Use the Laplace transform to solve the following initial value problem: y + 10y + 25y = 0 y(0) = - 3, y'(0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y (s) = and write the above answer in its partial fraction decomposition, Y(s) = A/s + a + B/(s+a)2 Y (s) = + Now by inverting the transform, find y(t) =

If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

sp2 hybridization

There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.

The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization

To learn more about bond angles

https://brainly.com/question/29690391

#SPJ4

The areas of each of Reuben's fields are given as follows:

Hence the total area of all of Reuben's fields is given as follows:

204,000 square feet.

The areas of the fields is given by the multiplication of each of the dimensions of the field, as the fields have a rectangular format.

Then the total area is obtained as the sum of the areas of each field.

The dimensions of each field are given as follows, from the table given by the image at the end of the answer:

Hence the areas of each of the fields are given as follows:

Then the total area is given as follows:

24,000 + 140,000 + 40,000 = 204,000 square feet.

The problem asks for the areas of each field and the total area.

The dimensions are given by the image shown at the end of the answer.

More can be learned about the areas of a rectangle at https://brainly.com/question/25292087

#SPJ1

Answer: We write J raised to the 9th power as J9 (which means J multiplied by J a total of nine times). "Sum" means "add them" so J9 + K

Step-by-step explanation:

Yes, it would be unusual for a  500 adult Americans to result in 210 or more who believe marriage is obsolete. The probability value is 0.39 for adult Americans.  

We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

We have given that 39% american adults women believes that marriage is now obsolete.

So,39% of 500 adult American women is =[(39/100)×500]

                                                                     =39×5=195

So,probability of adult women who believes marriage is obsolete is =(195/500)=0.39

Now, we need to check that whether 210 women believes marriage is obsolete or not.

So, number of favorable outcome is 210 and total number of outcomes=500.

Therefore, probability of adult women who believes marriage is obsolete is=(210/500)=0.42

Now,we can see that 195 women probability is lower than 210 women probability. It means that more number of women considered marriage is obsolete.

Hence, yes it is unusual and the  probability value of adult Americans is 0.39

To know more about probability, visit here:

https://brainly.com/question/11234923

#SPJ4

(Complete question) is:

would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?If so determine the probability, otherwise type 0 for this result NOT to be unusual

By solving a system of equations we will see that she sold 80 phones and 240 accessories.

Let's define the variables:

x = number of phones.

y = number of accessories.

We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:

y = 3x

x*$8 + y*$4 = $160

To solve the system, we can replace the first equation into the second one.

x*$8 + (3x)*$4 = $160

x*$8 + x*$12 = $160

x*$20 =  $160

x  = $160/$20 = 80

She sold 80 phones, and the number of accessories is:

y = 3x

y = 3*80 = 240

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer:

753

Step-by-step explanation:

Arithmetic sequences are sequences that change by a constant factor.

Explicit Rule

The formula that describes an arithmetic sequence is called the "explicit rule". This formula is f(x) = f(1) + d(x-1). Sometimes the rule will be written with [tex]a_{n}[/tex] instead of f(x) but the equations are still the same.

In this equation, f(1) is the first term of the sequence, d is the common difference, and x is the term. The common difference is the factor that the sequence changes by.

Setting Up the Equation

To set up the equation, we need to find f(1) and d.

The first term, f(1), is directly given to us in the equation. The first term written is -6, so f(1)=-6.

It is slightly more difficult to find d. But, one easy way to find d is by subtracting terms. Take the second term, 5, and subtract the first term, -6.

So, d = 11. Each term in the sequence increases by 11.

The final equation is f(x) = -6 + 11(x-1).

Finding the 70th Term

Now, all we have to do is plug 70 in for x. To find any term in the sequence, all you have to do is plug the term number in for x.

The 70th term in the sequence is 753.

The kiwi as per the given relation of ostrich and kiwi's height is equal to 22inches tall.

As given in the question,

Ostrich height is equal to 108 inches

Let us consider 'x' inches be the height of the kiwi.

Ostrich is 20inches more than four times of x.

Ostrich height  = 20 + 4x

⇒ 108 = 20 + 4x

Subtract 20 from both the sides we get,

108 - 20 = 20 + 4x -20

⇒ 88 = 4x

Divide by 4 on both the sides we get,

88/ 4 = 4x / 4

⇒ x = 22 inches

Therefore, as per the given relation of ostrich and kiwi's height , kiwi is 22inches tall.

The complete question is :

The height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?

