factorization of expression 4z(3a+2b-4c)+(3a+2b-4c)
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Step-by-step explanation:

Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.

The Wronskian of them functions be

W = (y1y2' - y1'y2)

y1 = (e^x)/2 = y1'

y2 = (xe^x)/2

y2' = (1/2)(x + 1)e^x

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.

Answer:

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Step-by-step explanation:

Answer:

[tex]x=8[/tex]

[tex]y=24[/tex]

Step-by-step explanation:

3x+2y=72

If y=3x, we plug it into our equation and get:

3x+2×3x=72

3x+6x=72

9x=72

Divide both sides by 9

x=8

Answer:

x = 8

Step-by-step explanation:

3x + 2y = 72

Put y as (3x), and solve for x.

3x + 2(3x) = 72

Multiply 2(3x).

3x + 6x = 72

Add like terms 3x and 6x.

9x = 72

Divide 9 into both sides and isolate x.

x = 72/9

x = 8

The value of x is 8.

Answer:

D. 32 sq. unit s

Step-by-step explanation:

4×18/2=32

Answer:

Type of error: Run-on(comma splice).

Best revision to fix it: Adding a semicolon after beginners .

Explanation:

A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.

In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:

'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'

Answer:

Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.

What type of error is present in the underlined sentence?

✔ run-on

Which is the best revision to fix the error?

✔ adding a semicolon after instrument

Step-by-step explanation:

Answer:

1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). (-435.36) dollars per week

Step-by-step explanation:

Weekly price decay of the product is represented by the function,

P(x) = [tex]95000.e^{-0.05x}[/tex]

And the price of the product changes over the period of 't' weeks is represented by,

x(t) = [tex]53+0.95t^2[/tex]

Function representing the rate of change in the profit with respect to the time will be represented by,

1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]

Since, P(x) = [tex]95000.e^{-0.05x}[/tex]

P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]

       = [tex](-4750).e^{-0.05x}[/tex]

Since, x(t) = 53 + 0.95t²

x'(t) = 1.9t

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]

By substituting x = 53 + 0.95t²

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]

   P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). For t = 7 weeks,

P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]

       = [tex](-63175).e^{-4.9775}[/tex]

       = (-63175)(0.006891)

       = (-435.356) dollars per week

       ≈ (-435.36) dollars per week

Answer:

Step-by-step explanation:

Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation

V ' ( t ) = − 26400 e^− 0.49 t .

t = time (in days)

.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:

V'(6) = − 26400 e− 0.49 (6)

V'(6) = -26400e-2.94

V'(6) = -26400×-0.2217

V'(6) = $5852.88

V'(6) = $5,853 to nearest dollars

V'(6) = 585300cents to nearest cent

To get v(6), we need to get v(t) first by integrating the given function as shown:

V(t) = ∫−26400 e− 0.49 t dt

V(t) = -26,400e-0.49t/-0.49

V(t) = 53,877.55e-0.49t + C.

When t = 0, V(t) = $170,000

170,000 = 53,877.55e-0 +C

170000 = 53,877.55(2.7183)+C

170,000 = 146,454.37+C

C = 170,000-146,454.37

C = 23545.64

V(6) = 53,877.55e-0.49(6)+ 23545.64

V(6) = -11,945.63+23545.64

V(6) = $11,600 (to the nearest dollars)

Since $1 = 100cents

$11,600 = 1,160,000cents

Answer:

x = -2 + 2 i or x = -2 - 2 i

Step-by-step explanation:

Solve for x:

x^2 + 4 x + 8 = 0

Subtract 8 from both sides:

x^2 + 4 x = -8

Add 4 to both sides:

x^2 + 4 x + 4 = -4

Write the left hand side as a square:

(x + 2)^2 = -4

Take the square root of both sides:

x + 2 = 2 i or x + 2 = -2 i

Subtract 2 from both sides:

x = -2 + 2 i or x + 2 = -2 i

Subtract 2 from both sides:

Answer:  x = -2 + 2 i or x = -2 - 2 i

Answer:

2.87 = AC

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp / hyp

sin 35 = AC /5

5 sin 35 = AC

2.867882182= AC

To the nearest hundredth

2.87 = AC

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

Answer:

yesseinafhinks

Step-by-step explanation:

Dividing by 10² is also the same thing as multiplying by 10^-2. In that case, we simply move the decimal places only 2 places back. That would give us 7.516, not 0.7516 (which is 3 times, not 2).

Answer:

Option D is correct

Step-by-step explanation:

Applying the cosine theorem for triangle ABC, you would have:

cos (angle BAC) = (BA^2 + CA^2 - BC^2)/(2*BA*CA)

                           = (10^2 + 18^2 - 20^2)/(2*10*18)

                           = 24/360

=> angle BAC = ~86 deg

Hope this helps!

Answer:

Each persons share is 6.03

Step-by-step explanation:

Divide the total cost by the number of students

48.24 / 8

6.03

Each persons share is 6.03

Answer:

$6.03

Step-by-step explanation:

A group of 8 students paid $48.24 for food.

Each of their shares would be divided among the 8 students.

48.24/8=6.03

Each student paid a share of $6.03.

Answer:

24024 are the total number of ways of choosing 4 campsites out of 14.

Step-by-step explanation:

We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.

It is a simple example of selection problem.

Number of ways to choose the first campsite = 14

Now, one campsite is chosen, 13 campsites are left.

Therefore,

Number of ways to choose the second campsite = 13

Now, one more campsite is chosen, 12 campsites are left.

Therefore,

Number of ways to choose the third campsite = 12

Now, one more campsite is chosen, 11 campsites are left.

Therefore,

Number of ways to choose the fourth campsite = 11

So, total number of ways for choosing 4 campsites out of 14:

14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024

Hence, answer is 24024.

Answer:

A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.

Answer:

N(L) = 20

The expected number of left handed people is 20.

Step-by-step explanation:

Given;

Percentage of left handed people P(L) = 10%

Total number of selected people N(T) = 200

The Expected number of left handed people N(L) is;

N(L) = Total number of selected people × Percentage of left handed people/100%

N(L) = N(T) × P(L)/100%

Substituting the given values;

N(L) = 200 × 10%/100%

N(L) = 200 × 0.1

N(L) = 20

The expected number of left handed people is 20.

Answer:

X<3

Step-by-step explanation:

4x-7 <5

4x < 5+7

4x < 12

X < 12/4

X < 3

Hope this helps..

Good Luck!

Answer:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Step-by-step explanation:

Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(14.4,1.1)[/tex]  

Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.05[/tex]   (a)

[tex]P(X<a)=0.95[/tex]   (b)

We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64

Using this value we can set up the following equation:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]

And we have:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Answer:

360 cm^2

Step-by-step explanation:

First find the area of the bottom

10*10 = 100

The find the area of one of the triangular shapes

A = 1/2 bh since it is a triangle

A = 1/2 ( 10)*13 = 65

Since there are 4 triangles ( 1 for each side), multiply by 4

4*65 = 260

Add the areas together

260+100 = 360

Answer:

1.90.93

2.90.27

Step-by-step explanation:

Answer:

one above correct

Step-by-step explanation:

1st - 90.93

2nd-90.27

Answer:

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000

Total start-up amount required, according to the details provided in the question = $1,264,000

Step-by-step explanation:

- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.

- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.

- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.

- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000

¡¡¡Espero que esto ayude!!!

English Translation

- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000

- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000

- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000

- Purchase of special equipment is needed to check the tires. Cost = $400,000

Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000

Hope this Helps!!!

Corrected Question

Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home.  Where is the gym?

Answer:

(D)15th Street and 14th Avenue

Step-by-step explanation:

Ping's Location: (3rd Street, 6th Avenue)

Ari's Location: (21st Street, 18th Avenue)

The gym is at point P which is [tex]\dfrac{2}{3}[/tex] the distance from Ping's home to Ari's home.

