Simplifying Radicals pls help with full calc

The Laplace transform of the solution y(t)=7+14t²·

The Laplace transform is an integral transform perhaps second only to the Fourier transforms in its utility in solving physical problems.

The Laplace transform is useful in solving linear ordinary differential equations such as arising in the analysis of electronic circuits.

The basic formula of Laplace transform:

\(F(S)=\int\limits^_\infty} _0 {f(t)}e^-stf' \,\)

Where s=σ+iw

F(s)=laplace transform.

s=complex number

t=real number>=0

t'=first derivative of the function f(t)

Now consider the given  integral equation:

\(\int\limits^t_0 sin[(2t-w)]y(w)} \, dw=7t^2\)

By integrating we get

⇒sin2t*y(t)=7t²-----(1)

Now, Apply the Laplace transform on both sides:

L{sin2t*y(t)}=7L{t²}

⇒L{sin2t} L{y(t)}=7(2!/s²+1)

Here we use    

\(L (t^n)=\frac{n!}{s^n+1}\)

⇒  \(\frac{2}{s^2+2^2} y(s)=\frac{14}{s^3}\)

\(y(s)=\frac{14}{s^3} *\frac{s^2+2^2}{2} =\frac{7(s^2+4)}{s^3} \\\\y(s)=7(\frac{s^2}{s^3} +\frac{4}{s^3} \\\\y(s)=7(\frac{1}{s} +\frac{4}{s^3} )\\\\y(s)=\frac{7}{s} +\frac{28}{s^3}\)

Taking Inverse Laplace transforms on both sides:

L-1={y(s)}=7L-1{1/s}=28L-1{1/s^3}

⇒y(t)=7(1)+28(t^2/2!)

⇒y(t)=7+14t²

This is a required solution.

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Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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Answer:

$240

Step-by-step explanation:

Amount to be saved = $1200

Number of months = 5

So, amount to be saved in each month

= Amount to be raised / Number of months

= $1200 / 5

= $240

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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Therefore, 31.8 ounces of the 17% alloy and (110 - 31.8) = 78.2 ounces of the 19% alloy should be mixed to form 110 ounces of the desired alloy.

Let's assume the number of ounces of the 17% alloy to be mixed is x, and the number of ounces of the 19% alloy to be mixed is 110 - x (since the total desired alloy is 110 ounces). To find the amount of copper in the resulting alloy, we can set up the equation:

0.17x + 0.19(110 - x) = 0.184(110)

Simplifying the equation:

0.17x + 20.9 - 0.19x = 20.264

Combine like terms:

-0.02x = -0.636

Divide both sides by -0.02:

x = 31.8

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Pave Construction provides services on account for bad dept of $40,000. Write-off of accounts receivable in 2022 is Allowance for Uncollectible Accounts (balance sheet) = $10,000. The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be  $30,000.The balance of Allowance for Uncollectible Accounts at the end of 2022 will be $25,000 (assuming actual write-offs of $15,000).

Adjusting entry for uncollectible accounts on December 31, 2021:

Bad Debt Expense (income statement) = $40,000 ([$160,000 - $110,000] * 0.25)

Allowance for Uncollectible Accounts (balance sheet) = $40,000

Write-off of accounts receivable in 2022:

Allowance for Uncollectible Accounts (balance sheet) = $10,000

Accounts Receivable (balance sheet) = $10,000

Balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022):

The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be $40,000 - $10,000 = $30,000.

Write-off of accounts receivable in 2022 (assuming actual write-offs of $15,000):

Allowance for Uncollectible Accounts (balance sheet) = $15,000

Accounts Receivable (balance sheet) = $15,000

Balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) (assuming actual write-offs of $15,000):

The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be $40,000 - $15,000 = $25,000.

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Answer:

4.5 .       ^14

Step-by-step explanation:

dont cheat in tests next time not everyone is as kind as me

Answer:

It would be 4.5 x 10^14

Step-by-step explanation:

Just multiply the decimals and for the exponents, you add them.

Answer:

A =13.5 yd^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

A = 1/2 (4.5) ( 6)

A =13.5 yd^2

Answer:

22.5

Step-by-step explanation:

7.5ydx6yd

=45yd

45yd/2

=22.5yd^2

Answer:

B 9

Step-by-step explanation:

Use the rule of exponents for a division. To divide two powers with the same base, write the same base and subtract the exponents.

\( \dfrac{a^m}{a^n} = a^{m - n} \)

Now do it with your numbers.

\( \dfrac{3^4}{3^2} = 3^{4 - 2} = 3^2 = 3 \times 3 = 9 \)

Answer: B 9

The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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Answer:

x = 4

Step-by-step explanation:

10(x - 1) = 8x - 2

10x - 10 = 8x - 2

10x = 8x + 8

2x = 8

x = 4

Answer:

3/36 and 7/36

Step-by-step explanation:

The new fractions with common denominator are 27/36 and 28/36

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, rewrite 3/4 and 7/9 so that they have a common denominator.

To make their denominator common, multiply, the first fraction by 9 and second denominator by 4,

Then,

3×9/4×9 = 27/36

7×4/9×4 = 28/36

Hence, the new fractions with common denominator are 27/36 and 28/36

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The value of the number is 57/16

The mathematical statement is given as:

Nine times a number y subtracted from 85 is seven times the sum of four and y

Remove the above mathematical statement as an algebraic expression

85 - 9y = 7(4 + y)

Open the bracket

85 - 9y = 28 + 7y

Collect the like terms

9y + 7y = 85 - 28

Evaluate the like terms

16y = 57

Divide both sides by 16

y = 57/16

Hence, the value of the number is 57/16

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The number of small ball bags she will need is 7 small bags, the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that;

Need of flour for cakes= 17 2/5 pounds

Now,

There are 4 large bags, and each one has 4 pounds.

She buys all of the large bags, she already has;

4x4=16

16 pounds. So, she only needs

17 2/5 -16= 1 2/5

=5/5+2/5

=7/5

1 2/5 pounds more, this fraction is equals to 7/5 pounds.

The small bags only contains 1/5 pounds of flour so,

7/5/1/5

=7*5/1*5

=7

Therefore, by algebra the answer will be 7 bags

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The complete question is;

Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags

With an MBA, there is a 0.9938 or 99.3%  probability that a randomly chosen candidate will receive a beginning salary of at least $20,000.

Given data,

The average beginning salary for people with an MBA is $35,000, and the standard deviation is $6,000, according to a normal distribution.

Mean = 35000 , Standard deviation = 6000

P(X>=20000)= P(x-u/σ > 20000 - 35000/6000)

                      =P(Z > -15000/6000)

                      =P(Z > -2.5)

                      =1-P(Z < -2.5)

                      = 1-0.0062

                      =0.9938

Hence, The probability that a randomly selected individual with an MBA degree will get a starting salary of at least $20,000 is 99.3%

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Hello!

Answer:

\(\huge\boxed{100 : 9}\)

If corresponding side lengths are in the ratio 10 : 3, the ratio of their areas will simply be the square (area is 2-dimensional).

Therefore:

10 : 3 ⇒ (10)² : (9)²

100 : 9 is the ratio of the areas.

I hope this helped you! :)

Ratio of the corresponding sides of rectangle

➾ 10 : 3

Areas will by in the ratio of 10² : 3²

➾ 100 : 9

let first rectangles sides be 10 l and 10 b ➾ The area will be 100 × l × b

So second rectangles sides be 3 l and 3b

➾ The area will be 9 × l × b

So the ratio of areas

➾100lb : 9lb

➾ 100 : 9

Answer: B, D, E

Step-by-step explanation:

Answer:

151.7 cm^3

Step-by-step explanation:

3.7 x 10 x 4.1 = 151.7

BRAINLIEST? TY!!

Answer:

151.7 cm^3

Step-by-step explanation:

If you didn't know already the volume of a rectangular prism is

length x witdh x height.

Multiply 10x4.1 and you will get 41

Then multiply 41 by 3.7 to get 151.7.

We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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Answer:

3. 60/37 hours

4. 35/12 hours

Step-by-step explanation:

3.

Nicole: 1 room in 6 hours; in 1 hour: 1/6 room

Alexandra: 1 room in 5 hours; in 1 hour: 1/5 room

Liana: 1 room in 4 hours; in 1 hour: 1/4 room

Combined in 1 hour:

1/6 + 1/5 + 1/4

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/6 + 1/5 + 1/4 = 1/x

10/60 + 12/60 + 15/60 = 1/x

37/60 = 1/x

x = 60/37

Answer: 60/37 hours

4.

Jake: 1 room in 7 hours; in 1 hour: 1/7 room

Karen: 1 room in 5 hours; in 1 hour: 1/5 room

Combined in 1 hour:

1/7 + 1/5

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/7 + 1/5 = 1/x

5/35 + 7/35 = 1/x

12/35 = 1/x

x = 35/12

35/12 hours

Answer: 35/12 hours

Answer

\(1/6\)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The answer is A

P.S i am emo

Answer:

y = -15x + 50

Step-by-step explanation:

the pattern in the x side is +1 and the pattern on the y side is -15 so it is 15/1 which = m in y = mx + b

then you multiple -15 times whatever x and add 50 to get y like

y = -15 x 2 + 50 = 20

Answer:

The product of (px + qy)(ax − by) is pax^2 + qaxby - pbx^2 - qby^2.

Step-by-step explanation:

Answer: apx^2-bpxy+aqxy-bqy^2

Step-by-step explanation: (px+qy)x(ax-by) Multiply each term in the first parenthesis by each term in the second parenthesis (FOIL). That would give you pxax-bpxy+aqxy-qyby. Then calculate the product pxax which would give you apx^2-bpxy+aqxy-qyby. Calculate the other product qyby which would give you apx^2-bpxy+aqxy-bqy^2.  

The 95% confidence interval for 2007 returns is -29.2% to 49.2%. We can calculate it in the following manner.

To calculate the 95% confidence interval for 2007 returns of stocks in the S&P 500, we first need to determine the margin of error. We can use the formula:

Margin of Error = z* (standard deviation / sqrt(n))

Where z* is the z-score for the desired level of confidence, which is 1.96 for a 95% confidence interval, standard deviation is 20%, and n is the sample size (which we assume to be 1).

So, Margin of Error = 1.96 * (0.20 / sqrt(1)) = 0.392

Next, we need to determine the range within which the true population mean is likely to lie. We can calculate this by adding and subtracting the margin of error from the sample mean. In this case, the sample mean is the average annual return over the period 1886-2006, which is 10%.

So, the 95% confidence interval for 2007 returns is:

10% +/- 0.392 or 9.608% to 10.392%

Therefore, we can be 95% confident that the true average annual return for stocks in the S&P 500 for the year 2007 falls between 9.608% and 10.392%.

Based on the provided information, the average annual return for stocks in the S&P 500 from 1886-2006 is 10%, and the standard deviation is 20%. To calculate a 95% confidence interval for 2007 returns, we can use the formula:

Confidence Interval = Mean ± (1.96 * Standard Deviation)

In this case, the mean is 10%, and the standard deviation is 20%. Plugging in these values, we get:

Confidence Interval = 10% ± (1.96 * 20%)

Confidence Interval = 10% ± 39.2%

Thus, the 95% confidence interval for 2007 returns is -29.2% to 49.2%.

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Answer:

  P'(-12, -18)

Step-by-step explanation:

The image of a point reflected over the y-axis is as far to the left of that axis as the original point is to the right. That is, the reflection changes the sign of the x-coordinate. The reflected point is ...

  P'(-12, -18)

Mean, because there are no outliers that affect the center

third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

complete question

A survey was taken of students in math classes to find out how many hours per day students spend

on social media. The survey results for the first., second-, and third-period classes are as follows:

First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3

Which is the best measure of center for second period and why? (5 points)

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The central idea of this passage is; - The Grimms' first collection of tales was a cultural study intended for a scholarly audience. Option D

This is further explained below.

Generally,  The Grimm brothers presented an oppressed and frightened young man who was left for dead in the woods by his brothers in their 1812 fairy tale. In exchange for seven years of protection from death, he gladly dons the devil's green cloak and vows never to shave or bathe again.

In conclusion, The most important point that should be taken away from this paragraph is that the Grimms' first collection of fairy tales was a cultural study that was aimed at an academic audience. The  Option D.

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Answer:

D: The Grimms’ first collection of tales was a cultural study intended for a scholarly audience.

The amount you will pay back by the end of the term is; 162.18 dollar.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + r)^{t}\)

Given that you borrow $101 at 7% compounded annually for seven years, then we have;

P = 101 dollar

Rate = 7%

Times = 7 yr

Therefore,

\(a = p(1 + r)^{t}\)

\(a = 101(1 + 0.07)^{7}\\\\a = 101 (1.07)^7\\\\a = $162.18\)

Hence, The amount you will pay back by the end of the term is; 162.18 dollar.

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Answer:

  (c)  f(g(3)) > g(f(3))

Step-by-step explanation:

The relationship between the function values can be found by evaluating the functions.

The order of operations tells us we must first evaluate g(3).

  g(x) = -3x +15

  g(3) = -3(3) +15 = 6

Then we can evaluate f(x) for x=6:

  f(x) = 7x

  f(6) = 7(6) = 42

So, the composition is ...

  f(g(3)) = 42

As above, we must first evaluate f(3):

  f(3) = 7(3) = 21

Then we can evaluate g(x) for x=21:

  g(21) = -3(21) +15 = -63 +15 = -48

That means the composition is ...

  g(f(3)) = -48

The first is greater than the second.

  42 > -48

  f(g(3)) > g(f(3))

Answer:

Answer is D.

30

Step-by-step explanation:

all angles add up to 180(applys to triangles)