Learn more about height here

brainly.com/question/10726356

#SPJ4

The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2

The standard form of a quadratic equation is;

y = ax² + bx + c

where a, b and c are constants

Thus, for the coordinate (10,0), we have;

0 = a(10)² + b(10) + c

100a + 10b + c = 0  -----(1)

For the coordinate (1,0), we have;

0 = a(1)² + b(1) + c

a + b + c = 0   -----(2)

For the coordinate (4,3), we have;

3 = a(4)² + b(1) + c

16a + b + c = 3  ------(3)

Using online simultaneous equation, we have;

a = 0.2 and b = -2.2 and c = 2

The quadratic function is;

y = 0.2x² - 2.2x + 2

Read more about Quadratic Equations at; https://brainly.com/question/25841119

#SPJ1

The resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]

A term's multiplicative history can be determined by an index, which is a discrete number. Indexes is the plural of index.

The exponentiation operator is the caret (). It is important to distinguish the exponent operator from the base-10 exponent sign. In a numeric literal, a base-10 exponent sign (scientific notation) can be represented by either an uppercase "E" or a lowercase "e."

[tex](125x^{7/3})^{-1/3}[/tex]

Using the indices law that states;

[tex](a^n)^m = a^{mn}[/tex]

Given,

[tex](125x^{7/3})^{-1/3}[/tex]

Since, [tex](125x^{7/3})^{-1/3}[/tex]= [tex][((5x)^3)^{7/3}]^{-1/3}[/tex]

= [tex][(5x)^7]^{-1/3}[/tex]

= [tex]5x^{-7/3}[/tex]

= [tex]\frac{1}{5x^{7/3}}[/tex]

Hence the resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]

To know more about indices refer to:

https://brainly.com/question/16933066

#SPJ1

The total cost of the set and the tax is 2653.6 dollars.

The Myer family purchased a bedroom set for $2,480.  The sales tax rate is  7 percent.

Therefore, the total cost of the set and the tax can be calculated as follows:

tax = 7% of 2480

tax = 7 / 100 × 2480

tax = 17360 / 100

tax = $173.6

Therefore, let's find the total cost of the set and tax.

total cost = 173.6 + 2480

total cost = 2653.6 dollars

learn more on sales tax rate here: https://brainly.com/question/24140373

#SPJ1

The total cost of the ingredient is $0.84 for 6 ounces.

Define fixed cost.

The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.

It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.

Solution Explained:
Given,

1 pound = $2.25

Since 1 pound = 16 ounces

So, 16 ounces = 2.25

      1 ounce = 2.25/16 = 0.14

Therefore, 6 ounces = 0.14 X 6 = 0.84

To learn more about fixed cost, use the link given
https://brainly.com/question/24868261
#SPJ4

a) Probability of exactly three boys is 0.3185

b) Probability of at least one boy is 0.9717

c) Probability of at least one girl is 0.9655

d) Probability of all of same sex is 0.06275

What is probability?

a) Probability of exactly three boys

Choose 3 out of 5 in C(5,3)=10 ways

So probability is:10*0.51^3*0.49^2

~0.3185

(b) Probability of at least one boy

p(at least one boy)=1-p( all girls)

=1-0.49^5

=0.9717

c) Probability of at least one girl

p(at least one girl)=1-p( all boys)

=1-0.51^5

=0.9655

d) Probability of all of same sex

p(all of same sex)=p(all boys)+p(all girls)=

0.51^5+0.49^5

=0.06275

To know more about probability check the below link:

https://brainly.com/question/13604758

#SPJ4

with the help of Advanced Placement statistics correct answer is option B.

what is Advanced Placement statistics?

In the United States, the College Board's Advanced Placement programme offers a college-level high school statistics course known as Advanced Placement Statistics.

explanation:

The data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair.

hence the correct option is B by Advanced Placement statistics

To learn more about Advanced Placement statistics from the given link

https://brainly.com/question/16346040

#SPJ4

Answer:2.25 gallons

Step-by-step explanation:

The total miles of the trip are 521.68 miles.

Addition in maths, a process of combining two or more numbers.

Given that, Rosie drives 317.88 miles before lunch and then  [tex]203\frac{4}{5}[/tex] miles before break,

Total miles = 317.88 +  [tex]203\frac{4}{5}[/tex] miles = 521.68 miles

Hence, The total miles of the trip are 521.68 miles.

For more references on addition, click;

https://brainly.com/question/29560851

#SPJ1

If a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.

Two or more expressions with an Equal sign is called as Equation.

A cyclist rides at an average speed of 18 miles per hour.

