What is the length of the missing side?

(your answer should be in decimal format up to two decimal place OR left as a square root)

Answer:

USSR

US

US

USSR

Step-by-step explanation:

The probability that each of the final rolls is at least as large as the roll preceding it is \(1/6^6\) or 1/46656.

Given data,

A fair die is rolled n times. We have to find the probability that each of the final rolls is at least as large as the roll preceding it.The probability that each of the final rolls is at least as large as the roll preceding it means the probability of getting each number greater than the preceding one. So, there will be no duplicates.

First, find the total possible outcomes on a fair die. The total possible outcomes on a fair die are 6 because the numbers are 1,2,3,4,5,6. The number of possible outcomes for each roll of the die is 6. Then the total number of possible outcomes on the nth roll of a die is\(6^n\). There will be only one possible sequence in which each of the final rolls is at least as large as the roll preceding it. Let's check it from the following table.

Roller 1Roller 2Roller 3Roller 4Roller 5Roller 61-2-3-4-5-6

Here, we got only one sequence 1,2,3,4,5,6 to have each number greater than the preceding one. So, the probability of getting this sequence is \(1/6^6\).

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Answer:

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Answer:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors. 360 is a highly composite number.

Step-by-step explanation:

23 × 32 × 5

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-10}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-2)}}} \implies \cfrac{-18}{1 +2} \implies \cfrac{ -18 }{ 3 } \implies - 6\)

The slope of the given function is -6.

Slope is a value that describes the steepness and direction of a line.

Given are the input and the output value of a function we need to find the slope of the function,

So,

m = y₂ - y₁ / x₂ - x₁

Taking first two ordered pairs,

(-2, 8) and (-1, 2)

So, the slope (m) = 8-2 / -2+1 = 6 / -1 = -6

Hence, the slope of the given function is -6.

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When you convert 5/13 to a decimal, the result is 0.38.

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.

Here,

We can use the division method to solve this question. To get a decimal, simply divide the numerator 5 by the denominator 13:

5 (numerator) ÷ 13 (denominator) = 0.38

When you convert 5/13 to a decimal, you get 0.38 as your answer.

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The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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Answer:

y = (-5/3)x+20

Step-by-step explanation:

Parallel lines have the same slope.

Answer:

336/13 books in 48 months

Step-by-step explanation:

14 books : 26 months

first, find how many books he reads in one month (by dividing the given rate by the number of months)

14 books : 26 months

/26             /26

7/13 books : 1 month

now multiply by the number of months that this problem requires

7/13 books : 1 month

*48               *48

336/13 books : 48 months

Answer:

4 or -4 !

Step-by-step explanation:

edit... isolate the variable, so divide 5 on both sides. then take the absolute value of d which is d. therefore d = 4 or -4! it's both positive and negative because absolute value you set it equal to a positive and negative!

Answer:

12/5

Step-by-step explanation:

4/5 divided by 1/3

=4/5*3/1

=4/5*3

=12/5

Answer:

C. (2x – 1)(2x + 1)

Step-by-step explanation:

4x² – 1 = (2x)(2x) – 1 = (2x – 1)(2x + 1)

The required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

Given equation is y = - 3/4 - 14

this is of the form y = mx + c

on comparing, m= - 3/4

And the points given are x = 0 and y =13

thus as we know that the equation of the line is

y - y₁ = m ( x- x₁ )

On substituting the values mentioned above we see that

y - 13 = - 3/ 4 ( x - 0 )

4 y - 52 = - 3 x

and on rearranging we get :

3x + 4y = 52

Thus the required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

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If the scale factor between the sides is 5, the scale factor between the surface areas will be 25, and the scale factor between the volumes will be 125.

When the scale factor between the sides of a shape is given, the scale factors between the surface areas and volumes can be determined by considering the relationship between the dimensions.

Let's denote the scale factor between the sides as "k."

For surface area:

The surface area of a shape is determined by the square of its linear dimensions. Therefore, the scale factor for the surface area will be k^2. In this case, if the scale factor between the sides is 5, the scale factor between the surface areas will be 5^2 = 25.

