How do you solve this equation: 2n=4x+2y;y?

Answer:

The amount of steel used = 94.38 \(m^{2}\)

Step-by-step explanation:

Height of the tank = 4.5 m.

Diameter of the tank = 4.2 m.

But,

radius = \(\frac{diameter}{2}\)

           = \(\frac{4.2}{2}\)

radius  = 2.1 m

Total surface area of a cylinder = 2\(\pi\)rh + 2\(\pi\)\(r^{2}\)

                                      = 2\(\pi\)r(r + h)

                                      = 2 x \(\frac{22}{7}\) x 2.1 (2.1 + 4.5)

                                      = 44 x 0.3 (6.6)

                                      = 87.12

Total surface area of a cylinder = 87.12 \(m^{2}\)

Since \(\frac{1}{12}\) of the steel was wasted, then;

\(\frac{1}{12}\) x 87.12 = 7.26 \(m^{2}\)

Actual area of steel sheet used = 87.12 + 7.26

                                                     = 94.38 \(m^{2}\)

Thus, 94.38 \(m^{2}\) of steel was used in making the tank.

The relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.

The relation of equipotence is an **equivalence relation** on the collection 2x, which represents all subsets of set x. The equivalence class of a set, with respect to the relation of equipotence, is known as the **cardinality** of the set.

An equivalence relation is a relation on a set that satisfies three properties: reflexivity, symmetry, and transitivity. Let's explore how the relation of equipotence satisfies these properties.

1. Reflexivity: For any set A in 2x, A is equipotent to itself. In other words, any set is equivalent to itself in terms of its cardinality. This satisfies the reflexivity property of an equivalence relation.

2. Symmetry: If set A is equipotent to set B, then set B is equipotent to set A. The notion of equipotence does not depend on the order or arrangement of elements within sets. So, if A has the same cardinality as B, then B also has the same cardinality as A. This satisfies the symmetry property.

3. Transitivity: If set A is equipotent to set B, and set B is equipotent to set C, then set A is equipotent to set C. If two sets have the same cardinality and one of them has the same cardinality as a third set, then the first set is also equipotent to the third set. This satisfies the transitivity property.

As a result, the relation of equipotence on 2x fulfills all the requirements of an equivalence relation. Each equivalence class, or set of sets, formed by this relation represents the sets that share the same cardinality.

The cardinality of a set is essentially a measure of the "size" or "number of elements" in that set. It is represented by a non-negative integer. For example, if set A has three elements, its cardinality is 3. The equivalence class of set A, with respect to the relation of equipotence, would consist of all sets that have the same cardinality as A, that is, all sets with three elements.

In summary, the relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.

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Now

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer:

Explainations to part A is written below.

Part B : x = 25 is the solution as length cannot be negative.

Step-by-step explanation:

Hey there, it's pretty simple!

The formula for the volume of a cube is

Volume = Length × Width × Height.

Let's assume length = x, height = 2x - 30, and width as 10

also note that volume is 5000, plugging this into the equation, we get

(x)(10)(2x - 30) = 5000

10x (2x-30) = 5000

x(2x-30) = 500

(this is how they got 500 and hence the -500 when we shift this to another side to create a quadratic equation).

2x^2 - 30x = 500

2x^2 - 30x - 500 = 0

Part b)

Factoring 2(x^2 - 15x - 250) = 0, we get

2 (−25) (+10)

tadah!

The antenna is approximately 104.6 feet tall and the distance between anchor 2 and the base of the antenna is approximately 66.3 feet.

Let's denote the height of the antenna as h and the distance between anchor 2 and the base of the antenna as x. We can use trigonometry to create two equations based on the angles α and β:

tan(α) = h / (54 - x)

tan(β) = h / x

We can rearrange the first equation to get h = (54 - x)tan(α), and we can rearrange the second equation to get h = xtan(β). We can then set these two expressions for h equal to each other and solve for x:

(54 - x)tan(α) = xtan(β)

54tan(α) - xtan(α) = xtan(β)

54tan(α) = xtan(α) + xtan(β)

54tan(α) = x(tan(α) + tan(β))

x = 54tan(α) / (tan(α) + tan(β))

Now that we have the value of x, we can substitute it back into one of the equations to find the height of the antenna:

h = (54 - x)tan(α) ≈ 104.6 feet

We can also substitute x into the equation for the distance between anchor 2 and the base of the antenna:

x = 54tan(α) / (tan(α) + tan(β)) ≈ 66.3 feet

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Answer:

Graph D

Step-by-step explanation:

it has the longest space

Answer : 1/2 gallon

Explanation:

There were a total of 5 gallons collected, as the question states.