We have to find the number of miles she ride in seven hours

Assume x be the number of miles she ride

Let us form a proportional equation

18/1 = x/7

Apply cross multiplication

18×7=x

126=x

Hence, if a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

This question is based on the probability. Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.

Given:

There are 5 marbles in a bag. Each marble is a different color. The colors are: red, orange, green, blue, purple. Two marbles are randomly drawn from the bag without replacement.

We need to determined the probability that the red marble is drawn first and the white marble is drawn second.

According to the question,

It is given that, there are 5 different marbles. In the first draw, you have a one out of 5 chance of getting the red is 1/5 .

In the second draw, there are 4 marbles remaining, so a one out of 4 chance of drawing a white marble i.e. 1/4.

Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.

⇒ 1/5 × 1/4 = 1/20

Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.

Learn more about Probability:

https://brainly.com/question/11234923

#SPJ4

a. sample mean = 7.1838

b. sample variance = 0.0004 and standard deviation = 0.0207

c. coefficient of variation = 0.29%

What is sample variance?

The expectation of a random variable's squared deviation from its population mean or sample mean is known as variance in probability theory and statistics. Dispersion is a measure of how far apart a group of numbers is from their mean value, and variance is a measure of dispersion.

A probability distribution's variance is defined as the mean of the squared deviation from the distribution's mean. The expected value, commonly known as the mean, is the value you will obtain on average if you take several samples of a probability distribution.

Solution Explained:

a) Mean x=∑x/n

=7.15+7.2+7.18+7.19+7.21+7.2+7.16+7.18/8

=57.47/8

=7.1838

b) Sample Variance S2=∑x2-((∑x)^2/n)/n-1

=(412.8531-(57.47)^2/8)/7
=412.8531-412.8501/7

=0.003/7

=0.0004

Sample Standard deviation S=√∑x^2-((∑x)^2)/n)/n-1

=√(412.8531-((57.47)^2/8))/7

=√412.8531-412.8501/ 7

=√0.003/7

=√0.0004 =0.0207

c) Coefficient of Variation (Sample) =

S/x X100%

=(0.0207/7.1838) X 100%

=0.29%

To learn more about sample variance, use the link given
https://brainly.com/question/28542390
#SPJ4

Using technology, the correlation coefficient is 0.997

We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.

The table is

                            x               y              x²            y²             xy

                          8              22             64          484            176

                         12              23            144          529            276

                         18             26             324         676           468

                         24             30            567         900         720

                          30           32              900        1024         960

                        32              33              1024     1089         1056

                         35             35             1225       1225         1225

                          37             36            1369        1369         1332

                          40             38           1600         1444         1520

    Total          236           275          7226         8740        7733

[tex]r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }[/tex]

applying the figures from the table we have

r=[tex]\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }[/tex]

Simplifying the expression we have

r=[tex]\frac{4697}{\sqrt{28340830} }[/tex]

r=0.88

r=0.9 approximately

Therefore the correct answer is 0.997 which is the correlation coefficient.

Learn more about correlation coefficient on https://brainly.com/question/15577278

#SPJ1

The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first number be A = 6 3/4

A = 27/4

Let the second number be B = 4 1/2

B = 9/2

Now , the equation is C = A/B

The value of C = A / B

Substituting the values of A and B in the equation , we get

Value of C = ( 6 3/4 ) /  ( 4 1/2 )

Value of C = ( 27/4 ) / ( 9/2 )

Value of C = ( 27 / 9 ) / 2

Value of C = 3 / 2

Therefore , the value of C is 3/2 or 1 1/2

Hence , The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ1

The boundary value and initial value statement are,

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].

What is Initial Value Problem?

In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.

Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.

Initial temperature [tex]T_i = 20^o[/tex]

Final temperature = [tex]T_f = 75^o[/tex]

Now we have to solve the given cases.

Consider the heat equation,

q = k(∂T / ∂x)                   ..(1)

(a) Now we have to find the boundary value

Boundary Value:

[tex]T_i = 20^oc, T_f = 75^oc\\[/tex]

⇒ ΔT = [75 - 20]

⇒ΔT = 55°c

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex]

Hence, the boundary value and initial value statement are,

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].

