Find the value of x.
12
2x
x=

Here books can be arranged in: a) 39,916,800 ways b) 17,280 ways c) 86,400 ways d) 86,400 ways e) 30,240 ways

a) When the books can be arranged in any order, the total number of ways is given by 11!, which is the factorial of the number of books that is 39,916,800 ways. b) We have 2! ways to arrange the group and within the group, the math books can be arranged in 6! ways and the biology books can be arranged in 5! ways which is 17,280 ways.

c) The math books can be arranged in 6! ways, and the remaining books can be arranged in 5! ways that is 86,400 ways. d) If the math and biology books must alternate, we consider them as one group. Within this group, the math and biology books can be arranged in 6! ways that is 86,400 ways.

e) When none of the biology books can be next to each other, we consider the arrangements of the math books and the spaces between them. There are 7 spaces available for the biology books to be placed, and we use the permutation formula 7P5 to calculate the number of arrangements which can be 30,240 ways.

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Answer:

-2x - 1

Step-by-step explanation:

3x - ( -2x - 1 )

=3x + 2x + 1

= 5x + 1

The two non negative real numbers with a sum of 64 that have the largest possible​ product are; 32 and 32.

Let the two numbers be x and y.

Thus, if their sum is 64, then we have;

x + y = 64

y = 64 - x

Their product will be;

P = xy

Putting (64 - x) for y in the product equation we have;

P = (64 - x)x

P = 64x - x²

Since the product is maximum, let us find the derivative;

P'(x) = 64 - 2x

At P'(x) = 0, we have;

64 - 2x = 0

2x = 64

x = 64/2

x = 32

Thus; y = 64 - 32

y = 32

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The two-column proof given below proves that the above statement is true.

For writing a two-column proof, we solve the equation step-by-step, giving an explanation for performing any operation on the equation. This should lead us to the final solution, which can help us check if the given conclusion is true.

        Statement                    Reason          

1. (5x + 1)/2  -  8  = 0              Given

2. (5x + 1)/2 = 8                     Simplification

3. (5x + 1) = 16                       Multiplying both sides with 2

4. 5x = 16 - 1                          Subtracting both sides by 1

5. 5x = 15                              Simplified

6. x = 15/5                             Dividing both sides by 5

7. x = 3                                  Simplified

So, we end up with the result x = 3.

But a solution has to satisfy the equation as well. So by resubstituting,

L.H.S. = [5(3) + 1]/2 - 8

          = [15 + 1]/2 - 8

          = 16/2 - 8

          = 8 - 8

          = 0 = R.H.S.

Thus, we have successfully proved that the given conjecture is correct, by a two-column proof and verification.

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There is no clear question here, however, the plan for the local newspaper, if the plan is long-term, is more comfortable for the consumers, but less comfortable if it is short-term.

Using a sample size of two days.

- For the local newspaper, we have

($5 × 2) + ($12) = $22

- For the rivals, we have

$8 × 2 = $16

Using a sample size of one hundred days.

- For the local newspaper, we have

($5 × 100) + ($12) = $512

- For the rivals, we have

$8 × 100 = $800

Applying the alternate exterior angles theorem, the value of x is: 22.

Angles that are formed outside of two parallel lines that are crossed by a transversal are said to be alternate exterior angles. Each lie alternatively along the transversal that intersects the two parallel lines.

According to the alternate exterior angles theorem any two angles that are alternate exterior angles have angle measures that are equal or congruent to each other.

The angles from the diagram, (5x - 5)° and (6x - 27)°, are alternate exterior angles.

Therefore:

(5x - 5)° = (6x - 27)° [alternate exterior angles theorem]

Solve for x

5x - 5 = 6x - 27

Add 5 to both sides

5x - 5 + 5 = 6x - 27 + 5 [addition property of equality]

5x = 6x - 22

Subtract 6x from both sides

5x - 6x = 6x - 22 - 6x [subtraction property of equality]

-x = -22

-x/-1 = -22/-1 [division property of equality]

x = 22

Therefore, applying the alternate exterior angles theorem, the value of x is: 22.

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The width of the single slit is 0.00135 mm and the second minimum will be at angle of 69.9º.

To find the width of the single slit, we can use the formula:

w = λL/d * sinθ

where w is the width of the single slit, λ is the wavelength of light, L is the distance from the slit to the screen, d is the distance between the slits and θ is the angle at which the first minimum is observed. By substituting the given values, we get:

w = (633*10^-9 m) (2L) / (d) * sin(28.0º) = 0.00135 mm

The angle of the second minimum can be found by using the formula: θn = sin^-1(nλ/w)

where θn is the angle at which the nth minimum is observed, n is the order of the minimum and λ and w are the wavelength and width of the single slit respectively. Substituting the values we get: θ = sin^-1(2*(633*10^-9 m) / (0.0175 mm)) = 69.9º

It is important to note that the above explanation is based on the assumption that the width of the single slit is much smaller than the distance between the slit and the screen (L) and the distance between the slits (d).

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

Rectangle but not a square

Step-by-step explanation:

Let's start by determining if it's a parallelogram.

The slope of side DE is undefined.

The slope of side EF is 0.

The slope of side FG is undefined.

The slope of side DG is 0.

Thia means we have 2 pairs of opposite parallel sides, meaning DEFG is a rhombus.

Now, let's determine if it's a rectangle. Since the slope of

side DE is undefined and the slope of side EF is 0, sides DE and EF are perpendicular. This means that angle DEF is a right angle, and thus DEFG is a rectangle.

To determine if DEFG is a rhombus, we can find the lengths of adjacent sides DE and EF.

The length of DE is 5.

The length of EF is 3.

Since the pair of consecutive sides (sides DE and EF) aren't congruent, DEFG is not a rhombus.

Since DEFG is not a rhombus, it also cannot be a square.

This means DEFG is a rectangle, but not a square.

A because 2 is half of 4 and 18 is half of 36.

Step-by-step explanation: because 2 is half of 4 and 18 is half of 36.

Let W = width then length = 5W + 3  

Area = W(5W + 3) = 5W2 + 3W = 92  

5W2 + 3W - 92 = 0 has a negative root and the positive root = 4 (by the quadratic formula)  

The length = 23 and the perimeter = 2(L + W) 2 * 27 = 54

I dont know if this is right because I cant see the last part in less its like that

The number of students in the entire class is 40.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

From the information given, when eating in the cafeteria at school, 65%, or 26, of the students in the class ate pizza.

Let the total number of people be illustrated as x.

This will be:

65% × x = 26

0.65x = 26

Divide

x = 26/0.65

x = 50

The total students is 40.

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It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.

We are asked the probability that an applicant scores below 552.

Now, using the formula of probability, we get

P(X < 552) = 0.8329

when the mean is given i.e. 460 and standard deviation is given i.e. 80.

Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

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Answer:

2

2 + 6 = 8

4 / 8 = 2

Hope this helps!

Answer:

8

Step-by-step explanation:

if c=4

the new equation would be:

4/2+6

4/2=2

2+6=8

have a nice day :) brainliest pls

Answer:

it is irrational,because the product of an irrational number and a non zero rational number is irrational

Answer:

there is 12 6th graders 30 7th graders and 12 8th graders and 20% is 8th graders please mark brainlyist

Answer:

PV= $925

Step-by-step explanation:

Giving the following information:

Money is borrowed at ​8% simple interest. After one​ year, ​$999 pays off the loan.

To calculate the original value of the loan, we need to use the following formula:

PV= FV/(1+i*n)

PV= 999/(1+0.08*1)

PV= $925

Answer:

A.  The graph that Larry created is a correct representation of his company's charges.

Step-by-step explanation:

The equation for the services charges, y, is made up of the $10 initial service call fee plus $5 times the number of hours, x.

y = 5x + 10

Try any 2 values for x to see if they fits the graph.

x(hr)   y($)

0        10

1         15

4        30

This is the line already drawn on the graph.  Larry did everything correctly, so options B, C, and D are all false/incorrect.

The general solution to the differential equation is y = [-(1/4)x^2 - (1/3)x + (C/4)]^(1/3).

To solve 2yy' + x^2 + y^2 + x = 0 using an appropriate substitution, we can substitute u = y^2. Taking the derivative of u with respect to x, we get du/dx = 2yy'. We can then rewrite the original equation as 2(u^(1/2))(du/dx) + x^2 + u + x = 0.

This is now a separable differential equation, where we can move the u term to the right side and the x terms to the left side: 2(u^(1/2))du/u = -(x^2 + x)dx. Integrating both sides, we get 4/3u^(3/2) = -(1/3)x^3 - 1/2x^2 + C, where C is the constant of integration.

Substituting back u = y^2, we get 4/3y^3 = -(1/3)x^3 - 1/2x^2 + C.

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Answer:

Step-by-step explanation:

y=9x^2-36

=> 9x^2-y-36=0

b^2-4ac

a= 9

b= -1

c= -36

D=y - (4x9x-36)

D=y+1296

-b(+/-) root Dwhole divided by 2a

1+root of y+1296 divided by 18

1+ y + 36 divided by 18

x= y+1+2

x=y+3

The correct answer is:

a. X = data; Y = random variable

In statistics, "data" refers to the collection of observations or measurements made on a particular variable or set of variables. X is typically used to represent the random variable of interest, which is defined before any data is collected.

