To express the polynomial 4a^3 + a^2 - 6a^5 + 2a^3 - 4a + 1 in standard form, which terms should be combined?

Answer:

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x.

The domain of the function is all real numbers

The true statements are:

The function is given as:

[tex]\mathbf{y = 3(2.5)^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{y = ab^x}[/tex]

Where: a represents the initial value, and b represents the rate

This means that:

[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function

By comparison:

[tex]\mathbf{b = 2.5}[/tex]

When b > 0, then the function represents an exponential growth

2.5 is greater than 0.

So, the function represents an exponential growth

Lastly, there is no restriction to the values of x.

So, the domain of the function is the set of all real numbers

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Answer:

1. [tex]$ \mu = \$306,500 $[/tex]

2. [tex]\sigma = \$24,500[/tex]

3. [tex]n = 150[/tex]

4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]

Step-by-step explanation:

The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500.

From the above information, we know that,  

The population mean is

[tex]$ \mu = \$306,500 $[/tex]

The population standard deviation is

[tex]\sigma = \$24,500[/tex]

Suppose a random sample of 150 Americans is selected

[tex]n = 150[/tex]

Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.

The sample mean would be the same as the population mean  that is

[tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

The sample standard deviation is given by

[tex]\sigma_x = \frac{\sigma}{\sqrt{n} }[/tex]

Where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.

[tex]\sigma_x = \frac{24,500}{\sqrt{150} } \\\\\sigma_x = \$ 2,000 \\\\[/tex]

Therefore, the required parameters are:

1. [tex]$ \mu = \$306,500 $[/tex]

2. [tex]\sigma = \$24,500[/tex]

3. [tex]n = 150[/tex]

4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]

Answer:

C. [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

You can use the formula to find the slope: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

(-1.5, 1.5) & (1.5, 0)

[tex]\frac{0-(-1.5)}{1.5-(-1.5)} =\\\\\frac{0+1.5}{1.5+1.5} =\\\\\frac{1.5}{3} =\\\\\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex]

Answer:

1 1/6

Step-by-step explanation:

Edwin used a quantity of 2.833 gallons of paint for the mural which is the difference between the quantity of paint at the beginning and the used for the bedroom.

We have been given that Edwin has 3 1/2 gallons of green paint. He uses 2/3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

To determine the quantity of paint Edwin used for the mural.

The quantity of paint Edwin used for the mural is the difference between the quantity of paint at the beginning and the used for the bedroom.

The quantity of paint used for the mural = 3 1/2 gallons - 2/3 gallons

The quantity of paint used for the mural = 3.5 - 0.66

The quantity of paint used for the mural = 2.833

Thus, Edwin used a quantity of 2.833 gallons of paint for the mural.

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Answer:

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.

Step-by-step explanation:

Confidence interval:

Depends on two things: The sample mean and the margin of error.

Lower end: Sample mean - margin of error

Upper end: Sample mean + margin of error

This means that the intervals are centered around the sample mean.

x% level:

x% of the intervals will contain the population mean in the long run.

So the true statements are:

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.

Answer:

[tex]y(x)=-0.028x+14.6[/tex]

Step-by-step explanation:

We are to write a linear equation that relates y in terms of x

The Birth Rate in 1994 =  14.6 births per thousand population.

The Birth Rate in 2004 =  14.32 births per thousand population.

A linear equation is of the form y=mx+b, where:

Step 1: Determine the birth rate per year

In 1994, x=0, y=14.6 thousands

In 2004, x=10, y=14.32 thousands

[tex]m=\dfrac{14.32-14.6}{10-0}\\=\dfrac{-0.28}{10}\\m=-0.028[/tex]

Substituting m into our linear equation, we have:

[tex]y(x)=-0.028x+b[/tex]

When x=10, y=14.32

[tex]14.32=-0.028(10)+b\\b=14.32+0.28\\b=14.6[/tex]

Therefore, a linear equation that relates y in terms of x is:

[tex]y(x)=-0.028x+14.6[/tex]

Answer:8 i ithink

Step-by-step explanation:

Answer:

12, go for 24.

Step-by-step explanation:

There are 6 sides of a cube.

There are 2 pairs of parallel line segments for each side.

6 x 2 = 12

Although that answer is not there, you should go for 24. Since there are 2 variables for each line segment, 12 x 2 = 24. Not sure, hope this helps.

