By selling a book for ₹500, a bookseller gains a profit of ₹30. For how much should he
sell it to gain a profit of ₹50 ?
Profit and loss chap

To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.

The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).

To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):

0.45 * 40 = 0.5x + 0.25(40 - x)

Simplifying the equation:

18 = 0.5x + 10 - 0.25x

Combining like terms:

0.25x = 8

Dividing both sides by 0.25:

x = 32

Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

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The pharmaceutical company uses the quantitative variable to conducts an experiment.

Variables:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Given,

A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.

And  the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.

Here we need to find the kind of variable is the company​ studying.

Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.

So, the experiment uses the Qualitative Variable.

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The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

We have to assume that ΔABC and ΔDEF are similar.

If the triangles are similar,

Then the proportionality is:

AB/BC=DE/EF

4/3=12/x

Therefore, the proportionality used in the given diagram is 4/3=12/x.

So, option 4 is correct.

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Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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Answer: she must sell 6 large photos and 6 small photos

Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300

Answer:

A), C), E)

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3/5 of 250 = 150 ebooks

1/10 of 250 = 25 no pref

150 + 25 = 175

250 - 175 = 75  tradtional

150-75 - 75

We have the following equation

We must factor this, in this case with the fourth case factorization.

The solution is the following:

Using the binomial distribution, it is found that the number of students that would be expected to select a gold-wrapped candy  from the bag is given by:

The candies are chosen with replacement, which means that for each student, the probability of choosing a gold wrapped candy is independent of any other student, hence the binomial distribution is used.

The expected value of the binomial distribution is:

\(E(X) = np\)

In this problem:

Then, the expected value is:

\(E(X) = np = 15\times \frac{1}{3} = 5\)

Hence, option B is correct.

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Answer:

The car would be going 305mph as the average, because it took an hour to go 305 miles.

The solution to the given differential equation, x²y'' + xy' - y = ln(x), using variation of parameters is: y(x) = C₁x + C₂x ln(x) + x ln²(x)/2,

where C₁ and C₂ are constants.

To solve the differential equation using variation of parameters, we first find the solutions to the homogeneous equation x²y'' + xy' - y = 0. Let's denote these solutions as y₁(x) and y₂(x).

Next, we find the Wronskian W(x) = y₁(x)y₂'(x) - y₁'(x)y₂(x) and calculate the integrating factors u₁(x) = -∫(y₂(x)ln(x))/W(x) dx and u₂(x) = ∫(y₁(x)ln(x))/W(x) dx.

Using these integrating factors, we can determine the particular solution yₚ(x) = -y₁(x)∫(y₂(x)ln(x))/W(x) dx + y₂(x)∫(y₁(x)ln(x))/W(x) dx.

Finally, the general solution is given by y(x) = yₕ(x) + yₚ(x), where yₕ(x) is the general solution to the homogeneous equation.

Solving the homogeneous equation x²y'' + xy' - y = 0 gives the solutions y₁(x) = x and y₂(x) = x ln(x).

After calculating the Wronskian W(x) = x² ln(x), we obtain the integrating factors u₁(x) = -ln(x)/2 and u₂(x) = -x/2.

Plugging these values into the particular solution formula, we find yₚ(x) = C₁x + C₂x ln(x) + x ln²(x)/2.

Hence, the general solution is y(x) = C₁x + C₂x ln(x) + x ln²(x)/2, where C₁ and C₂ are arbitrary constants.

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1. Convergence or divergence of the series Σ (n=2 to ∞) ln(n)/n: Diverges.

2. Convergence or divergence of the series Σ (n=1 to ∞) (n!)²/(2n)!: Converges.

3. Convergence or divergence of the series Σ (n=1 to ∞) ln(n)/(n² ln(n)/(ln(n))²: Converges.

1. Convergence or divergence of the series Σ (n=2 to ∞) ln(n)/n:

Using the integral test:

∫ ln(n)/n dn = ∫ ln(u) du (where u = n)

= u ln(u) - u + C

= n ln(n) - n + C

Taking the limit as n approaches infinity:

lim (n ln(n) - n) = ∞

Since the limit diverges to infinity, the series Σ ln(n)/n also diverges.

2. Convergence or divergence of the series Σ (n=1 to ∞) (n!)²/(2n)!:

Using the ratio test:

lim [(n+1)!²/(2(n+1))!] * [(2n)!/(n!)²]

= lim [(n+1)²/(2n+2)(2n+1)]

= 1/4

Since the limit is less than 1, the series Σ (n!)²/(2n)! converges.

