Out of 300 students, 55% are absent. How many students are at school?

Answer: \(7.39466666\)

Step-by-step explanation:

Setting \(x=2.2\) and \(n=3\),

\(e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666\)

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

\(\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}\)

To approximate \(e^{2.2}\) with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

\(e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\)

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

\(\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}\)

Therefore, the approximate value of \(e^{2.2}\) is:

\(\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}\)

Note: To obtain a more accurate approximate value, increase the value of n.

The value of the variable is; x = π³ - π/π

Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.

These algebraic expressions are also comprised of arithmetic operations, such are; Division

Multiplication, Subtraction, Floor division, Addition, Bracket, Parentheses

From the given information, we have that;

y = π³

y = πx + π

Substitute the values, we have;

π³ =  πx + π

Collect like terms

π³ - π = πx

Divide both sides by the coefficient of x

x = π³ - π/π

Thus, the value is x = π³ - π/π

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Answer:

18m-20

Step-by-step explanation:

4(3m-2)+3(2m-4)=

12m-8+6m-12=

collect like terms

12m+6m-8-12=

18m-20

Answer:

thousandths

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

the coordinates are all different

If One of the 200 business majors at a college is to be chosen for the student senate. The outcomes that correspond to a business major who is enrolled in both accounting and business law is: x = 33 - y.

Since we know that 92 students are enrolled in either course, we can write this number in the intersection of the two circles, which represents the number of students enrolled in both courses. Let x be the number of students enrolled only in accounting, and y be the number of students enrolled only in business law.

Our Venn diagram now looks like this:

       Accounting

         (77-x)       (x)

             ___________

            |           |

    Total |   (92)    |  y

   Business|___________|

       Law |           |

          |     x     |  

          |___________|

             (64-y)    |

                     Total

                    Business

                     Majors

We know that there are 200 business majors in total, so the sum of the four regions in the diagram must add up to 200. Therefore:

x + y + (77-x) + (64-y) + 92 = 200

Simplifying this equation, we get:

x + y = 33

We want to find the number of outcomes that correspond to a business major who is enrolled in both accounting and business law. From the Venn diagram, we can see that this is represented by the intersection of the two circles, which has a value of x.

Therefore, there are x = 33 - y outcomes that correspond to a business major who is enrolled in both accounting and business law. The value of y can range from 0 (if all 33 students enrolled only in accounting) to 33 (if all 33 students enrolled only in business law).

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

785.4

I think it is right

Answer:

Solution: Here, Radius of cylindrical tank (r)=2ml Height of cylindrical tank (h)=8ml volume of that cylindrical tank (v)=?

Now,

we know that,

Volume of cylindrical(v)=V=πr2h=3.14×2×2×8=100.48ans.

Using the calorie count C for a serving of food C =5h + 8f + 5​p, the formula for f is derived to be; f = (C - 5h  - 5​p) / 8

An equation is an expression that shows the relationship between two or more numbers and variables.

WE have been Given data that C =5h + 8f + 5​p

Where C is the calorie count, h is the number of grams of carbohydrate, f is the number of grams of fat and p is the number of grams of protein

Now solving for f in the given equation;

C = 5h + 8f + 5​p

Then f the subject of formula;

C - 5h  - 5​p = + 8f

8f = C - 5h  - 5​p

Now dividing through by 8

f = (C - 5h  - 5​p) / 8

Hence, The number of grams of fat, f, contained in a serving of food is; f = (C - 5h  - 5​p) / 8

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Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

Answer:

b.  e^9.45 = x

see last example and this explains whole numbers and decimals.

Step-by-step explanation:

Another example we can Solve  100=20e^2t .

Solution

100 = 20e^2t

5 = 20e ^2t

in 5 = 2t

Therefore  t = in5/ 2

Step 1 was ; Divide by the coefficient of the power

Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions

Step 3 was; Divide by the coefficient of t

Another example;

Solve  e^2x−e^x = 56 .

Solution

Analysis

When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation  e^x=−7  because a positive number never equals a negative number. The solution  ln(−7)  is not a real number, and in the real number system this solution is rejected as an extraneous solution.

Another example is;

Solve  e^2x=e^x+2 .

Answer

Q&A: Does every logarithmic equation have a solution?

No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.

Last example determines decimals ;

Solve  lnx =3 .

