Which is the simplified form of the expression StartFraction (6 Superscript negative 4 Baseline) Superscript negative 9 Baseline Over 6 Superscript 6 Baseline EndFraction? StartFraction 1 Over 6 Superscript 42 Baseline EndFraction StartFraction 1 Over 6 Superscript 19 Baseline EndFraction 6 Superscript 6 6 Superscript 30

The limit lim x → n − ⌊ x ⌋ is equal to n because the floor function ⌊ x ⌋ approaches n from values less than n as x approaches n from the left.

To evaluate the limit lim x → n − ⌊ x ⌋, we need to understand the concept of the floor function ⌊ x ⌋. The floor function returns the largest integer that is less than or equal to x. For example, ⌊3.7⌋ = 3 and ⌊-2.5⌋ = -3.

When we take the limit as x approaches n from the left (denoted by the minus sign in x → n − ⌊ x ⌋), we are essentially asking what happens to the function as x gets closer and closer to n from values less than n. Since n is an integer, the floor function ⌊ x ⌋ will always be equal to n when x is between n and n+1. Therefore, as x approaches n from the left, ⌊ x ⌋ will approach n.

So the limit lim x → n − ⌊ x ⌋ is equal to n. This makes sense intuitively, as we are essentially taking the integer part of a number that is very close to n from values less than n, so it would make sense for the integer part to be equal to n itself.

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There are 176,851 ways to assign the 100 pages to the four printers.

Since there are no restrictions on how many pages a printer can print, we can think of this problem as distributing 100 identical pages among 4 distinct printers. This is an example of a "balls and urns" problem, which can be solved using the stars and bars formula.

The stars and bars formula states that the number of ways to distribute k identical objects among n distinct containers is:

C(k+n-1, n-1)

where C represents the combination function. In this case, we have k = 100 identical pages and n = 4 distinct printers. Therefore, the number of ways to assign the pages to the printers is:

C(100+4-1, 4-1) = C(103, 3) = 176,851

So there are 176,851 ways to assign the 100 pages to the four printers.

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Answer:

385

Step-by-step explanation:105÷3=35 35×11=385

Answer:

Last year we had M students.

This year we have N students.

Now, the question ask "by what percentage the number of students grow".

So we are considerating a growth, this means that we must think that M as the 100%.

Then we have that N - M is the difference between the students of last year and this year.

this means that this year we have N - M more students that last year, so the percentage of growth is:

((N - M)/M)*100%

Now you need to replace the values for N and M.

You also can notice that if N is smaller than M, you will have a negative percentage, this means that instead of a growth, we have a decrease in the number of students.

A=148°

B=148°

Step-by-step explanation:

180-38=148°

because A and B are equal, they're both 148°

Answer: x < -8/15

Step-by-step explanation: i took the test, I hope this helps! :)

Answer:

1)D

2)A

Step-by-step explanation:

1)\(-7a-2x+5a-6x\\-7a+5a-2x-6x\\-2a-8x\)

The last choice is the correct answer.

2)

\(16bc-8ab=8b(2c-a)\)

The answer is the first choice

PLEASE MARK ME AS BRAINLIEST

Answer:

mean that your number cold promble be thorugh 12-100 to equal defined the varible to number is an futions of intrution grade promage

The expected one-period return for the asset is given by the expression 0.0675 + 0.045 + 0.03 + 0.04p + 0.04, where 'p' represents an unknown probability.

The given probability distribution represents the one-period return for an asset, with corresponding probabilities assigned to each return value. To find the expected one-period return, we need to calculate the weighted average of the returns, where the weights are the probabilities.

Let's calculate the expected one-period return step by step:

1. Multiply each return value by its corresponding probability:

  0.27 * 0.25 = 0.0675

  0.18 * 0.25 = 0.045

  0.10 * 0.30 = 0.03

  p * 0.04 = 0.04p

  0.20 * 0.20 = 0.04

2. Sum up the products calculated in step 1:

  0.0675 + 0.045 + 0.03 + 0.04p + 0.04

3. Set the sum equal to the expected one-period return, denoted as E(R):

  E(R) = 0.0675 + 0.045 + 0.03 + 0.04p + 0.04

Therefore, the expected one-period return of the asset is 0.0675 + 0.045 + 0.03 + 0.04p + 0.04.

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To find the absolute maximum and absolute minimum of the function f(x,y) = 2x^2 - 4x + y^2 - 4y +1 on the closed triangular plate bounded by the lines x = 0,y = 2,y = 2x in the first quadrant, we need to consider the critical points and the boundary of the plate.