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Answer:

Step-by-step explanation:

We assume the concern is with systems of linear equations. Systems of non-linear equations will have some of the same issues.

A system of equations is nicely solved by graphing if the graph(s) can be made easily and if the solutions can be easily read from the graph. If those conditions are not met, then solving a system graphically may not be feasible.

The attached graph shows a system of equations that would be difficult to solve graphically by hand. (A graphing calculator helps immensely.)

The system in our example is ...

We have chosen the second equation to have a slope similar to that of the first equation, so that the lines gradually come together. That makes it difficult to read the point of intersection from the graph. The second equation also has no obvious integer solutions, so graphing it in the first place can be difficult. If the solutions have a fractional part, the exact value of the fraction may be impossible to determine from the graph.

In short, ...

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:

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:

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:

The height (corresponding to the [tex] \\ 92^{nd}[/tex] percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)

Step-by-step explanation:

Roughly speaking, the [tex] \\ 92^{nd}[/tex] percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.

To answer this question, we already know that:

Strategy for solving the question

For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.

Z-scores

To find the [tex] \\ 92^{nd}[/tex] percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

Cumulative standard normal distribution and corresponding table

We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.

In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).

Using z = 1.40 in [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ 1.40 = \frac{x - 69}{3}[/tex]

Then, solving for x:

Multiplying by 3 at each side of the equation:

[tex] \\ 1.40 * 3 = x - 69[/tex]

Adding 69 at both sides of the equation:

[tex] \\ (1.40 * 3) + 69 = x[/tex]

[tex] \\ x = (1.40 * 3) + 69[/tex]

[tex] \\ x = 4.20 + 69[/tex]

[tex] \\ x = 73.20[/tex]

That is, the [tex] \\ 92^{nd}[/tex] percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.

This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.  

The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.  

Answer:

The range would decrease by 2

Step-by-step explanation:

The range is the difference between the highest number and the lowest number.

8 is the highest number and 1 is the lowest number here, so to find the range we would subtract 1 from 8.   8-1=7

But since 8 is being replaced by 6, we would subtract 1 from that instead.

6-1=5

The range decreased from 7 to 5, so it decreased by 2.

Hope that helps :)

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:

[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:

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

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!!!

Answer:x<-18

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

-1/2x+3>12

Step 2: Subtract 3 from both sides.

-1/2x+3-3>12-3

-1/2x>9

Step 3: Multiply both sides by 2/(-1).

(2/-1)*(-1/2x)>(2/-1x)*(-1/2x)

X<-18

:D

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:

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:

[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:

Step-by-step explanation:

Hello!

The variable of interest is:

X: height of seaweed.

X~N(μ;σ²)

μ= 10 cm

σ= 2 cm

You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

P(X≤x)= 0.30

P(X≥x)= 0.70

Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.

P(Z≤z)= 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

z= -0.52

Now you have to clear the value of X:

Z= (X-μ)/σ

Z*σ= X-μ

X= (Z*σ)+μ

X= (-0.52*2)+10= 8.96

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm

I hope this helps!

Answer:-0.53 and 9.72

Step-by-step explanation:

Answer:

Step-by-step explanation:

Correlation describes how strongly pairs of given variablé are related. In this case, a detailed analysis that was carried out shows that the number of days missed by employees explains 60% of the variation in salary increases and also impressed upon this fact that employees who missed more days of work during the year received smaller raises than those who missed fewer days.

From the analysis, we can draw a conclusion that there is a correction between days missed and variation in salary increase and that this type of correction is a negative correlation where an increase in the number of days missed will lead to a decrease in the raises awarded to each employee.

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:

D. 32 sq. unit s

Step-by-step explanation:

4×18/2=32

Answer:

second side = s  first side = s +1  third side = s +2

39 feet = s + (s+1) + (s +2)

39 feet = 3s +3

36 feet = 3s

s = second side = 12 feet

first side = 13 feet

third side = 14 feet

Step-by-step explanation:

p-value < 0.05, reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

Given, data of toiletry distributors.

Total number of observations

= 170 + 105 + 80 + 45

= 400

Expected count = [tex]p_i \times 400[/tex]

Calculation table is attached below.

Test statistic:

Chi square score

= 6.429 + 0.438 + 0.000 + 7.779

= 14.645

Degree of freedom:

df = 4-1

=3

p-value = CHIDIST(14.645,3)

= 0.00215

Therefore , p-value < 0.05

Reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

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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.

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 .