Solution

lnx^x=3=e^3

Use the definition of the natural logarithm

Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

It shows values of graphs of  y=lnx  and  y=3  cross at the point  (e^3,3) , which is approximately  (20.0855,3) .

See graph below.

Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))

Answer:

t=1/50

Step-by-step explanation:

2/5t=20

2=100t

2/100=t

t=1/50

The value of the inverse function f-¹ (3) is (e) 11

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

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

The recipe is

1/4 cup water for every 1/2 cup of flour.

let x represent the number of cups of flour needed for 1.5 cups of water. The equation would be

1/4 = 1/2

1.5 = x

Crossmultiplying, it becomes

1/4 * x = 1.5 * 1/2

0.25x = 0.75

x = 0.75/0.25

x = 3

3 cups of flour would be needed for 1.5 cups of water

Answer:

62.5 % is write answer.

Step-by-step explanation:

Please like my answer to make me brain list.

Explanation:

"5 hours 50 minutes" is close to "6 hours"

Let's subtract 6 hours from 17:25

It would drop us to 11:25 since 17-6 = 11.

When we subtracted 6 hours, we subtracted 10 extra minutes that we shouldn't have done. To fix this, add 10 minutes on to go from 11:25 to 11:35

Answer:

The traveler started at 11:35

Step-by-step explanation:

The question already gives you the time that the traveler arrived which is 17:25 and how long it took them to get to the desired location which was 5 hours 50 minutes. So what you need to do is subtract the time the traveler arrived to how long it took to get there.

Equation:

17:25 - 5:50

= 11:35

8318 microns is the intensity of an earthquake in Hawaii.

The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. This scale was developed for the Southern California earthquake recorded by the Wood He Anderson seismograph whose epicenter was less than 600 km (373 mi) from the seismometer location. However, today's seismometers can be calibrated to calculate the Richter magnitude, and modern methods of measuring earthquake magnitude are designed to give results consistent with those measured using the Richter scale. Developed.

The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to scale by the seismograph.

Using the formula,

\(M = log \frac{i}{s}\\ 3.92 = log\frac{i}{1 micron} \\10^3.92 = \frac{i}{s} \\i = 8318\)

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Answer:

the answer will be 60

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

its 36

Step-by-step explanation:

Answer:

1.917

Step-by-step explanation:

The difference between 4.091 and 2.174 will be;

⇒ 1.917

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The numbers are,

⇒ 4.091 and 2.174

Now,

Since, The numbers are,

⇒ 4.091 and 2.174

Hence, The difference the number 4.091 and 2.174 is,

⇒ 4.091 - 2.174

⇒ 1.917

Thus, The difference between 4.091 and 2.174 = 1.917

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The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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Answer: A

because slope are

Answer:

1. Is a continuous random variable

2. Is a discrete random variable

3. Is not a random variable

Step-by-step explanation:

1. The exact Weight of quarters in circulation in the united states is a continuous random variable. This is because a random variable such as this can take uncountable and infinite number of values.

2. The shoe sizes if humans is an example of discrete random variable. This is a discrete random variable because it has countable number of values.

3. Political party affiliation is not a random variable.

Thank you!

Answer:

The radius is 5 cm

Step-by-step explanation:

The formula for the area of a circle is :  \(\p*radius^2\)

To work out the length of the radius you would first need to divide the area of  78.5 cm by pi (pi=3.14), this gives you \(25cm^2\\\). This is because by dividing the area by pi we are isolating the value of the radius squared.

The final step is to work out the radius. You can do this by finding the square root of the radius squared which is 25, this gives you 5 cm. This means that the radius is 5 cm. This is because the square root is a number that when squared equals that number.

1) Divide 78.5 by pi.

\(78.5/\pi=25cm^2\)

2) Find the square root of 25 cm squared.

\(\sqrt{25} =5 cm\)

In this question pi is 3.14

The solution of the expression is x=0 and it is the only solution that is an integer.

An expression in mathematics is a combination of numbers, variables, and mathematical operations that evaluates to a numerical value or an algebraic expression.

To do this, we need to pick a range of x values and substitute them into each equation to find the corresponding y values.

Next, we need to find the points of intersection between the two curves. These are the x values where the two curves cross each other and have the same y value. To find these points, we will set the two equations equal to each other and solve for x:

=> x=5x−x³

Expanding this equation, we get

=> 4x³+x=0.

Factoring this equation, we get

=> x(4x²+1)=0.

This gives us two solutions, x=0 and x=±i√(1/4), where i is the imaginary unit. Since x can only take on real values, x=0 is the only solution that is an integer.

Complete Question:

Use the open space to show all of your work. This includes: sketching the curves, finding and labeling the points of intersection, setting up the appropriate definite integral(s), and evaluating them. Place your numerical answer for the area of the region in the box. Leave your answer in exact form.

y = x,

y = 5x−x³

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It looks like you want to compute the double integral

\(\displaystyle \iint_D (x+y) \,\mathrm dx\,\mathrm dy\)

over the region D with the unit circle x ² + y ² = 1 as its boundary.

Convert to polar coordinates, in which D is given by the set

D = {(r, θ) : 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π}

and

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

Then the integral is

\(\displaystyle \iint_D (x+y)\,\mathrm dx\,\mathrm dy = \iint_D r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \int_0^{2\pi} \int_0^1 r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \underbrace{\left( \int_0^{2\pi}(\cos(\theta)+\sin(\theta))\,\mathrm d\theta \right)}_{\int = 0} \left( \int_0^1 r^2\,\mathrm dr \right) = \boxed{0}\)

Answer:

g(4) = 10

f⁻¹(11) = 1

h{g(4)} =

if h(x) = (10/x) – 3 = 7

if h(x) = 10/(x – 3) = 10/7

____________

f⁻¹(x) = (x - 4) / 7

Answer:

6y - 5x = 6

Step-by-step explanation:

im a god thats how

1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)

2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)

3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)

4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)

5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)

6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)

7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)

8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)

9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)

10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)

11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)

12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)

13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)

14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)

Here are the journal entries for the given transactions:

1. Bricks and timber purchased for construction:

Debit: Bricks (Asset) - Rs 60,000

Debit: Timber (Asset) - Rs 35,000

Credit: Bank (Liability) - Rs 95,000

2. Transfer to fixed deposit account:

Debit: Fixed Deposit (Asset) - Rs 13,000

Credit: Current Account (Asset) - Rs 13,000

3. Appointment of Mr. S.N. Rao as Accountant:

Debit: Salary Expense (Expense) - Rs 300

Debit: Security Deposit (Asset) - Rs 1,000

Credit: Accountant (Liability) - Rs 300

4. Goods sold to Shruti:

Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000

Credit: Sales (Income) - Rs 80,000

5. Goods purchased from Richa:

Debit: Purchases (Expense) - Rs 60,000

Credit: Accounts Payable - Richa (Liability) - Rs 60,000

6. Goods sold to Shilpa:

Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000

Credit: Sales (Income) - Rs 50,000

7. Goods sold to Garima:

Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000

Credit: Sales (Income) - Rs 1,00,000

8.Purchase of land:

Debit: Land (Asset) - Rs 2,00,000

Debit: Brokerage Expense (Expense) - Rs 2,000

Debit: Registration Charges (Expense) - Rs 15,000

Credit: Bank (Liability) - Rs 2,17,000

9. Goods and cash taken away by proprietor:

Debit: Proprietor's Drawings (Equity) - Rs 65,000

Credit: Goods (Asset) - Rs 25,000

Credit: Cash (Asset) - Rs 40,000

10. Goods sold to Charu:

Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000

Credit: Sales (Income) - Rs 1,20,000

Credit: Cost of Goods Sold (Expense) - Rs 80,000

Credit: Profit on Sales (Income) - Rs 40,000

11. Rent paid for the building:

Debit: Rent Expense (Expense) - Rs 60,000

Credit: Bank (Liability) - Rs 60,000

12. Goods sold to Sunil:

Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000

Credit: Sales (Income) - Rs 24,000

Credit: Cost of Goods Sold (Expense) - Rs 20,000

Credit: Profit on Sales (Income) - Rs 4,000

13. Goods purchased from Nanda and supplied to Helen:

Debit: Purchases (Expense) - Rs 1,000

Debit: Accounts Payable - Nanda (Liability) - Rs 1,000

Credit: Accounts Receivable - Helen (Asset) - Rs 1,300

Credit: Sales (Income) - Rs 1,300

14. Goods received from Rohit and Sons and supplied to Madan:

Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)

Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700

Debit: Accounts Receivable - Madan (Asset) - Rs 3,000

Credit: Sales (Income) - Rs 3,000

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