For volume:

The volume of a shape is determined by the cube of its linear dimensions. Hence, the scale factor for the volume will be k^3. Given that the scale factor between the sides is 5, the scale factor between the volumes will be 5^3 = 125.

Therefore, if the scale factor between the sides is 5, the scale factor between the surface areas will be 25, and the scale factor between the volumes will be 125.

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Answer:

(6,6)

Step-by-step explanation:

Hope this helps!

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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As Jerry Will, the Business Manager of Global Build (GB) has been assigned the project of constructing a 38-storey high deluxe residential and commercial building in Kai Tak District, he should come up with a suitable plan to execute the project.

Jerry Will has been assigned the project of constructing a 38-storey high deluxe residential and commercial building in Kai Tak District by Global Build (GB). Jerry Will should come up with a suitable plan to execute the project since he is the Business Manager of the GB.

Jerry Will will have to handle several tasks to accomplish the project. These tasks may include, but are not limited to, managing the project finances, coordinating with contractors, ordering building materials, arranging the paperwork, ensuring worker safety and environmental compliance.

Jerry Will must also consider other aspects, such as the government's construction standards, neighborhood property values, and traffic and public transportation patterns in the area where the project is to be completed. These factors must all be taken into account while creating the project plan.

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In the Fitzhugh- Nagumo model the values of the v for the electric impulse model are 1 and a.  

The electric impulse is the bitsy electric signal, which is  transferred along a medium.  

The  discriminational equation for the electric  eventuality in a neuron is given as,

\(dv/ dt = - v [ v^{2} - (1 + a)v +a]\)

 Then, a will be a positive constant to such an extent that

  Where, dv/ dt =  0. the value of v has to be find out.   Put this value in the below equation,

0 < a < 1

 At the below equation as,  

\(dv/ dt = - v [ v^{2} - (1 + a)v +a]\)

\(-v[v^{2} - (1 + a)v+a] =0\\-v[v^{2} -v-va+a]=0\\-v[v(v-1)-a(v-1)]=0\\-v[(v-1)(v-a)]=0\)

Equating all the factors equal to zero we get,  v =  0, 1,

and In this manner, the values of the v for unchanging v are,1 and.

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11)The Maclaurin series for \(f(x) = (1+x)^2\) is:  f(x) = Σn=0 (1/[(n+1)(n+2)]) \(x^n\)

12)The Maclaurin series for f(x) = 1+x is:\(f(x) = 1 + 2x + 3x^2 + 4x^3 + ..\).

11)To use the binomial series to find the Maclaurin series for the function \(f(x) = (1+x)^2\).

The binomial series is given by:
\((1+x)^r\) = Σn=0 (r choose n) \(x^n\)
where (r choose n) is the binomial coefficient.
Substituting r=2 into the formula gives:
(1+x)^2 = Σn=0 (2 choose n) x^n
= Σn=0 (2!/n!(2-n)!) x^n
= Σn=0 (1/[(n+1)(n+2)]) x^n
Therefore, the Maclaurin series for \(f(x) = (1+x)^2\) is:
f(x) = Σn=0 (1/[(n+1)(n+2)]) \(x^n\)
12)To use the binomial series to find the Maclaurin series for the function f(x) = 1+x.

The binomial series is given by:
\((1+x)^r\) = Σn=0 (r choose n) x^n
Substituting r=1 into the formula gives:
(1+x)^1 = Σn=0 (1 choose n) \(x^n\)
= Σn=0 \(x^n\)
Therefore, the Maclaurin series for f(x) = 1+x is:
f(x) = Σn=0 \(x^n = 1 + x + x^2 + x^3 + ...\)
However, the given answer is not correct. The correct Maclaurin series using the binomial series for f(x) = 1+x is:
f(x) = Σn=0 [(n+1) choose n] \(x^n\)
= Σn=0 [(n+1)!/(n!1!)] \(x^n\)
= Σn=0 (n+1) \(x^n\)
=\(1 + 2x + 3x^2 + 4x^3 + ..\).
Note that this is an infinite series and includes all powers of x.

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For a z-score, We  transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions i.e. D.

What exactly is the z-score?

