If the marked price of an article is Rs 400 and sold it at a discount of 10%, find the net selling price of the article.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

E 16 cm

5cm + 5cm = 10cm

3cm + 3cm = 6cm

10cm + 6cm

= 16 cm

5×3=15 so 15 is your answer

Answer:

10,048

Step-by-step explanation:

40,000(0.2512)=10,048

Answer:

Step-by-step explanation:

Answer:

d. 75,595

Step-by-step explanation:

Given the estimated regression equation :

y=550 + 30x1 + 9x2

if number of items made (x) = 2500 ; number of stores stocking the product (x2) = 5

Predicted profit (y) will be :

Substitute the values x1 = 2500 and x2 = 5 into the estimated regression model:

y=550 + 30(2500) + 9(5)

y = 550 + 75000 + 45

y = 75595

Hence, the predicted profit will be 75,595

Answer:

y = 3

Step-by-step explanation:

4y + 3 = 15  First subtract 3 from each side.

4y + 3 - 3 = 15 - 3   The 3 on the left will cancel.

4y = 15 - 3

4y = 12       Divide each side by 4

4y/4 = 12/4     The 4 on the left will cancel because 4/4 = 1

y = 12/4

y = 3

Answer:

x = 24

Step-by-step explanation:

by the similarity theorem

the ratios of corresponding sides are in proportion , that is

\(\frac{x}{9}\) = \(\frac{16}{6}\) ( cross- multiply )

6x = 9 × 16 = 144 ( divide both sides by 6 )

x = 24

To describe the center of the data, we can use either the mean or the median.

To describe the variation of the data, we can use either the range or the interquartile range (IQR).

Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.

To find the median and IQR:

Arrange the data in order from smallest to largest.

Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.

Find the first quartile, which is the median of the lower half of the data.

Find the third quartile, which is the median of the upper half of the data.

Calculate the IQR as the difference between the third quartile and the first quartile.

Here are the steps applied to the dot plot:

We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.

The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.

The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.

The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.

The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.

Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.

Answer:

9 inches

Step-by-step explanation:

Answer:

y = {1, 3, 7}

Step-by-step explanation:

Given

y = ½x + 3

Domain: {-4, 0, 8}

Required

Determine the range of the function

To do this, we simply substitute each value of the domain in the given expression

We start with the first

Substitute -4 for x in y = ½x + 3

y = ½ * -4 + 3

y = -2 + 3

y = 1

Then 0

Substitute 0 for x in y = ½x + 3

y = ½ * 0 + 3

y = 0 + 3

y = 3

Lastly, 8

Substitute 8 for x in y = ½x + 3

y = ½ * 8 + 3

y = 4 + 3

y = 7

Hence, the range of the function is:

y = {1, 3, 7}

Answer:1,3,7

Step-by-step explanation:

Answer: C=2

I know it seems difficult but it’s not as bad as it looks.

Step-by-step explanation:

First you add 7 to both sides of the equation as shown:

3c-7+7=-c+1+7

Then you simplify giving you the equation 3c=-c+8

Then you add C to both sides of the equation: 3c+c=-c+8+c

Then you combine like terms giving you the equation of 4c=8

After that you divide both numbers by 4 giving you the fraction of 8/4 otherwise know as 2. Hope this helps, best of luck.

Answer:

$368.27

Step-by-step explanation:

495.00*0.20=$99

495-99=396

396-35=361

361*1.07=386.27

Answer

= speed = distance/time

5 hour and 45 min= 5.75hours

Speed = 299/5.75

Final answer Speed = 52miles per hour

Answer:

51.38% probability that they requested regular gas

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question, we have that:

Event A: Not filling the tank

Event B: Regular gas

40% of the customers request regular gas

This means that \(P(B) = 0.4\)

Of those customers requesting regular gas, 70% only fill up part of their tank.

This means that \(P(A|B) = 0.7\)

Probability of not filling the tank:

70% of 40%(regular gas)

100 - 60 = 40% of 35%(unleaded gas).

100 - 50 = 50% of 25%(premium gas).

So

\(P(A) = 0.7*0.4 + 0.4*0.35 + 0.5*0.25 = 0.545\)

What is the probability that they requested regular gas?

\(P(B|A) = \frac{0.4*0.7}{0.545}\) = 0.5138

51.38% probability that they requested regular gas

Answer:

9

Step-by-step explanation:

Since the scale factor is 12/8 = 1.5, to find LA we have to multiply FI by 1.5 which is 6 * 1.5 = 9.

Using conditional probability, it is found that there is a 0.3266 = 32.66% probability that the person first went on tour T2.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

The percentages associated with a return are:

Hence:

\(P(A) = 0.75(0.5) + 0.667(0.3333) + 0.5(0.1667) = 0.6806611\)

The probability of both returning and first going on T2 is:

\(P(A \cap B) = 0.667(0.3333)\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.667(0.3333)}{0.6806611} = 0.3266\)

0.3266 = 32.66% probability that the person first went on tour T2.

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9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.

So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.

So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.

I'm not good in math ok bye

A) Atra = 0.5 ( 7 + 3 ) x 3 = 15 cm^2

B) Atri1 = 1/2 x 3 x 2 = 3 cm^2

Atri2 = 1/2 x 3 x 2 = 3 cm^2

Arec = 3 x 3 = 9 cm^2

Atra = Atri1 + Atri2 +  Arec = 3 + 3 + 9 = 15 cm^2

ok done. Thank to me :>

Answer:1+1=2

Step-by-step explanation:

Yeah Bio

Answer:

The inverse represents the temperature F corresponding to a temperature C.

The domain of the inverse function is all real numbers.

194°F

Step-by-step explanation:

Let C= y

y= 5/9 (F - 32),

F= 9/5y + 32

But y= C, hence;

F= 9/5 C +32

The inverse represents the temperature F corresponding to a temperature C.

Given;

F= 9/5 C +32

The domain of the inverse function is all real numbers.

Given C= 90°

F= 9/5 C +32

F= 9/5 (90°) +32

F= 194°F

Answer:

9

Step-by-step explanation:

1.2x4 =8

2.8+1=9

hope this helped

\(\framebox {60.46}\)

\(\text {Remove 0 from 74.8. You don't need it.}\)

\(\text {Do Keep Change Change (KCC)}\)

\(\text {Keep: 135.26}\\\text {Change: - into +}\\\text {Change: 74.8 into -74.8}\)

\(\text {Add: 135.26 +-74.8=60.46}\)

\(\text {Hope this helps!}\)

\(\text {-LimitedX}\)

Answer:

60 cm is the answer

Step-by-step explanation:

Answer: c

Step-by-step explanation:

i got it right

Answer:

C) Yes, because substituting these values into both equations forms two true statements.

Step-by-step explanation:

x = 1

y = 2

The system of equations is:

y = -3x + 5..........................(1)

5x = 4y - 3.......................(2)

Substitute equation (1) into equation (2)

The equation becomes:

5x = 4(-3x + 5) - 3

5x = -12x + 20 - 3

5x = 12x + 17

5x + 12x = 17

17x = 17

Divide both sides by 17

17x / 17 = 17 /17

x = 1

Substitute the value of x into equation (1)

y = -3x + 5

y = -3(1) + 5

y = -3 + 5

y = 2

Answer:

D) no solution

Step-by-step explanation:

2x - 4y = 14

X + 2y = 7

2x - 4y + x + 2y = 14 + 7

2x - 4y + x + 2y = 21

3x - 2y = 21

no solution

Answer:

x=2y+7

step by step explanation:

2x-4y=14

2(x-2y)=14

x-2y=14/2

x-2y=7

x=2y+7

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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