There are 3 x's above 1/4, 2 x's above 3/8, 4 x's above 5/8 and 1 x above 1. This is a total of

3+2+4+1 = 10 x's. This means there were 10 trees.

If 5 gallons is evenly distributed among 10 trees, this would give us the ratio 5/10, which simplifies to 1/2 gallon per tree.

....this answer is not from me. The same question was asked on brainy and I've copy pated it, it is the right answer tho. Credit goes to "MsEHolt" for answering.

Answer:

Reuben will have to pay $19,183.77 when he starts to pay the loan off after 3 years.

Step-by-step explanation:

There are 3 important parts to this equation:

1) 16,902

2) 4.5%

3) 3 years

First, let's find the interest rate in decimal form. This is easy enough to do.

take the interest rate (4.5%) and divide by 100. You can do this in your head by moving the decimal point but I will just write it out for the example:

4.5/100 = 0.045

Now that we have that number. we want to get the dollar amount for the interest. this is done by taking the loan amount and multiplying it by the decimal form of the percentage:

16,902 * 0.045 = 760.59

Since the interest rate is NOT compounding the rest is simple.

760.59 * 3 = 2,281.77

2,281.77 + 16902 = 19,183.77

Hope this helps.

Answer:

x= -11

Step-by-step explanation:

Rearrange terms

\(-1=\frac{5+x}{6} into -1=\frac{x+5}{6}\)

Multiply all terms by the same value to eliminate fraction denominators

\(-1=\frac{x+5}{6} \\6(1)=6(\frac{x+5}{6} )\)

Cancel multiplied terms that are in the denominator

\(6(-1)=6 (\frac{x+5}{6} )6(-1)=x+5\)

Multiply the numbers

\(6(-1)=x+5\\-6=x+5\)

Subtract 5 from both sides of the equation

\(-6=x+5\\-6-5=x+5-5\)

Simplify

Subtract the numbers

Subtract the numbers

Move the variable to the left

Answer:

B: -18 ÷ 3

Step-by-step explanation:

-18 because 1/4 is closer to 18

3 because 2/3 is closer to 3 than 2

Hope This helps! (Edgenunity Sucks!)

Answer:

She can either have 7 sweets or 17 sweets.

Step-by-step explanation:

Variable x = number of sweets Pat has

x < 20

Counting by 5's (5, 10, 15) that will result in 2 left over (5 + 2, 10 + 2, and 15 + 2). This leaves 3 possible options as to how many sweets Pat has: 7, 12, and 17.

Counting by 2's (2, 4, 6 . . . 18) that will result in 1 left over (6 + 1, 10 + 1, 16 + 1) This leaves 2 possible options, given the other numbers from counting by 5's were eliminated.: 7 and 17.

The correct option is b) 7.888. The number of people in the museum is at a maximum at time t ≈ 7.888 hours using Newton-Raphson method.

To find the time t when the number of people in the museum is at a maximum for 1 < t < 11, we need to find the maximum value of the net rate of people entering the museum, which is the difference between the rates of people entering and leaving the museum.

Given the functions f'(t) = 380(\(1.02^t\))(t – 4) and g'(t) = 240 + 240 sin t, let's define a new function h(t) representing the net rate of people entering the museum:

h(t) = f'(t) - g'(t)

Now, we need to find the critical points of h(t) to locate the maximum value. To do this, we will find the derivative of h(t) and set it equal to 0.

h'(t) = f''(t) - g''(t)

To find the second derivatives, we differentiate f'(t) and g'(t) with respect to t:

f''(t) = 380(\(1.02^t\))(1 - 4t + \(t^2\))
g''(t) = 240 cos t

Now, we find h'(t):

h'(t) = 380(1.02^t)(1 - 4t + \(t^2\)) - 240 cos t

Set h'(t) = 0 and solve for t within the interval 1 < t < 11:

380()(1 - 4t + \(t^2\)) - 240 cos t = 0

This equation is transcendental and is best solved using a numerical method such as the Newton-Raphson method. Using a calculator or software, we find the approximate value of t as:

t ≈ 7.888

Therefore, the correct option is b) 7.888, the number of people in the museum is at a maximum at time t ≈ 7.888 hours (Option B).

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The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.

The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.

Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.

The following formula gives the likelihood that we will discover a value for X between c and d,

\(P(c\leq X\leq d)=\frac{d-c}{b-a}\)

Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.

Then,

\(P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%\)

The answer is 14.29%.

The complete question is -

The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?

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The graph of the linear equation is on the image at the end,

Here we want to graph the linear equation:

y = k*x + 5

We know that this line passes through the point (-6, 14), replacing these values we will get:

To graph it, we need to find another point on the line, evaluating in x = 0 we will get:

y = k*0 + 5

y = 5

So we also have the point (0, 5)

Now you just need to graph the two points (-6, 14) and (0, 5) and draw a line that connects them.

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Answer:

s = 3

Step-by-step explanation:

s+3 = 2(s)

s+3 = 2s

s = 3.

This question is an example of mid-segment theorem. You take the segment given and you multiply the small segment by 2 and make the small segment equal to the larger segment.

Which of the following tests would be administered to see if the percentage of votes in a city’s mayoral election matches what is being reported by the local newspaper?

Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions

Answer:

5(3)^(n-1)

a*b^n

5 is the second value (n-1), so a=5

the amount triples (*3) every minute, so b=3

D, or an = 5(3)^n-1, is correct!

Let’s break this down...

5 is the number of files that we have in the first minute. The 3 triples the 5. Since there is an exponent, the growth is exponential and will always triple the product before it.

Hope this helps :)

Answer:The answer would be 20 books divide 15 \ 1.50 equals 10 then multiply 10 by 2

Step-by-step explanation:

The number of books sold by Holly and Ethan to get a profit of $30 will be 20.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Holly and Ethan decide to sell some of their books at a flea market. The booth rental costs $15, and they will sell each book for $1.50.

The number of books will be calculated as,

1.5x = 30

x = 30 / 1.5

x = 20

Therefore, the number of books sold by Holly and Ethan to get a profit of $30 will be 20.

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Answer:

B

Step-by-step explanation:

250*.16=40

250*.36=90

250*.16=40

250*.32=80

40+90+40+80=250

Answer:

A(-2/3)

B(-1/6)

C(1/2)

D(4/3)

Step-by-step explanation:

There are 6 tics in each section.

That means each tic is 1/6

A(-4/6) -> (-2/3)

B(-1/6)

C(3/6) -> (1/2)

D(8/6) -> (4/3)

His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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Answer:

One factor of the polynomial is (x+1) . which expression represents the other factor, or factors, of the polynomial 2x^2 + 3x+1?

Factors means splitting one value in multiplicative values like if we take an equation like 2x^2 + 3x + 1

Then we can divided these equation in two parts like

2X^2 + 3x +1

= 2x^2 + 2x+x+1

= 2x^2+x+2x+1

=x(2x+1)+1(2x+1)

= (2x+1)(x+1)

So if again we multiply these two factor it will give 2x^2+3x+1 so form here we can say that (2x+1) and (x+1) are the two factors of 2x^2 + 3x+ 1

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Disclaimer: the question was given incomplete on the portal. Here is the Complete Question.

Question: One factor of a polynomial is (x+1) . which expression represents the other factor, or factors, of the polynomial 2x^2 + 3x + 1 ?

Your question was incomplete. Please refer the content below:

One factor of a polynomial is (x+1) . which expression represents the other factor, or factors, of the polynomial 2 x² + 3 x + 1 ?

We get that if one factor of the polynomial 2 x² + 3 x + 1 is (x+1), then the other factor is (2x+1).

Factor means that we have to split an expression into multiple values and make the power of the variable linear.

For a quadratic equation, there will be 2 factors.

We have the polynomial

2 x² + 3 x + 1

Using middle term splitting, we get that:

= 2 x² + 2 x + x + 1

Taking common factor:

= 2 x ( x + 1) + 1 (x + 1)

= (2 x + 1)( x + 1)

Therefore, we get that if one factor of the polynomial 2 x² + 3 x + 1 is (x+1), then the other factor is (2x+1).

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Answer:

It is D and if you don't the y-values increase by 9.

Answer:

Nanda would take 60 minutes to complete the job alone.

Step-by-step explanation:

Let's say the amount of work required to finish the job is 'x'

If we call the speed of Trisha "T", of Mona "M" and of Nanda "N", we have that:

x = T * 80 -> T = x/80

x = M * 120 -> M = x/120

If Trisha and Mona worked together for 30 minutes, we can write that the amount of work completed is:

(T + M) * 30

Then, they 3 completed the work after 10 minutes, so we have that:

(T + M) * 30 + (T + M + N) * 10 = x

30T + 30M + 10T + 10M + 10N = x

40T + 40M + 10N = x

Replacing T by x/80 and M by x/120, we have:

40x/80 + 40x/120 + 10N = x

x/2 + x/3 + 10N = x

10N = x - x/2 - x/3

10N = (6x - 3x - 2x)/6

10N = x/6

N = x/60 -> x = N * 60

So Nanda would take 60 minutes to complete the job alone.

Answer:

the answer is b

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

what r the option and its regular 2

Answer:

y-axis

Explanation:

Quadrant I: ( + , + )

Quadrat II: ( - , + )

Quadrant III: ( - , - )

Quadrant IV: ( + , - )

x-axis = ( +/- , 0 )

y-axis = ( 0 , +/- )

Edit: You mentioned that x and y axis are options too therefore, the answer was changed.

The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.

The term "son of a mention" is not familiar in mathematics. The correct term might be "son of a gun" or "son of a function."A differential equation used to model your specific engineering course is called an engineering differential equation. Such equations are used to predict, control, and monitor various physical processes, ranging from the dynamics of mechanical systems to the motion of fluids and gases, and electrical and electronic circuits. It's essential to know the form of the differential equations, the initial and boundary conditions, and the physical meaning of the parameters to use them effectively in modeling physical systems.

The following MATLAB code represents a simple for loop with a nested if-else statement and a plotting command. The code generates a signal with two segments: a rising ramp from zero to three and a falling ramp from three to zero. The signal has a total duration of 10 seconds, a sampling interval of 0.05 seconds, and a plotting delay of 0.002 seconds.

01 t=0 02 while t<10 03

if

(t<5) 04 y=3*(1-exp(-t)); 05 else if

(t>=5) 06 y=3*exp(-t+5); 07 ends 08 end 09

t = t + 0.05 10 pauses (0.002)

The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.

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Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by:

\(\mu = 38, \sigma = 2\)

As a proportion, the probability that a data value is between 37 and 41 is the p-value of Z when X = 41 subtracted by the p-value of Z when X = 37, hence:

X = 41:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41 - 38}{2}\)

Z = 1.5

Z = 1.5 has a p-value of 0.933.

X = 37:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{37 - 38}{2}\)

Z = -0.5

Z = -0.5 has a p-value of 0.309.

0.933 - 0.309 = 0.624,

0.624 = 62.4% probability that a data value is between 37 and 41.

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In finance, interest is the cost of borrowing money or the compensation paid to an individual or organization for lending money. It is usually expressed as a percentage of the amount borrowed and is calculated over a specific period of time.

1. To calculate the total interest payment for the first year, follow these steps in Excel:

Step 1: Enter the given values in separate cells.
Loan amount: $250 million in A1
Monthly installment: $5 million in A2
Number of installments: 60 in A3

Step 2: Calculate the monthly interest rate (i) using the RATE function.
In cell A4, type the formula: =RATE(A3, -A2, A1)

Step 3: Calculate the annual interest rate (I) by multiplying the monthly interest rate by 12.
In cell A5, type the formula: =A4*12

Step 4: Calculate the total interest for the first year by multiplying the annual interest rate by the loan amount.
In cell A6, type the formula: =A1*A5
The total interest payment for the first year is approximately $17 million.

2. To calculate the effective interest rate (j12) of the loan, use the following formula in Excel:

In cell A7, type the formula: =(1+A4)^12-1
The effective interest rate (j12) is approximately 7.4% p.a.

3. To calculate the principal repayment during the first year, follow these steps:

Step 1: Calculate the total amount paid in the first year by multiplying the monthly installment by 12.
In cell A8, type the formula: =A2*12

Step 2: Subtract the total interest payment for the first year (calculated in Step 1) from the total amount paid in the first year.
In cell A9, type the formula: =A8-A6
The principal repayment during the first year is approximately $43 million.

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