Evaluate 1/4xy if x=−2/3 and y=3/5 . Write your answer as a fraction in simplest form.

To calculate the price of a bond that pays interest, we could begin with the general formula for the present value of a stream of cash flows.

Bonds are debt instruments that pay periodic interest and return the principal at maturity. The price of a bond is the present value of its expected cash flows, discounted back to the present at an appropriate interest rate. The general formula for the present value of a stream of cash flows is:PV = C1 / (1+r)^1 + C2 / (1+r)^2 + ... + CT / (1+r)^T Where :PV = the present value of the cash flows Ct = the cash flow at time t (in our case, the interest payment)T = the maturity date of the bondr = the required rate of return.

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The surface temperature is found to be  approximately 11°C.

Given:

Pipe inner diameter, di = 4cm

= 0.04m

Pipe outer diameter, do = 4.6cm

= 0.046m

Thermal conductivity of stainless steel, kss = 15 W/m.K

Thickness of glass wool insulation, L = 3.5cm

= 0.035m

Thermal conductivity of glass wool insulation, kgi = 0.038 W/m.K

Outer emissivity of the insulation, εo = 0.3

Heat transfer coefficient inside the pipe, hi = 80 W/m2.K

Film temperature, Tfilm = 10°C = 283K

Air velocity, V = 2m/s

Air viscosity, μ = 1.426 × 10–5m2/s

Air thermal conductivity, ka = 0.02439 W/m.K

Air Prandtl number, Pr = 0.7336

Outer surface temperature of the insulation is T∞ = 3°C = 276K

The surface temperature of the insulation is given by;

Ts = T∞ + q″Rout/hsq″

= hi (Tsteam – Ts) …(1)

The overall resistance to heat transfer from steam to the surrounding air and surfaces is given by;

Rtot = Ri + Rk + Ro + Rconv + Rrad

Ri = (ln(do/di))/(2πkss)

= (ln(0.046/0.04))/(2 × π × 15)

= 0.0001926 m2.K/W…(2)

Rk = L/(2πkgi)

= 0.035/(2π × 0.038)

= 0.0145 m2.K/W…(3)

Ro = 1/(2πεoσout) [(1/do) – (1/di)]

= [1/(2π × 0.3 × 5.67 × 10–8)][(1/0.046) – (1/0.04)]

= 0.004685 m2.K/W…(4)

Rconv = 1/hs

= 1/hi

= 0.0125 m2.K/W…(5)

Rrad = 1/(εoσout) [(1/do) – (1/di)]

= [1/(0.3 × 5.67 × 10–8)][(1/0.046) – (1/0.04)]

= 0.0028 m2.K/W…(6)

Rtot = Ri + Rk + Ro + Rconv + Rrad

= 0.0001926 + 0.0145 + 0.004685 + 0.0125 + 0.0028

= 0.0346776 m2.K/W…(7)

From equation (1);

q″ = hi (Tsteam – Ts)

q″ = (Tsteam – Ts)/Rtot

(Tsteam – Ts) = q″ Rtot

(Tsteam – Ts) = hi

q″ Rtot TsTsteam = Ts + hi

q″ RtotTsteam = 276 + (80 × π × 0.04 × 0.6)/3600 × (693.7 – 276 + 0.24 × 5.67 × 10–8 × [(693.7)4 – (276)4])

Tsteam = 693.7K

Ts = T∞ + q″Rout/hs

Ts = 276 + (693.7 – 276) × 0.004685/80

Ts = 284.54K

The surface temperature is 284.54 - 273.15 = 11.39 °C.

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Answer:

26.6

Step-by-step explanation:

(12*5)-(8.35*4)

60-33.4

26.6

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

The value of ΣXY based on the data is 575.

To calculate ΣXY, we need to multiply each value of X with its corresponding value of Y and then sum them up. Let's perform the calculations:

For the first set of values, X = 4 and Y = 123. So, XY = 4 * 123 = 492.

For the second set of values, X = 4 and Y = 8. So, XY = 4 * 8 = 32.

Now, let's add up the individual XY values:

ΣXY = 492 + 32 = 524.

Therefore, the value of ΣXY is 524.

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Yes.

It is true that if v1, v2, ..., vp are vectors in Rⁿ, then Span{v1, v2, ..., vp} is the same as the column space of the matrix [v1 v2 ... vp].

True, let A = [v1 v2 ... vp] be the matrix columns are the given vectors.

The column space of A is the set of all linear combinations of the columns of A, which is exactly the same as the span of the vectors v1, v2, ..., vp.

In other words, any vector that can be written as a linear combination of the columns of A is also in Span{v1, v2, ..., vp}, and vice versa.

The tools of linear algebra to study the span of a set of vectors, by considering the column space of the corresponding matrix.

Techniques like row reduction and rank to determine if a set of vectors is linearly independent or spans the whole space Rⁿ.

Yes, the given vectors should be used as the matrix columns in A = [v1 v2... vp].

The span of the vectors v1, v2,..., vp is exactly the same as the column space of A, which is the set of all linear combinations of the columns of A.

This means that any vector that can be expressed as a linear combination of columns from A is also a vector in Spanv1, v2,..., vp and vice versa.

By taking into account the column space of the associated matrix, the techniques of linear algebra may be used to examine the range of a collection of vectors.

To establish if a group of vectors spans the whole space Rn or is linearly independent, use methods like rank and row reduction.

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The given expression is

To solve the product, we have to use the distributive property

Then, we move all the terms to the left side to combine like terms

Now, we use the quadratic formula to find the solutions

Where a = 1, b = -5, and c = -204. Let's replace these values

There are two solutions

The expected net gain E(X) in the context of this problem is given as follows:

E(X) = -$0.5.

The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:

The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

Hence the expected net gain for this game is calculated as follows:

E(X) = -1 x 0.99 + 49 x 0.01.

E(X) = -$0.5.

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Answer:

You are correct with B!!

Step-by-step explanation:

(x⁹)²

We have to multiply 9 x 2, regardless of the parenthesis for this one.

9 × 2 is 18.

We cannot simply 18 further.

Carry the x in front of 18.

x¹⁸

Answer:

The price elasticity of demand, when using the midpoint​ formula, would be B.1.29.

How to find the price elasticity of demand ?

Price elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

where:

Q1 = initial quantity demanded = 20 units

Q2 = final quantity demanded = 15 units

P1 = initial price = $8

P2 = final price = $10

Substituting the values:

Price elasticity of demand = ((15 - 20) / ((15 + 20) / 2)) / (($10 - $8) / (($10 + $8) / 2))

= (-5 / 17.5) / (2 / 9)

= (-0.2857) / (0.2222)

= -1.2857

= 1. 29

According to the mapping diagram, the above is a function since there are no two values in set B where there is only one value in Set A mapped to them.

Mapping diagram:

A mapping diagram has two parallel columns. First column refers the domain of a function f , and the next column for its range. The lines or arrows are drawn from domain to range, to represent the relation between any two elements.

Given,

Here we have the two sets Set A and Set B.

And we need to fill  in the blanks below in order to justify whether or not the mapping shown represents a function.

We know that, a function has a very unique attribute of having one output attributed to each input.

Here the Set A is the domain while set B denotes the range.

And in each value in the domain would have exactly one value in the range which would be different for each value in the domain.

Therefore, this mapping diagram illustrates a 1 input to 1 output relationship, so it is a function.

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In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Answer:

not at all

Step-by-step explanation:

The change in U and H for given sample of an ideal gas by keeping the pressure constant is given by ∆H = 184179.58 J and ∆U = 184179.58 J.

To calculate the change in internal energy (∆U) and enthalpy (∆H) of the gas, use the equation,

∆U = ∆H - ∆(PV)

The pressure (P) is constant, the work done (∆(PV)) is zero.

Therefore, we can simplify the equation to,

∆U = ∆H

To find the change in enthalpy (∆H), we can use the equation,

∆H = ∫(Cp dT)

The specific heat capacity of the gas (Cp) as a function of temperature (T),

we can integrate the equation over the temperature range to calculate the change in enthalpy.

∆H = ∫(Cp dT) between the initial temperature (T₁) and final temperature (T₂).

∆H = ∫[(34.45 + (4.98 × 10⁻³)T - (1.44 × 10⁵)(T⁻²)) dT]

between T₁ = 6.64 °C and T₂ = 464.34 °C.

∆H = [34.45T + (4.98 × 10⁻³)(T²)/2 + (1.44 × 10⁵)(T⁻¹)]

between T₁ = 6.64 °C and T₂ = 464.34 °C.

∆H = [34.45(464.34) + (4.98 × 10⁻³)((464.34)²)/2 + (1.44 × 10⁵)((464.34)⁻¹)] - [34.45(6.64) + (4.98 × 10⁻³)((6.64)²)/2 + (1.44 × 10⁵)((6.64)⁻¹)]

∆H ≈ 184179.58 J

Since ∆U = ∆H , the change in internal energy (∆U) is also approximately 184179.58 J.

Therefore, the change in U and H by keeping the pressure constant is equal to ,

∆H = 184179.58 J

∆U = 184179.58 J

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To find the expected value of T, we use the formula E(T) = 1/λ. Plugging in λ=3, we get E(T) = 1/3. Therefore, the expected value of T is 1/3.

Suppose a random variable T is exponential with λ=3. To solve the integral, we first need to find the antiderivative of \(e^{(-3t)}\), which is (-1/3) × \(e^{(-3t)}\). Plugging in the limits of integration, we get (-1/3) × \(e^{(-429)}\) + (-1/3) × \(e^{(-429)}\). Simplifying this expression, we get 0.0029. This value represents the probability that T will be between 1 and 43.

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The upper control limit (UCL) and lower control limit (LCL) for the given process can be calculated using the formula: UCL = X(bar) + A3 × σ and LCL = X(bar) - A3 * σ. Based on the provided data, with X(bar) = 50 and the standard deviations of the three samples given as 5, 3, and 7, the values of UCL and LCL can be determined.

To calculate the UCL and LCL, we use the formula UCL = X(bar) + A3 × σ and LCL = X(bar) - A3 × σ. Here, X(bar) represents the sample mean, A3 is a constant factor (given as 1.954), and σ denotes the standard deviation. Given X(bar) = 50 and the standard deviations for the three samples as 5, 3, and 7, we can calculate the overall standard deviation by taking the average of the individual sample standard deviations. Thus, σ = (5 + 3 + 7) / 3 = 5. Using these values in the formulas, we find UCL = 50 + 1.954 × 5 = 59.77 and LCL = 50 - 1.954 × 5 = 40.23. Therefore, the upper control limit is approximately 59.77 and the lower control limit is approximately 40.23 for the given process.

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Using the hypergeometric distribution, it is found that there is a 0.1515 = 15.15% probability that you pick at least 3 green balls.

The balls are chosen without replacement, hence the hypergeometric distribution is used.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that you pick at least 3 green balls is:

\(P(X \geq 3) = P(X = 3) + P(X = 4)\)

Hence:

\(P(X = 3) = h(3,12,4,5) = \frac{C_{5,3}C_{7,1}}{C_{12,4}} = 0.1414\)

\(P(X = 4) = h(4,12,4,5) = \frac{C_{5,4}C_{7,0}}{C_{12,4}} = 0.0101\)

Then:

\(P(X \geq 3) = P(X = 3) + P(X = 4) = 0.1414 + 0.0101 = 0.1515\)

0.1515 = 15.15% probability that you pick at least 3 green balls.

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Answer:

Your answer would be -1/12

Step-by-step explanation:

have a great day!

Answer:

-1/12

Step-by-step explanation:

-1/3 ÷ 4

= -1/3 × 1/4

= -1/12

Hoped this helped.

Answer:

its the third answer

Step-by-step explanation:

The third anwser is 66% which we can noow nominate any lower.

The second answer is 60% we can get rid of that.

the first is 55% we can get rid of that.

and the fourth is 62.5% so we can get rid of that.

Answer:

the third one or c

Step-by-step explanation:

The solution to the linear programming problem 0.3x₁ + 0.1x₂ ≤ 1.8 using the simplex method shows that the problem has optimal solutions.)

Convert the inequality into an equation by subtracting 1.8 from both sides:
0.3x₁ + 0.1x₂ - 1.8 ≤ 0

Introduce slack variables to convert the inequality into an equation:
0.3x₁ + 0.1x₂ + s₁ = 1.8

Set up the initial simplex tableau:

┌───┬───┬───┬───┬───┐
│   │ x₁ │ x₂ │ s₁ │  1│
├───┼───┼───┼───┼───┤
│  1│ 0.3│ 0.1│  1  │1.8│
└───┴───┴───┴───┴───┘
```

Select the pivot column. Choose the column with the most negative coefficient in the bottom row. In this case, it is the second column (x₂).

Select the pivot row. Divide the numbers in the rightmost column (1.8) by the corresponding numbers in the pivot column (0.1) and choose the smallest positive ratio. In this case, the smallest positive ratio is 1.8/0.1 = 18. So the pivot row is the first row.


The simplex method is an iterative procedure that systematically improves the solution to a linear programming problem. It starts with an initial feasible solution and continues to find a better feasible solution until an optimal solution is obtained. In each iteration, the simplex method selects a pivot column and a pivot row to perform row operations, which transform the current tableau into a new tableau with improved objective function values. The process continues until the objective function values cannot be further improved or the linear programming problem is unbounded.

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The correct answer is

0.3x1+0.1x2≤2.7→0.3x1+0.1x2≤1.8 Work Through The Simplex Method Step By Step. How The Solution Changes (I.E., LP Has Optimal

Answer:

His average speed is

12 km/hr

.

Step-by-step explanation:

Remember the triangle of Speed, Distance and Time. If you remember it, you'll ace these kinda questions.

I had trouble with these formulas but the triangle helped me a LOT! Anyways, let's get back to the question. The formula for average speed is pretty much the same as the formula for just speed. The average speed formula is

Average speed

=

Total Distance

Total Time

So......

48 km

4 hr

=

12 km/hr

My source

I hope this explanation helps you!

Answer: what is $9.27 tho????

Answer:

0.19

Step-by-step explanation:

Since we can't have a fraction of a year, we need to round up to the equation nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

V(1) = 0.85 * 12,900 = $10,965

V(2) = 0.85 * 10,965 = $9,320.25

\(V(n) = 0.85^n * 12,900\\0.85^n * 12,900 < 3,000\\n > log(3,000/12,900) / log(0.85)\\n > 6.48\\\)

Since we can't have a fraction of a year, we need to round up to the nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

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Answer:

9 years

Step-by-step explanation:

As the car depreciates at a constant rate of 15% each year, we can use the exponential decay formula to find the value of the car after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

Given the purchase price of the car is $12,900, a = 12900.

Given the car will depreciate at a rate of 15%, r = 0.15.

Substitute the values of a and r into the formula to create a function for the value of car after t years is:

\(f(t)=12900(1-0.15)^t\)

\(f(t)=12900(0.85)^t\)

To calculate after how many years the value of the car will be less than $3,000, substitute f(t) < 3000 and solve for t.

\(\implies 12900(0.85)^t < 3000\)

Divide both sides by 12900:

\(\implies (0.85)^t < \dfrac{3000}{12900}\)

\(\implies (0.85)^t < \dfrac{10}{43}\)

Take natural logarithms of both sides:

\(\implies \ln (0.85)^t < \ln\left(\dfrac{10}{43}\right)\)

Apply the log power law:

\(\implies t \ln (0.85) < \ln\left(\dfrac{10}{43}\right)\)

Divide both sides by ln(0.85), remembering to change the direction of the inequality sign since ln(0.85) is negative:

\(\implies t > \dfrac{\ln\left(\dfrac{10}{43}\right)}{\ln (0.85)}\)

\(\implies t > 8.9750695...\)

We need to round up to 9 years, since we can't have a fraction of a year.

Therefore, the value of the car will be less than $3,000 after 9 years.

Answer:

5+what gives u 10 5+5=10

Answer: 1 and 1/5

Step-by-step explanation:

To determine how many fifths are in 1 1/4, we need to convert the mixed number 1 1/4 into an improper fraction. To do this, we multiply the denominator by the whole number and add the numerator, then place that sum over the original denominator.So we get 1 1/4 = (4 x 1 + 1) / 4 = 5/4.

Now, we can divide 5 by 4 to find how many fifths are in 1 1/4. 5 divided by 4 is equal to 1 with a remainder of 1. This means that there is 1 whole fifth in 1 1/4 and one-fifth left over.

Therefore, the answer is 1 and 1/5.

So, there are 1 and 1/5 fifths in 1 1/4.

\(answer \\ (3x - 5)(2x + 2) \\ solution \\ {6x}^{2} - 4x - 10 \\ = {6x}^{2} - (10 - 6)x - 10 \\ = {6x}^{2} - 10x + 6x - 10 \\ = 2x(3x - 5) + 2(3x - 5) \\ = (3x - 5)(2x + 2) \\ hope \: it \: helps\)

Answer:

x = 1⅔ or -1

Step-by-step explanation:

6x² -4x - 10

a=6, b=-4, c=-10, ac= -60

factors -10 & 6

6x² + 6x - 10x -10 =0

(6x² + 6x) - (10x - 10) =0

6x(x +1) - 10(x+1) =0

(6x-10)(x+1)=0

6x-10=0 or. x+1=0

6x= 10 or x= -1

x= 10/6 or. x= -1

x=1⅔ or x= -1

Answer:

  A)  40%

Step-by-step explanation:

25% of yards have 6-8 trees; 10% of yards have 8-10 trees; 5% of yards have more than 10 trees. So, a total of 25% +10% +5% = 40% of yards have 6 trees or more. If a yard is randomly chosen, the probability it will have 6 or more trees is 40%.

Answer:

80%

Step-by-step explanation:

You have to find the rate for the bike so you divide 30 by 2 and you get 15. After you do that, you make a problem to find the percentage so you take x/100 and 12/15 then you take 12 times 100 and that gives you 1200 then you divide by 15 and get 80. So that means the answer is 80%