and degree. An example of like terms would be 2x and 7x or 8b and 20b. When we see like terms in an equation we combine them ( add them together ). Note that this is only when the like terms are on the same side of the equal sign.

Applying what we just learned to find the answer

We have the equation 24b - 10b = 126

==> First step is to combine like terms 24b and -10b ( 24b - 10b = 14b)

14b = 126

==> next step is to get rid of the "14" on b. 14 is being multiplied by b. The inverse of multiplication is division so to get rid of the 14 we would divide by 14 but whatever we do to one side we must do to the other so we divide both sides by 14. ( 14b / 14 = b and 126 / 14 = 9 )

we are left with b = 9

Answer:

Up 6 over 8, 6/8, or .75/100

Step-by-step explanation:

I'm not sure how to explain it but yeah I'm pretty sure this is it

Answer:

4n+2=15

Step-by-step explanation:

If you count 4 n's and then add 2, the bar is the same length as the 15 bar. ~logic~

Answer:

-13x+5

Step-by-step explanation:

Distributive Property

-4 (2.5x) + (-4)(-1.25) - 3x

Multiply 2.5 by -4

- 10x - 4 * 1.25 - 3x

Multiply -4 by 1.25

- 10x + 5 -3x

Subtract 3x from -10x

-13x + 5

Hope this helped!

Answer:

5-2x=4-2x+4+x=8-x

x=5-8=-3

Answer:

The answer is B. One solution.

The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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