That is, Point P divides the line segment in the ratio 2:1.

We use the section formula:

[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]

m:n=2:1, [tex](x_1,y_1)=(3,6), (x_2,y_2)=(21,18)[/tex]

[tex]=\left(\dfrac{2*21+1*2}{2+1}, \dfrac{2*18+1*6}{2+1}\right)\\=\left(\dfrac{45}{3}, \dfrac{42}{3}\right)\\=(15,14)[/tex]

The gym is located at 15th Street and 14th Avenue.

Answer:

The recurrence relation for aₙ is  aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8

Step-by-step explanation:

Solution

Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.

Ternary sequence is sequence with each of digits either 0, 1 or 2.

Now

Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.

Let us first find few initial values of aₙ

For n = 1

a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.  

This 1-digit sequence can be either 0 or 1 or 2.

Thus,

a₁ = 3

For n =2

a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.

This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.

here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)  

But one of these 9 sequence there are consecutive 0's .... (00)  

So we eliminate this one sequence.

So, a₂ = 8

Now

let us find the recurrence relation

Fir n ≥ 3

aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.

For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2

Let assume the 1st digit of this n - digit ternary sequence is 1.  

Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.

For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1

So,

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.

Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.

So  

If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:

aₙ-1 + aₙ -1 = 2aₙ -1

For the second case: if 1st digit of this n - digit ternary sequence is 0

If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,

If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.

So there are 2 choices for 2nd digit.  

After this there are more n-2 digits.  

Then

For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them  

For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.

Now,

The total number of sequence in this case is given as:

2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)

Hence  

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3

Now,

The recurrence relation for aₙ is shown below:

aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3

With the initial conditions as a₁ =3; a₂ = 8

Answer:

The GDP gap is 9 % when there is 4.5 % unemployment.

Step-by-step explanation:

The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:

[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]

The GDP gap at a given increase in unemployment can be estimated by the following expression:

[tex]\frac{g}{u} = r[/tex]

[tex]g = r\cdot u[/tex]

Where:

[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.

[tex]u[/tex] - Increase in unemployment rate, measured in percentage.

[tex]g[/tex] - GDP gap, measured in percentage.

If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:

[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]

[tex]g = 9\,\%\,GDP[/tex]

The GDP gap is 9 % when there is 4.5 % unemployment.

Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.

5100*0.50 = 2550

200*0.25 = 50

0*0.25 = 0

Add up those results: 2550+50+0 = 2600

The expected value of gamble B is $2600

Based on the information given, the null hypothesis will be that there's no difference in the distribution of current sales.

The alternate hypothesis will be that's there's a difference in the distribution of current sales.

Also, it should be noted that the test statistic is 23.0951. The p-value is 0.00003 and the conclusion is that the distribution of sales among the departments has changed.

Learn more about null hypothesis on:

https://brainly.com/question/15980493

The null hypothesis would be that there is no difference in the prevalence of current sales based on the information provided. This alternative hypothesis says there was variance in the distribution of current sales.

Learn more:

brainly.com/question/14578907

Answer:

19305

Step-by-step explanation:

We simply take the percentage of 29700 to find how many people were added.

29700(0.35) = 10395 <== so 10395 people have been added

Subtract it from the current:

28700 - 10395 = 19305 people before.

Answer:I believe that it is A but i am not fully sure

Step-by-step explanation:

Answer:

The nearest penny will be £9146.6

Step-by-step explanation:

A = P[1 + (r/n)]^(nt)

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)

A = 8300 [ 1 + {0.002}]^(49)

A= 8300 [ 1.002 ]^(49)

A = 8300 [ 1.102 ]

A = £9146.6

What is Compound Interest (CI) ?

Compound Interest is all about adding interest to principal amount of loan , deposit .

Answer:

B and D

Step-by-step explanation:

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