Mr.khatiwada. is a unmarried secondary level mathematics teacher in a community school.His monthly salary is Rs 39990with Rs 2000 allowance and gets one months basic salary as festival expense.if 10%and next 13%of his basic salary is deposited in his provident fund and civil investment trust respectively,how much income tax should he pay in this year.​

Answer:  [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation [tex]u = e^{2x}+10[/tex]

Apply the derivative and multiply both sides by 7 like so

[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]

Integrating leads to

[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]

Answer:

16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

12+16=28

28/2=14

please give brainliest!

hope this helps :)

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

Answer:

(-∞, 1/5)

Step-by-step explanation:

[tex]f\left( x\right) =\frac{3x-1}{\sqrt{1-5x} }[/tex]

f is defined ,if and only if ,

1 - 5x > 0

⇔ 1 > 5x

⇔ 1/5 > x

⇔ x < 1/5

color : 40p + 50f + 90

b&w : 15p+20f + 45

p = 26

f = 45

[substitute the values given]

color : 40(26) + 50(45) + 90

b&w : 15(26)+20(45) + 45

[solve the equation]

color : 3380

b&w : 1335

[subtract to see how much ink is saved]

3380 - 1335 = 2045

Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent

Given Data

Let us find 30% of $3000

= 30/100* $3000

= 0.3*$3000

= $900

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Answer:

They would have $3 dollars left over.

Step-by-step explanation:

If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.

Answer:

A because it shows that the calculations are correct as well as combination pattem

(4)

1. 11.444 repeater

2. 0.58333 repeater

3. 6.7333 repeater

4. 27.5454 repeater (on both 5 and 4)

5. 1.482517482517 (482517 repeater)

6. 2.285714285714 (285714 repeater)

7. 7.5666 repeater

8. 60.60606060 (60 repeater)

(5)

1. 0.666 (repeater)

2. 0.3666 (repeater)

3. 1.1818181818 (18 repeater)

4. 0.418181818 (18 repeater)

92.16 pi cm^3.

Step-by-step explanation:

Shape of a party hat : conical

Volume of a cone = (1/3)(pi)(r^2)(h)

(pi(1/3)(23.04)(12))cm^3

Therefore, approximately

92.16 pi cm^3.

Answer:c

Step-by-step explanation:heheh

Answer: C

Step-by-step explanation:

Let's replace every copy of x with 7 and simplify.

[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\[/tex]

Which is clearly false. This is probably the set of steps you followed to get "no solution".

Why is there no solution? Well let's subtract 9 from both sides to isolate the square root

[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\[/tex]

Recall that the result of a square root operation is never negative. The range of [tex]y = \sqrt{x}[/tex] and [tex]y = \sqrt{5x+1}[/tex] is the set of nonnegative numbers. There is no way we can have the left hand side result in -6

If there was a negative sign out front the square root and we have this instead

[tex]-\sqrt{5x+1}+9 = 3\\\\[/tex]

then the answer would be x = 7

Unfortunately, there isn't such a negative sign, so we stick with "no solutions".

[tex]15 \div 3( - 2) + | - 10| \\ 5( - 2) + 10 \\ - 10 + 10 \\ 0[/tex]

Hope it helps

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Answer:

-12

Step-by-step explanation:

What you have to do is plug -4  into the function as a puzzle. So, replace all x with -4.

f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12

f (-4) = 7x ( 1-4 ) - 4 (-4)

       = -28 + 16

      = -12

An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.

A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.

Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

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No, Number 82296 is not a perfect square.

And, We multiply by 82296 in the number 82296 to amke a perfect square.

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The number is,

⇒ 82296

Now,

If the number 82296 is a perfect square number.

So, We get;

⇒ x² = 82296

⇒ x = √82296

⇒ x = 286.87

So, This number is not a perfect square number.

If we multiply by the number 82296 in the number 82296, we get;

⇒ 82296 × 82296

⇒ (82296)²

Thus, It become a perfect square number.

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Answer:

Step-by-step explanation:

Comment

Answer (-4,5,6)

B

A function assigns the values. The function will move down by 3 units.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.

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Answer:

Step-by-step explanation:

Remark

Always the easiest way to study these questions is to get a graph. The one below shows

Red: y = x^2

Blue: y= 3(x + 1)^2

You will notice that (x+1)^2 shifts the graph Left -- the opposite to what you might think.

The 3 is a little harder. It narrows the red mother graph. Which choice says that?

The choice is between b and d. Why. Because the blue graph is to the left of the red one.

You have to learn the meaning of compressed. A better word might be narrows.

Answer

B

There are several ways

Let's check all

A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The decimal form of 2 2/5 can be written as,

2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4

Hence, the decimal form of 2 2/5 is 2.4.

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Answer:

20%

Step-by-step explanation:

The theoretical probability that applesauce and broccoli will both offered on monday is 20%.

A combination is a way of selecting items from a collection where the order of selection does not matter. It is calculated by

[tex]^{n} C_{r} = \frac{n!}{(n-r)!}[/tex]

Where,

[tex]^{n} C_{r}[/tex] is the total number of combinations.

n is the total number of objects

r is the number of objects selected.

The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.

According to the question.

There are total 6 dishes.

Manger have to choose three dishes for monday.

Now the total number of combination of selecting 3 dishes from 6 dishes

[tex]=^{6} C_{3}[/tex]

[tex]= \frac{6!}{3!(6-3)!}[/tex]

[tex]= \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

[tex]=20[/tex]

So, the manager has total 20 choices to select three dishes randomly out or 6 dishes.

Also, it is given that for monday applesauce and broccolli will both offered so the number of choices or combination or the three dishes will be

Therefore, the theoretical probability that applesauce and brocoli will both be offered on monday

[tex]= \frac{4}{20}\times100[/tex]

[tex]= \frac{1}{5} \times 100\\= 20\%[/tex]

Hence, the theoretical probability that applesauce and broccoli will both offered on monday is 20%.

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The algebraic expression is (7 + 3m)/27 < n

The statement is given as:

"The quotient of seven more than three times a number m and the number 27 is less than n"​

The numbers are represented as n and m

Quotient means divide

So, we have:

The quotient of seven more than three times a number m and the number 27 is represented as:

(7 + 3m)/27

The result is less than n.

So, we have:

(7 + 3m)/27 < n

Hence, the algebraic expression is (7 + 3m)/27 < n

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Answer:380

Step-by-step explanation:sort the list, take center value or mean of center values if even number of items in list

Answer:

P= 4a would be the answer

Using the zero product property, we can set each factor equal to zero.

First Factor [tex]x^{4}+5x^{2}-36[/tex]

[tex]x^{4}+5x^{2}-36=0\\(x^{2}+9)(x^{2}-4)=0\\x^{2}+9=0, x^{2}-4=0\\x=\pm 3i, x=\pm 2[/tex]

Second Factor [tex]2x^{2}+9x+5[/tex]

Using the quadratic formula, we get [tex]x=\frac{-9 \pm \sqrt{41}}{4}[/tex].

Answer:   [1, infinity)

===========================================================

Explanation:

Let's isolate x in the first inequality mentioned.

x + 7 ≥ 4

x + 7-7 ≥ 4-7

x ≥ -3

I subtracted 7 from both sides to undo the +7.

Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.

11x - 8 ≥ 3

11x - 8+8 ≥ 3+8

11x ≥ 11

11x/11 ≥ 11/11

x ≥ 1

------------------

The two solutions we found were

x ≥ -3 and x ≥ 1

Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.

Notice that the two inequalities overlap for x ≥ 1

In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.

The two solutions intersect to form x ≥ 1

The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity

Then that turns into the interval notation of [1, infinity)

The square bracket includes the endpoint 1.

If needed, use the infinity symbol in place of the word "infinity".

Answer:

[1, ∞)

Step-by-step explanation:

To solve a compound inequality, first separate it into two inequalities and solve them separately:

Solution of Inequality 1:

x + 7 ≥ 4

⇒ x ≥ 4 - 7

⇒ x ≥ -3

Solution of Inequality 2:

11x - 8 ≥ 3

⇒ 11x ≥ 3 + 8

⇒ 11x ≥ 11

⇒ x ≥ 1

As both graphs overlap for x ≥ 1, this is the solution.

Therefore, in interval notation:  [1, ∞)

Answer:

10 teams (1 remainder)

Step-by-step explanation:

if each team has 3 players and there are 30 friends, divide that and youll end up with 10 teams. you will also have 1 remaining player