First, we find the critical points of the function by taking the partial derivatives with respect to x and y and setting them equal to zero:

fx = 4x - 4 = 0
fy = 2y - 4 = 0

Solving these equations, we get the critical point (1,2).

Next, we need to consider the boundary of the plate. The boundary consists of three line segments:

1. The line segment from (0,0) to (0,2), given by y = 2x.
2. The line segment from (0,2) to (1,2), given by x = y/2.
3. The line segment from (1,2) to (0,0), given by y = -2x + 2.

We need to evaluate the function at the endpoints of each of these line segments and at any additional critical points that lie on the boundary.

Endpoint 1: (0,0)
f(0,0) = 1

Endpoint 2: (0,2)
f(0,2) = 5

Endpoint 3: (1,2)
f(1,2) = -1

Critical point on the boundary:
x = y/2, y = 2
Substituting y = 2x into the function, we get
f(x,y) = 2x^2 - 4x + 4 - 8x + 1
= 2x^2 - 12x + 5
Taking the derivative with respect to x and setting it equal to zero, we get
fx = 4x - 12 = 0
Solving for x, we get x = 3/2. Substituting this back into y = 2x, we get y = 3.
So the critical point on the boundary is (3/2,3), and
f(3/2,3) = 1/4.

Comparing the values of the function at the critical points and the endpoints of the boundary, we see that the absolute maximum is 5 and occurs at (0,2), while the absolute minimum is -1 and occurs at (1,2).

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Answer:

beleive its 35

Step-by-step explanation:

Answer:

The mode hear is 32

Step-by-step explanation:

The mode is the number seen the most in a selected group.

Here is a Mnemonic to help remember what the 3 M's are:

'Hey diddle, diddle

the medians in the middle

add and divide for the mean

the mode is the one that you see the most

and the range is the difference between'

Answer:

1.5

Step-by-step explanation:

To find the mean, we must add all of our terms, and then divide by the number of terms.

\(1.8+1.7+1.3+1.1+1.2+1.6+1.8\)

Solve:

\(1.8+1.7+1.3+1.1+1.2+1.6+1.8=10.5\)

Since we have seven terms, we must divide our total (\(10.5\)), by seven.

\(10.5\) ÷ \(7\)

Solve:

\(10.5\) ÷ \(7=1.5\)

Therefore, the mean is \(1.5\)

Answer:

1.5

Step-by-step explanation:

mean=sum of the terms/no of terms

mean= 1.8+1.7+1.3+1.1+1.2+1.6+1.8 /7

mean=10.5/7

to remove the decimal point, multiply 10 in both numerator and denominator since there is  one digit after the decimal point in 10.5

mean=10.5×10/7×10

mean=105/70

mean=3/2

mean=1.5

hope it helps you!

Answer:

The number of times a variable appears in a date set is called a constant.

Answer:

$ 175

Step-by-step explanation:

Create an equation:

5000 = ax + 2900

a > 75

x = 12 months

5000 = 12a + 2900

12a = 2100

a = 175

Answer:

Muscular strength and muscular endurance

Step-by-step explanation:

you are using strength to push up your body and you are using the muscular endurance because you are doing it over and over again

Researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

a. The wordings of the questions contain the word "destroyed" and "80 acres per minute," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

b. The question contains the phrase "vanishing tropical forests," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

c. The question is loaded with the phrase "man-made extinction of animal and plant species," hence, the respondents could lean more towards the idea of the need to prevent it. The question is likely to elicit responses directed toward prevention and preservation.

d. The question contains the phrase "changes in the earth’s atmosphere," which suggests a link between the destruction of tropical forests and changes in the earth’s atmosphere. The question is likely to elicit responses that lean towards agreeing with the statement made in the question. 

Therefore, researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

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Answer:

Step-by-step explanation:

The true number sentence is the third option:

6.8*1.3 = 8.84

Here we have number sentences of the form:

A*B = C

This is true only when the value of the product A*B is equal to the value of C.

One key thing to identify the correct one is remembering the rule of signs:

(+)*(-) = (-)

(+)*(+) = (+)

(-)*(+) = (-)

(-)*(-) = (+).

The only option that meets that rule is:

6.8*1.3 = 8.84

Where the product of two positive numbers gives another positive number (and the equality is true) so we conclude that this number sentence is true.

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The position of the mass in the undamped spring-mass system can be represented by the equation u(t) = (A cos(ωt) + B sin(ωt)) / k. Therefore, position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

In this case, the external force acting on the system is 108 cos(4t) lb. To determine the position of the mass, we need to solve the differential equation that represents the motion of the system.