The z-score is a statistical measurement that describes a value's relationship to the mean of a collection of values. The z-score formula is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Mean:- The sum of a collection of numbers divided by the total number of numbers in the set is known as the arithmetic mean, sometimes known as the arithmetic average or simply the mean or average. A survey, experiment, or observational research is usually used to create the collection.

Now,

As Z-scores are standardized scores that identify and define each score's exact placement within a distribution. We may conduct meaningful comparisons of z-scores across various samples or groups by converting our data (raw score).

hence,

          We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions.

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Money invested by a man = $10,500

No.of years for which he invested his money = 7

Rate of interest = 5.5%

We know that :

\( \tt \: Simple \: interest = \frac{Principal × Rate × Time}{100} \)

Principal = 10500

Rate = 5.5%

Time = 7 years

Simple interest the man payed :

\( = \tt\frac{10500 \times 55 \times 7}{10 \times 100} \)

\( = \tt \frac{4042500}{1000} \)

\( \color{plum}=\tt 4042.50\)

Therefore, the simple interest payed by the man = $4042.50

Money invested by the man (principal) = $10,500

The simple interest he payed = $4042.50

We know that :

\(\tt \: amount = principal + interest\)

The amount the man collected after a period of 7 years :

\( = \tt10500 + 4042.50\)

\( =\tt 14520.50\)

Thus, amount = $14520.50

Therefore the amount he collected after a period of 7 years = $14520.50

The required answer is a vector in R^5, then we would set b = 5.

To determine the values of a and b in the linear transformation defined by T(x) = Ax, we need to consider the dimensions of the matrix A and the vector x.

We know that A is an 8x9 matrix, which means it has 8 rows and 9 columns. We also know that x is a vector in R^a, which means it has a certain number of components or entries.
The matrix A has 8 rows and 9 columns, which means it maps 9-dimensional vector to 8-dimensional vectors .
To ensure that the matrix multiplication Ax is defined and results in a vector in R^b, we need the number of columns in A to be equal to the number of components in x. In other words, we need 9 = a and b will depend on the number of rows in A and the desired output dimension of T(x).

Therefore, a = 9 and b can be any number between 1 and 8, inclusive, depending on the desired output dimension of T(x). For example,

if we want T(x) to output a vector in R^5, then we would set b = 5.

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2sec²x/(2-sec²x) is the equivalent equation of 2sec(2x).

The equation that has one or more trigonometric ratio with known and unknown angles. From the equation we can determine the unknown value.

Two trigonometric equations are called equivalent equation to each other when both have same values of variables.

2sec(2x) = 2/cos2x= 2/(cos²x-sin²x)

2/{cos²x-(1-cos²x)= 2/{2cos²x-1}

2/{2/sec²x-1}= 2sec²x/(2-sec²x)

hence, the above is the equivalent equation.

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Answer:

The answer is

\( \huge y - 5 = 23(x + 4) \\ \)

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question the points are (-4, 5) and a slope of 23

We have the final answer as

\(y - 5= 23(x + 4)\)

Hope this helps you

Answer:

hi how r u

Step-by-step explanation:

Answer:

  3x -2y -4z +2

Step-by-step explanation:

As the Order of Operations tells you, start with the inner brackets and work outward. Per the distributive property, a minus sign in front of brackets changes the sign of every term inside.

  2x -{y +3z -[x +3 -(2 +y) -4] +[-3z -5] +4z}

  = 2x -{y +3z -[x +3 -2 -y -4] -3z -5 +4z}

  = 2x -{y +3z -[x -y -3] -3z -5 +4z}

  = 2x -{y +3z -x +y +3 -3z -5 +4z}

  = 2x -{-x +2y +4z -2}

  = 2x +x -2y -4z +2

  = 3x -2y -4z +2

Joe score above the mean is 1.65.

A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilises the sum of the series' values, and the geometric mean method, which uses the average of a group of products.

Nonetheless, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.

Given that, Joe got a score of 81.75, the class average was 71 and the standard deviation is 6.5.

So the Joe Scores above the mean is

(81.75 - 71)/6.5

= 10.75/ 6.5

= 1.65

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Answer:

489,100

Step-by-step explanation:

489,147.2547

489,100