To know more about initial value problem, click on the link

https://brainly.com/question/29594052

#SPJ4

Complete question:

Complete question is attached below,

The constant of proportionality is 1/3 and the equation is y = 1/3x

The table of values represents the given parameter

From the table of values, we have the following ordered pair

(x, y) = (3, 1)

The constant of proportionality (k) is then calculated as

k = y/x

So, we have

k = 1/3

Recall that, we have

k = y/x

Substitute k = 1/3

y/x = 1/3

So, we have

y = 1/3x

Hence, the equation is

y = 1/3x

Read more about proportional relationship at

https://brainly.com/question/14425347

#SPJ1

It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:

[tex]H_{0}[/tex] : μ = 24

If it differs from 24 years, the alternative premise is tested, so:

[tex]H_{1}[/tex] :  μ ≠ 24

The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:

z = x -  μ÷ σ/[tex]\sqrt{n}[/tex]

The parameters in this issue have the following values:

x(mean) = 25

μ = 24

σ = 2

n=16

As a result, the test statistic's value is:

z = 25-24÷ 2/[tex]\sqrt{16}[/tex]

z = 2

The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.

The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.

Given that the test's p-value is 0.0228 0.05, we may say that:

It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

To learn more about  probability:

https://brainly.com/question/11234923

The output firm will get maximum profits when the quantity is 4 units and the company will charge a price of $15 for maximum profit.

The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3

Demand for the product that the firm produces is given by P = 27- 3Q.

The total cost is calculated by adding fixed cost and variable cost.

TC = FC + VC

Average total cost = total cost / quantity

Quantity  price (37 - 3Q) fixed cost variable cost  total cost average cost

1                27 - 3(1) = 24      24            3 (1)                 27             27

2               27 - 3(2) = 21      24            3(2) = 6           30            15

3                27 - 3(3) = 18      24            3(3) = 9           33            11

4               27 - 3(4) = 15       24           3(4) = 12          36             9

5               27 - 3(5) = 12       24           3(5) = 15          39            7.8

Upon analysing the table we can say that

B) the number of output units is 4

C) Maximum profit is when price is $15

Therefore, the maximum profit is when the output units is 4 and the company will charge a price of $15 for maximum profit.

To learn more about marginal cost refer here

https://brainly.com/question/12231343

#SPJ4

By using the concept of permutation, it can be calculated that

Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]

                                                                                          = [tex]\frac{2}{7}[/tex]

What is permutation?

Permutation is the arrangement technique that determines how many possible arrangement that can be made in a set where the order of arrangement matters.

Here, concept of permutation is used

Number of 7 number combinations that can be formed using the number 3795523 = [tex]\frac{7!}{2! \times 2!}[/tex] = 1260

The two 3's are always together

Number of 7 digit numbers formed = [tex]\frac{6!}{2!}[/tex] = 360

Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]

                                                                                          = [tex]\frac{2}{7}[/tex]

To learn more about permutation, refer to the link-

https://brainly.com/question/12468032

#SPJ4

Answer: Neither (5/2, 0)

Step-by-step explanation:

-4x + 7 = 2y - 3

+3 +3

2y = -4x + 10

(Divide both sides by 2)

y = -2x +5

—————————————————

-4x + 7 = 2(-4x + 10) - 3

-4x + 7 = -8x + 20 - 3

-4x + 7 = -8x + 17

+8x -7 +8x -7

8x - 4x = 17 - 7

4x = 10

(Divide both sides by 4)

x = 5/2

—————————————

y = -2(5/2) + 5

y = -5 + 5

y = 0

——————————

Check Work:

-4x + 7 = 2y - 3

-4(5/2) + 7 = 2(0) -3

-10 + 7 = 0 - 3

-3 = -3 ✔️

The equation for of graph of  g(x) = 3x-4  

y = afb(x +c) + d

where a represent the vertical stretch

b represent the horizontal stretch

c represent the horizontal translation

d represent the vertical translation

from the equation we are given g(x) has a vertical stretch and a vertical translation ( y-axis represent up and down therefore its a vertical translation)

The equation of g(x) is:

g (x) = 1/2(6x) - 4

g(x) = 3x-4  

Therefore, the equation for of g(x) = 3x-4  

Learn more about function here: https://brainly.com/question/17043948

#SPJ1

The rate of change of the perimeter is  4 in/sec .

In the question ,

it is given that ,

the length of the rectangle is [tex]=[/tex] 1 inch

the width of the rectangle is = 6 inch

the rate of increasing length is (dL/dt) = 4 in/sec

rate of shrinking width is (dW/dt) = -22 in/sec ,

We know that the perimeter of the rectangle is = 2(L + W) ,

that is , P = 2L + 2W ,

Differentiating perimeter with respect to time "t" ,

we get ,

dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )

Substituting the values from above ,

we get ,

= 2 × (4) + 2 × (-2)

= 8 - 4

= 4

Therefore , the required rate of change is = 4 in/sec .

Learn more about Rate Of Change here

https://brainly.com/question/29654834

#SPJ4