Using Newton's second law, F = ma, and considering that the mass m = 24 lb, the equation becomes:

24 * d^2u/dt^2 = 108 cos(4t)

Simplifying, we have:

d^2u/dt^2 = 4.5 cos(4t)

This is a second-order linear homogeneous differential equation with a constant coefficient. The solution to this equation will be a linear combination of the homogeneous and particular solutions.

The homogeneous solution, representing the free oscillation of the system, is u_h(t) = C1 cos(2t) + C2 sin(2t).

The particular solution, representing the forced motion caused by the external force, can be assumed in the form u_p(t) = A cos(4t) + B sin(4t).

By substituting u_p(t) into the differential equation, we can determine the values of A and B.

Solving the differential equation for the particular solution, we find:

A = 18 and B = 0

The complete solution for the position of the mass in feet is:

u(t) = (18 cos(4t)) / 4

Simplifying further, we get:

u(t) = 4.5 cos(4t)

Therefore, the position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

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Given that the area of the floor in Robert's square bedroom is \(49 m²\). To find the length of his bedroom, We know that the area of the square = side × side .

Area of the floor in Robert's bedroom = \(49 m²\)∴

Side of the square =\(√49\)

= 7m Therefore, the length of his bedroom is 7 meters. The length of the Robert's bedroom is 7 meters.

Note: It is important to note that the area of a square is given by A = \(side²\). We can calculate the side of the square by taking the square root of the area of the square i.e side = \(√A.\)

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Answer:

Inequality Form:

X ≥ 7

Interval Notation:

[ 7 , ∞ )

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

X ≥ 7

Interval Notation:

[ 7 , ∞ )

i think its this

In theory, Option D. All of these stages occurs at prisoner classification.

Prisoner classification occurs during transfer, in preparation for release, and after problems occur. All of these stages are important for assessing an inmate's risk and providing appropriate security.

Prisoner classification involves assessing an inmate's risk level and providing an appropriate security level based on the results. This assessment is conducted during various stages, such as during transfer to another institution, in preparation for release, and after the inmate encounters problems. The classification process may involve evaluating an:

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Answer:

$66,646.40 is the answer

Step-by-step explanation:

75% of the men professors are tenured.

Let's assume there are 100 professors at the university for easier calculations. Given that 60% of the professors are women, we have 60 women professors.

Given that 70% of the professors are tenured, we have 70 tenured professors.

Since 90% of the professors are women, tenured, or both, we can calculate the total number of professors who are women or tenured or both:

90% of 100 professors = 0.9 * 100 = 90 professors

Since we know that 60 of them are women, we can subtract that from the total to find the number of tenured professors who are not women:

90 professors - 60 women professors = 30 tenured professors who are not women

Now, let's calculate the number of men professors:

Total professors - Women professors = Men professors

100 professors - 60 women professors = 40 men professors

Out of the 40 men professors, 30 of them are tenured. Therefore, the percentage of men who are tenured is:

(30 tenured men / 40 men professors) * 100% = 75%

Therefore, 75% of the men professors are tenured.

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None of the options are correct. And the given triangle is a right-angle triangle.

Given that,
Which of the following statements justifies why the triangle shown below is not a right triangle is to be determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
A triangle that follows the Pythagoras theorem, are right an angles triangle,
For the given triangle,?
13² = 4² + 12²
169 = 25 + 144
169 = 169
So, the given triangle holds the property of Pythagoras' theorem,

Thus, None of the options are correct. And the given triangle is a right-angle triangle.

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Answer:

Step-by-step explanation:

you can complete the square or use a calculator online that does it for you.

the equation is in the for y = a(x-h)^2 + k

it should be y = (x + 3)^2 + 3

Answer:

The correct answer is \(y = - (x - 3)^{2} +21\).

Step-by-step explanation:

To solve this equation (y = \(-x^{2} +6x + 12\)), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve \(y = -x^{2} +6x - 9 + 12\).

Then, you want to add the -9 to the other side of the equation to get \(y - 9 = -x^{2} + 6x - 9 + 12\).

Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with \(y - 9 = -(x^{2} -6x+9) + 12\).

Now, we use an identity in algebra that is difference of two squares identity. This says that \(a^{2} -2ab +b^{2} =(a-b)^{2}\).

So, we will then factor the trinomial -\(x^{2} -6x+9\) to get \(-(x-3)^{2}\). Our new and updated equation is \(y-9 = -(x-3)^{2} +12\).

Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us \(y = -(x-3)^{2} +21\).

This is our final equation.

Answer:

48º

Step-by-step explanation: