What is the height of the cuboidal box of length 28.5cm, breadth 16.5cm and lateral surface area 1350 sq.cm?​

Nishi invests £2500 at a 4% interest rate per year. After 2 years, her investment will grow to £2650. The amount will increase further to £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years.

1. To calculate the amount Nishi will have after a certain number of years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

2. In this case, Nishi invests £2500 at a 4% interest rate per year. Since the question doesn't specify the compounding frequency, we'll assume it's compounded annually (n = 1). Plugging in the values, we get:

After 2 years:

A = £2500(1 + 0.04/1)^(1*2)

A = £2500(1.04)^2

A ≈ £2650

After 4 years:

A = £2500(1 + 0.04/1)^(1*4)

A = £2500(1.04)^4

A ≈ £2806

After 8 years:

A = £2500(1 + 0.04/1)^(1*8)

A = £2500(1.04)^8

A ≈ £3071

After 9 years:

A = £2500(1 + 0.04/1)^(1*9)

A = £2500(1.04)^9

A ≈ £3123.84

3. Therefore, Nishi will have approximately £2650 after 2 years, £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years, assuming an annual compounding frequency.

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An area of 18 x 30 = 540 square meters, which is half the area of his backyard.

Steve is turning half of his backyard into a chicken pen. Given that his backyard is a 24 meters by 45 meters rectangle, the area of the whole backyard is

24 x 45 = 1080 square meters.

If half of the backyard is to be turned into a chicken pen, then the area of the chicken pen will be

1080/2 = 540 square meters.

Since the area of a rectangle is calculated by multiplying its length by its width, the dimensions of the chicken pen will depend on the desired shape of the pen.

Steve can decide to make the chicken pen a square or a rectangle or any other shape.

However, if he decides to make the pen a rectangle, he will have to make sure that the length and width are such that their product is equal to 540 square meters.

For example, he can make the chicken pen a rectangle with a length of 18 meters and a width of 30 meters.

This will give an area of 18 x 30 = 540 square meters, which is half the area of his backyard.

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There were 671 liars living on the island initially out of 2013 people living on the island.

Let's assume the number of truthtellers is x and the number of liars is y.

According to the given information, each day one person says that when they leave the island, the number of truthtellers will be equal to the number of liars.

This implies that the person speaking must be a liar.

On the first day, if the person speaking is a liar, then the number of liars on the island will increase by one (y+1) and the number of truthtellers will remain the same (x).

The equation can be written as:

x = y + 1

On the second day, if the second person speaking is also a liar, the number of liars will increase by one again (y+2) and the number of truthtellers will remain the same (x).

The equation becomes:

x = y + 2

We can generalize this pattern for each day:

x = y + k

After 2013 days, there is no one left on the island, so x + y = 0.

Substituting this into the equation, we get:

(y + k) + y = 0

Simplifying, we find:

2y + k = 0

Since y represents the number of liars, we want to find a value of y that satisfies this equation.

To do that, we need to find a value of k such that 2013 + k is divisible by 2.

By observing that 2013 is odd, we can conclude that k must be an odd number.

The smallest odd number that satisfies this condition is k = 1.

Substituting k = 1 into the equation, we get:

2y + 1 = 0

Solving for y, we find:

y = -1/2

However, the number of liars cannot be negative, so we can disregard this solution.

Therefore, there were 671 liars living on the island initially.

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she used 4/27 cups of cereal to make the snack mix.

Let's say the amount of cereal Nancy used was "x".

Since she used twice as many peanuts as she did cereal, the number of peanuts she used would be "2x".

Total, she used 6 3/4 cups of peanuts and cereal to make the snack mix.

Thus, we can write an equation as follows:6 3/4 = 2x + x

Convert mixed number 6 3/4 to an improper fraction:6 3/4 = (27/4)

Now we can solve the equation: (27/4) = 3x

(combining like terms)

Multiplying both sides by 4/27 gives us:1 = (4/27) * 3x

Now we can solve for "x":x = 4/27Since "x" represents the amount of cereal Nancy used,

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The steps used to solve the system of equations are as follows: Apply the Addition Property of Equality to eliminate the variable y. Solve for x using the Division Property of Equality. Substitute the value of x into one of the equations to find the value of y. Therefore, the solution to the system of equations is x = 1 and y = 1.

To solve the system of equations, we can follow these steps:

Step 1: Apply the Addition Property of Equality to eliminate the variable y.

By adding the two equations together, the y-terms will cancel out, resulting in:

(3x - 2y) + (2x + 2y) = 1 + 4

Simplifying the equation, we get:

5x = 5 (Addition Property of Equality)

Step 2: Solve for x using the Division Property of Equality.

Dividing both sides of the equation by 5, we find:

x = 1 (Division Property of Equality)

Step 3: Substitute the value of x into one of the equations to find the value of y.

Using the first equation, we substitute x with 1:

3(1) - 2y = 1

Simplifying the equation, we have:

3 - 2y = 1

Rearranging the equation, we get:

-2y = -2

Dividing both sides of the equation by -2, we find:

y = 1 (Division Property of Equality)

Therefore, the solution to the system of equations is x = 1 and y = 1.

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Marven and three of his friends rent a car with insurance for 5 days but lost their coupon. If each person spent $75, then which car did they rent The total amount of money they paid is $75 * 4 = $300.