On the other hand, a statistic is a function of the data that is used to estimate a population parameter or describe some aspect of the data. An estimator is a formula or algorithm used to calculate a statistic based on a sample of data. The values of the estimator when applied to a particular sample are called estimates.

Therefore, X is not an estimator or estimate but rather the random variable being studied, while Y represents the values of X observed in a particular sample, making it a random variable as well.

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The final value theorem cannot be used for the given system output Y(s) = 1 / (s³ + 4s²) because the system is unstable. The correct option is A.

The final value theorem is used to find the steady-state value of a system's output y(t) as t approaches infinity, given the Laplace transform of the output Y(s). The final value theorem states that the steady-state value of y(t) is equal to the limit of s * Y(s) as s approaches 0.

For the final value theorem to be applicable, the system must be stable, meaning that all the poles of the system's transfer function must have negative real parts. In an unstable system, at least one of the poles has a positive real part.

In this case, the system has the transfer function Y(s) = 1 / (s³ + 4s²), which has poles at s = 0 and s = -2. The pole at s = 0 has a zero real part, indicating that the system is unstable.

Therefore, the correct answer is A. The final value theorem cannot be used because the system is unstable.

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Complete question:

The output of a system is Y(s)= 1/ s³+4s². The final value theorem cannot be used:
A. because the system is unstable
B. because there are poles
C. because there are two
D. because there are zeros system is at the imaginary axis poles at the origin at the imaginary axis unstable

After formula for the volume of a cylinder, the increase in water level results in approximately 260 more cubic feet of water in the tank.

The current water level is 10 feet, which is 120 inches. When the water level increases by 2 inches, the new water level will be 122 inches.

The radius of the tank is half of the diameter, which is 30 feet or 360 inches.

The current volume of water in the tank can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height of the water level.

V = π(360²)(120) ≈ 15,465,920 cubic inches

When the water level increases by 2 inches, the new height of the water level is 122 inches.

The new volume of water in the tank can be calculated using the same formula:

V = π(360²)(122) ≈ 15,914,693 cubic inches

The difference in volume between the two levels is:

15,914,693 - 15,465,920 = 448,773 cubic inches

To convert cubic inches to cubic feet, we divide by 1728:

448,773 ÷ 1728 ≈ 259.6 cubic feet

Rounding to the nearest cubic foot, we get:

260 cubic feet

Therefore, the increase in water level results in approximately 260 more cubic feet of water in the tank.

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To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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The nominal scale of measurement is associated with numbers that have no values. So, it is the correct level of measurement that can be used if participants were asked to choose their favorite picture from a set of six.

It is given to us that -

Participants were asked to choose their favorite picture from a set of six

We have to determine the level of measurement to be used for this situation.

Here, we can see that there are no specific values mentioned. The only information that we have are there is a set of six from which the participants have to choose.

For this type of measurement, we have to use Nominal scale of measurement.

Nominal scale of measurement is a level of measurement where numbers are represented as specific "labels" or "tags". These "labels" or "tags" help to classify and analyze an object.

Since the nominal scale of measurement operates on non-numeric values, it is the correct level of measurement that can be used if participants were asked to choose their favorite picture from a set of six.

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The cook can make 30 pizzas using the 144 ounces of tomato sauce available

To determine how many pizzas the cook can make with the available sauce, we'll need to divide the total ounces of tomato sauce by the ounces of sauce used per pizza.
First, we need to convert the mixed number 4\(\frac{3}{4}\) into an improper fraction. To do this, multiply the whole number (4) by the denominator (4) and then add the numerator (3).
4 × 4 = 16
16 + 3 = 19
So, 4\(\frac{3}{4}\) is equivalent to \(\frac{19}{4}\)
Now we can set up our division problem:
\(\frac{144 ounces }{\frac{19}{4}ounces/pizza }\)= number of pizzas
To divide by a fraction, we multiply by its reciprocal:
144 × \(\frac{4}{19}\)= number of pizzas
Multiplying the fractions:
144 × \(\frac{4}{19}\) = \(\frac{576}{19}\) = number of pizzas
Since the cook can only make whole pizzas, we need to round down to the nearest whole number.
576 ÷ 19 = 30 (rounded down)

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Answer:

0.006

Step-by-step explanation:

4/52x4x51=0.0060331825

round=0.006

The probability of randomly drawing a chip number that is smaller than 201 is 0.541

The given parameters are

Plastic chips = 1 to 370

This means that

Chips = 370

There are 200 sections that are smaller than 201

This means that the probability is

P = 200/370

Evaluate

P = 0.541

Hence, the probability of randomly drawing a chip number that is smaller than 201 is 0.541

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Answer:

8%

Step-by-step explanation:

The reason why is his grade is 72% right and it increased to 80%.

Subtract 80 from 72 which equals 8.