3. Convergence or divergence of the series Σ (n=1 to ∞) ln(n)/(n² ln(n)/(ln(n))²:

Simplifying the expression:

Σ ln(n)/(n² ln(n)/(ln(n))²

= Σ (ln(n) * (ln(n))²)/(n² ln(n))

= Σ (ln(n))/(n²)

Using the integral test:

∫ (ln(n))/(n²) dn = ∫ (1/n²) d(ln(n))

= -1/n

Taking the limit as n approaches infinity:

lim (-1/n) = 0

Since the limit is finite, the series Σ ln(n)/(n² ln(n)/(ln(n))² converges.

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the complete question is:

Determine whether the following series converge or diverge:

1. ∑(n=2 to ∞) (ln(n) / √n)

2. ∑(n=1 to ∞) [(n!)² / (2n)!]

3. ∑(n=1 to ∞) [ln(n) / (n² ln(n) ln(ln(n)))]

Please provide a brief explanation for each series indicating whether it converges or diverges.

Answer:

A

Step-by-step explanation:

-16t^2 + 24t= 0

-2t^2+3t =0

3t= 2t^2

3= 2t

t=1,5

Answer:

84

Step-by-step explanation:

I just use an online calculator.-

www.calculator.net/triangle-calculator

The number of hours that Jessica work is 30 hours

From the question, we have the following parameters that can be used in our computation:

P = (12h + 30)/2

The amount paid is given as

P = 195

substitute the known values in the above equation, so, we have the following representation

(12h + 30)/2 = 195

So, we have

(12h + 30) = 390

This gives

12h = 360

Divide

h = 30

Hence, the number of hours is 30

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Answer: just graph these two equations

option a: y = 5x + 10

option b: y = 7.5x

and then tell at what number of event would having a card and not having a card is cheaper.

Step-by-step explanation:

the initial cost, $10, is your b value for the equation y = mx + b so yo would start here on the y axis. but for the second option you start at zero since you don't have a b value

Answer:

use this hope help you

option a: y = 5x + 10

option b: y = 7.5x

and then tell at what number of event would having a card and not having a card is cheaper.

Step-by-step explanation:

The number in the log as a power of the base y = -6.

What is  logarithmic identity ?

Logarithmic identities are mathematical formulas or rules that are used to manipulate logarithmic expressions. These identities are derived from the properties of logarithms and can be used to simplify or solve logarithmic equations.

The following are some commonly used logarithmic identities:

Product rule: log_a (x * y) = log_a (x) + log_a (y)

This identity states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.

Quotient rule: log_a (x / y) = log_a (x) - log_a (y)

This identity states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.

According to the question:
To write the number in the log as a power of the base, we can use the following logarithmic identity:

log_a (x) = y is equivalent to\(a^y = x\)

Using this identity, we can rewrite the logarithmic expressions as follows:

y = log3 243 can be written as \(3^y = 243\)

y = log2 1/64 can be written as \(2^y = 1/64\)

Now, we can solve for y by taking the appropriate power of both sides of each equation:

For the first equation, we can write:

\(3^y = 243\)

\(3^y = 3^5 (since 243 = 3^5)\)

Therefore, y = 5.

For the second equation, we can write:

\(a^y = 1\)

Since any non-zero number raised to the power of 0 is equal to 1, we have:

\(a^y = a^0\)

Therefore, y = 0.

For the third equation, we can write:

\(2^y = 1/64\)

\(2^y = 2^-6 (since 1/64 = 2^-6)\)

Therefore, y = -6.

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Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.

Answer:

well your answer is 778 but I forgot how to use an area model

Step-by-step explanation:

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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Car total cost = 17850

The sales tax rate = 6.25%

Cost of car = 16800

Car total cost = Cost of car + Tax

Car total cost = 16800 + 1050

Car total cost = 17850

Answer:

62

Step-by-step explanation:

Substitute n = 16 into the sequence rule

s(16) = 4(16) - 2 = 64 - 2 = 62

The solution of the given angle of the equation is y＝17＋x

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have given angle as:

angle 1 = angle2,

m∠1＝m∠2

m∠ 1 = x + 14,

m∠2 = y - 3

Since m∠1＝m∠2

Substitute the value of m∠1 and m∠2 in the above equation,

⇒ x＋14＝y－3

Rearrange the terms in the above equation and solve for y,

⇒ －y＝- 3－x－14

⇒ －y－17－x

⇒ y＝17＋x

Thus, the solution of the given angle of the equation is y＝17＋x

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The largest interval I over which the solution is defined is (-∞, ∞).               I = (-∞, ∞)

To solve the given initial-value problem, we can use the method of separation of variables as follows:
1. Separate the variables by moving all terms with y to the left side of the equation and all terms with x to the right side:
y/y' = ex/x
2. Integrate both sides of the equation with respect to their respective variables:
∫y/y' dy = ∫ex/x d
ln(y) = ex + C
3. Solve for y:
y = e^(ex + C)
4. Use the initial condition y(1) = 9 to find the value of C:
9 = e^(e + C)
C = ln(9) - e
5. Substitute the value of C back into the equation for y:
y = e^(ex + ln(9) - e)
6. Simplify the equation:
y = 9e^(ex - e)
7. The largest interval I over which the solution is defined is (-∞, ∞), since there are no restrictions on the values of x or y therefore, the solution to the initial-value problem is y(x) = 9e^(ex - e) and the largest interval I over which the solution is defined is (-∞, ∞).

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The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.

To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.

During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:

Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents

The original price of a can of green beans was 50 cents.

To find the percent increase or decrease in the price, we can use the following formula:

Percent increase or decrease = ((New value - Old value) / Old value) x 100%

Substituting the values, we get:

Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%

Percent increase or decrease = (-0.0833 / 0.5) x 100%

Percent increase or decrease = -16.67%

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Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

Answer:

~8.5

Step-by-step explanation:

Knowledge Needed

Pythagorean Theorem:

\(a^2+b^2 = c^2\)

Plug in 2 known values to solve.

Question

\(a^2+b^2 = c^2\\(8)^2 + (3)^2 = c^2\)

64 + 9 = c^2

c^2 = 73

Find the square root of both sides.

\(\sqrt{c^2} = \sqrt{73}\)

c = \(\sqrt{73}\)

~8.5

Answer:

c = 8.5

Step-by-step explanation:

The Pythagorean theorem is

\(a^{2} +b^{2} =c^{2}\)

Since we know a and be, we simply square them, then add those values together, and take the square root of the final value

\(8^{2} = 64\)

\(3^{2} = 9\)

\(64 + 9 = 73\)

\(\sqrt{73} = 8.5\)

c = 8.5

The Ferris wheel spins steadily at an angle of 4 radians per minute. 2v/80.24 radians per minute is the constant angular speed at which the Ferris wheel turns.

Using the formula: one can determine the Ferris wheel's diameter.

C = 2πr

where r denotes the Ferris wheel's diameter. If we substitute r = 38 feet, we obtain:

C = 2π(38) ≈ 238.76 feet

The Ferris wheel completes one rotation every eight minutes, so the calculation for angular speed is:

ω = θ/t

where t is the time it takes for one rotation to be completed and is the angle in radians at which the Ferris wheel rotates. The angle is equivalent to two radians, or one full rotation, so we have:

Radians per minute Equals 2/8 = 4

As a result, the Ferris wheel spins at a steady rate of /4 radians per minute.

b. The Ferris wheel's circumference can be calculated using the same method as C = 2πr

C = 2π(32) ≈ 201.06 feet

t = sqrt(2πr^2)/v = sqrt(2π(32)^2)/v ≈ 80.24/v

ω = θ/t = 2π/(80.24/v) = 2πv/80.24 radians per minute.

Because of this, the Ferris wheel spins at a constant rate of 2 v/80.24 radians per minute.

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A type of article that provides a quantitative summary of the evidence is a systematic review and meta-analysis.

A systematic review is a comprehensive and rigorous approach to synthesizing existing research literature on a specific topic. It involves a systematic search for relevant studies, an assessment of their quality and relevance, and a synthesis of the findings.

A meta-analysis, on the other hand, is a statistical method that combines the results of multiple studies to generate a quantitative summary of the evidence.

Systematic reviews and meta-analyses are considered the highest level of evidence in evidence-based medicine and other fields. They provide an objective and rigorous assessment of the available evidence, helping to guide clinical practice, policy decisions, and further research.

By pooling data from multiple studies, meta-analyses can provide more precise estimates of treatment effects or other outcomes of interest.

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