We can further write the above equation as:250x + 300y + 350z + 400u = 300Based on the given condition, we know that Marven and three of his friends spent $75 each, so the total amount of money they paid is $300. Hence:250x + 300y + 350z + 400u = 300Now we can simplify the equation by dividing each term by 50:5x + 6y + 7z + 8u = 6We have to find the values of x, y, z, and u. The simplest way to solve the equation is by trial and error.

We can substitute values and check if they satisfy the equation. We need to consider the following conditions: The variables x, y, z, and u must be non-negative integers. The sum of x, y, z, and u must be 1.The only set of values that satisfies the above conditions is x = 1, y = 1, z = 0, and u = 0. This means that they rented a compact car and a mid-size car for 5 days each, respectively. Therefore, the car they rented is a compact car and a mid-size car.

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The ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3. To simplify the ratio of Sam’s shells and Thandeka’s shells, we need to divide both numbers by their greatest common factor, GCF.

In this case, we have:Sam’s shells = 8Thandeka’s shells = 12Factors of 8: 1, 2, 4, 8Factors of 12: 1, 2, 3, 4, 6, 12The common factors of 8 and 12 are 1, 2, and 4.

However, we need to find the greatest common factor of 8 and 12 to simplify the ratio. Therefore, the greatest common factor of 8 and 12 is 4.

Hence, dividing both numbers by 4 gives us:

Sam’s shells ÷ GCF = 8 ÷ 4 = 2

Thandeka’s shells ÷ GCF = 12 ÷ 4 = 3

Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.Another way to solve the problem is by finding the ratio between the two numbers.

Thus:Ratio = Sam’s shells :

Thandeka’s shellsRatio = 8 : 12

To simplify the ratio, divide both numbers by the greatest common factor of 8 and 12 which is 4.

Ratio = (8 ÷ 4) : (12 ÷ 4)Ratio = 2 : 3

Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.

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To sketch an angle of 210° in standard position in a UV-coordinate system, you would start by placing the initial side of the angle along the positive x-axis and then rotate the terminal side counter-clockwise by 210°. The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.

In a UV-coordinate system, the initial side of an angle is placed along the positive x-axis. To sketch an angle of 210°, you would start by drawing a horizontal line (the initial side) extending to the right. Then, you rotate the terminal side of the angle counterclockwise from the initial side. Since 210° is greater than 180°, the terminal side will extend beyond the positive x-axis.

To determine the reference angle, you can subtract the given angle from the nearest multiple of 180°. In this case, the nearest multiple of 180° is 180° itself. Subtracting 210° from 180° gives you 30°. Therefore, the reference angle for the angle of 210° is 30°.

To summarize, you would sketch an angle of 210° in standard position by starting with the initial side along the positive x-axis and rotating the terminal side counterclockwise. The reference angle for this angle is 30°, which is the acute angle formed between the terminal side and the x-axis.

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The change in Samuel's score is 50

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

Beginning = -14 points

Final = 36 points

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

Change = Final - Beginning

Substitute the known values in the above equation, so, we have the following representation

Change = 36 + 14

Evaluate

Change = 50

Hence, the change is 50

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Question

Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was – 14 points. After building a high-rise apartment building, his score rose to 36 points.

What was the change in Samuel's score?

So the ratio of the first measurement to the second measurement is approximately 73.33%.

The diameter of ball A is 33 mm.

The diameter of ball B is 4.5 cm.

1 cm = 10 mm

4.5 cm = 4.5 × 10 mm

= 45 mm

To find the ratio of the first measurement (ball A) to the second measurement (ball B), we divide the diameter of ball A by the diameter of ball B.33 mm ÷ 45 mm = 0.7333...

We can simplify this fraction by multiplying both the numerator and denominator by 100 to get a percentage:

0.7333... × 100% = 73.33...%

Ratio of the first measurement to the second measurement = 73.33%.

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The inequality $-8\pi\leq n\leq 10\pi$ represents a range of values for the integer $n$. To determine the number of integers that satisfy this inequality, we need to find the range of integers within this interval.

The difference between the maximum and minimum values of the interval is $10\pi - (-8\pi) = 18\pi$. Since we are dealing with integers, we need to consider the number of whole numbers within this range.

To convert this to the number of integers, we divide the length of the interval by the spacing between consecutive integers, which is 1. So, the number of integers within the range is $18\pi / 1 = 18\pi$.

However, since we are counting integers, we need to round this number to the nearest whole number. As $\pi$ is an irrational number, we cannot evaluate its exact decimal value. Therefore, the number of integers that satisfy the given inequality is approximately $18\pi \approx 56$.

Hence, approximately 56 integers satisfy the inequality $-8\pi\leq n\leq 10\pi$.

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The sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.

For the shapes to be similar, the corresponding angles need to be congruent and corresponding sides need to be proportional. The sequence applied to shape I that proves shape I is similar to shape II involves a translation and a dilation.

Translation: A translation is a transformation in which each point of the shape is moved a certain distance in a certain direction. In this case, Shape I is translated 4 units right and 3 units up to get Shape III. Dilation: A dilation is a transformation in which each point of the shape is stretched or shrunk in size, relative to a fixed point called the center of dilation.

In this case, