An article is sold for Rs 3051 after allowing Rs 300 discount on the marked price and adding 13% value added tax. What is the discount percent allowed on the marked price of the article? Find it.​

Answer:

Step-by-step explanation:

According to an AARP survey, approximately 40% of retirees in America return to work post-retirement. This figure, however, is not static and could vary due to numerous factors such as economic conditions or personal circumstances.

The percentage of Americans who choose to go back to work after retiring varies depending on a wide range of factors such as their personal financial situation, their health, and their personal interests. According to a survey by AARP, around 40% of Americans choose to work again after retirement. However, these numbers can fluctuate year to year based on various economic and social factors. Therefore, it's essential to note that this percentage isn't fixed and can change over time.

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Answer:

\(-\frac{17}{4}\\-3.95\\-\sqrt{15}\\-3\frac{6}{7}\\-3\frac{1}{4}\\-3.2\)

Step-by-step explanation:

From smallest to largest:

\(-\frac{17}{4}\\-3.95\\-\sqrt{15}\\-3\frac{6}{7}\\-3\frac{1}{4}\\-3.2\)

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer: 235.5 feet

Step-by-step explanation:

In this case, we have to calculate the circumference of the track. The circumference will be calculated as:

= 2πr

Diameter = 75 feet.

Radius = 75/2 = 37.5 feet

Circumference = 2πr = 2 × 3.14 × 37.5 = 235.5feet

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

23040

This is because math.

The range of the data is R = 9

Given data ,

Let the range of the data be R

Now , the value of R is R = maximum value - minimum value

Let the data be A = { 5, 9.5, 3, 12, 6, 8, 4.5, 10, 6.5 }

The range of a set of data, we need to subtract the minimum value from the maximum value.

The minimum value in this set of data is 3 (which occurs in the third week), and the maximum value is 12 (which occurs in the fourth week).

Therefore, the range is:

range = maximum value - minimum value = 12 - 3 = 9

Hence , the value of the range for this set of data is 9

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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The area of the parallelogram can be found by multiplying its base (the longer side, which is √3) by its height (√2). So the area of the parallelogram is √6 square units.

To find the area of the parallelogram, we first need to determine its height. Since the sides of the parallelogram are given as √2 and √3, we can see that the height is equal to the length of the shorter side of the parallelogram, which is √2.

In this case, the base of the parallelogram is given as √2, and the height is given as √3.

Area = Base * Height

= √2 * √3

= √(2 * 3)

= √6

Therefore, the area of the parallelogram is √6 square units.

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The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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Answer:

x₂ = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to \(\frac{5}{6}\)

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 9) and (x₂, y₂ ) = (x₂, - 1)

m = \(\frac{-1-9}{x_{2}-9 }\) , that is

\(\frac{-10}{x_{2}-9 }\) = \(\frac{5}{6}\) ( cross- multiply )

5(x₂ - 9) = - 60 ( divide both sides by 5 )

x₂ - 9 = - 12 ( add 9 to both sides )

x₂ = - 3

Answer:

Credit to the guy that has already answer. HE IS CORRECT!! THE ANSWER IS D=7/9 AND 6!!!!!!!!!!!!!!!

Step-by-step explanation:

click on the link below it shows a screenshot of the correct answer!!

Stay Safe Guys!!!!

Answer:

The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped

Step-by-step explanation:

The given table is presented as follows;

\(\begin{array}{ccl}t&h(t)&Description\\0&20&Initial \ height\\0.5&18.8&Rock \ in \ downward \ motion\\1&15.1&\\1.5&9&\\2&0.4&The \ height \ just \ before \ the \ rock \ hits \ the \ ground \\2.5&-10.6&The \ calculated \ height \ after\ the \ rock \ hits \ the \ ground \\3&-24.1&Calculated \ height \ after\ the \ rock \ hits \ the \ ground\end{array}\)

Therefore, the rock hits the ground between t = 2 seconds and t = 2.5 seconds after it is dropped.

Answer:

the answer is 4 x 10^4  or 40,000

Step-by-step

the answer is 40,000 but you need to put it in scientific notation which equals 4 x 10 to the 4th power

4 x 10^4

The side length of each face of a cube is equal to 2 feet.

We know, Total surface area of a cube = 6a², where a is the side length of the cube.

Here, a = 2 feet

∴ Total surface area of the given cube is equal to

⇒ 6(2)²

⇒ 6(4)

⇒ 24 sq. ft.

∴ Total surface area of the given cube is 24 sq. ft.

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Answer: Greater than

Step-by-step explanation:

36/0.6 = 60

60 is more than 36

Answer:

No it is not a rational number. A rational number consists of decimal on it

Answer:

1262(2)^x

Step-by-step explanation:

Answer:

44%

Step-by-step explanation:

100 + 20 = 120/100

(1.2)^2=1.44

144 - 100 = 44%

Answer:

Option A is correct

Step-by-step explanation:

Bobby = 1/8

Danny = 1/5

Let's add up both fractions:

1/8 + 1/5 =

1*5/8*5 + 1*8/5*8 =                   (multiplying both the numerator and                              

5/40 + 8/40 = 13/40                 denominator by the opposite denominator)

Together, they both cut 13/40 of the entire lawn.

Let's check each option:

A) Together the boys didn't even cut half the yard.

True, half of the yard is 20/40, and 13/40 < 20/40

B) The boys were able to cut more than half the yard.

False, half of the yard is 20/40, and 13/40 is not greater than 20/40

C) The boys cut almost three-fourths of the yard.

False, three-fourths of the yard is 30/40, and 13/40 is not close.

D) Together the boys cut almost the entire yard.

False, the entire yard is 40/40 and 13/40 is not close.

-Chetan K

The first four terms in the power series expansion of f(x) = e^(2x) about x = 0 are 1, 2x, 2x^2, and (4/3)x^3

The first four terms in the power series expansion of the function f(x) = e^2x about x = 0 are:
f(x) = e^2x = 1 + 2x + 2x^2 + (4/3)x^3 + ...

This can be obtained by using the formula for the Taylor series expansion of e^x:
e^x = 1 + x + (x^2/2!) + (x^3/3!) + ...

and replacing x with 2x to get:
e^(2x) = 1 + 2x + (4x^2/2!) + (8x^3/3!) + ...

Simplifying the coefficients of the terms gives:
f(x) = e^(2x) = 1 + 2x + 2x^2 + (4/3)x^3 + ...

Therefore, the first four terms in the power series expansion of f(x) = e^(2x) about x = 0 are 1, 2x, 2x^2, and (4/3)x^3.

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Answer:

skewed right

Step-by-step explanation:

Answer:

Cost price of 5 orange=(60/50)*5=6k

Now to get 50% profit

Selling price of group of 5 orange

=6*1.5=9k.

Answer:

x = 2

Step-by-step explanation:

First, you cross multiply then that will give you

9x - 3 = 5x + 5

collect like terms

9x - 5x = +5 + 3

= 4x = 8

Divide both sides by the coefficient of x that's 4

= 2

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

We have,

\(u = sin^{-1)}(2x)\)

dv = 4 dx

Taking the derivative of u, we get:

du/dx = 1 / √(1 - (2x)²)

Integrating dv, we get:

v = ∫4 dx = 4x

Now, applying the integration by parts formula:

∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu

Plugging in the values, we have:

∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx

At this point, we need to evaluate the integral on the right side.

Let's perform a substitution to simplify it:

Let u = 1 - (2x)²

Differentiating u with respect to x, we get:

du/dx = -4(2x) = -8x

Solving for dx, we have:

dx = -du / (8x)

Substituting these values, the integral becomes:

∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))

Simplifying, we get:

∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du

= -∫(1 / (2√u)) du

= -√u + C

Substituting back the value of u, we have:

∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C

Therefore,

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

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The complete question:

a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.

The series ∑n=1infinitynnn5+10−−−−−−√5 converges. This can be answered by the concept of Sequence.

To determine the convergence or divergence of the given series, we will use the alternating series test. This test applies to series of the form ∑(-1)ⁿ b_n, where b_n is a positive sequence and decreases monotonically to zero as n approaches infinity.

Let's consider the sequence b_n = n^(-5/2) + 10^(-5/2). This sequence is positive and decreases monotonically to zero as n approaches infinity. To see this, note that n^(-5/2) < n⁻² and ∑n=1^[infinity] n⁻² is a convergent p-series with p = 2. Similarly, 10^(-5/2) is a fixed positive constant, and therefore, b_n is a positive sequence that decreases monotonically to zero as n approaches infinity.

Now, we need to show that the series ∑(-1)ⁿ b_n converges. To do this, we will apply the alternating series test. The alternating series test states that if a series of the form ∑(-1)ⁿ b_n satisfies two conditions:

b_n is positive and decreases monotonically to zero as n approaches infinity.

The alternating sum of the series, ∑(-1)ⁿ b_n, converges,

then the original series ∑ b_n converges.

For our series, we have shown that the sequence b_n = n^(-5/2) + 10^(-5/2) is positive and decreases monotonically to zero as n approaches infinity. We now need to show that the alternating sum of the series, ∑(-1)ⁿ b_n, converges.

The alternating sum of the series is:

∑n=1^[infinity] (-1)ⁿ (n^(-5/2) + 10^(-5/2))

We can split this sum into two separate series:

∑n=1^[infinity] (-1)ⁿ n^(-5/2) and ∑n=1^[infinity] (-1)ⁿ 10^(-5/2)

The first series is an alternating series that satisfies the conditions of the alternating series test. Therefore, it converges.

The second series is a constant series that alternates signs. Therefore, it also converges.

Since both series converge, the alternating sum of the series, and hence the original series ∑ b_n, converges by the alternating series test.

Therefore, the series ∑n=1^[infinity] (-1)ⁿ (n^(-5/2) + 10^(-5/2)) converges.

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Would produce market a quantity of 2 and make a profit of $1.

The graph shows the market supply and demand curves for a perfectly competitive firm. If the market price is $3, the firm would be operating at the intersection of the demand curve (D) and the marginal cost curve (MC). At that price, the firm would produce a quantity of 2 and incur a total cost of $2 (the area of the rectangle formed by the marginal cost and quantity). Since the market price is higher than the marginal cost, the firm would make a profit of $1 (the area of the triangle formed by the market price and quantity).

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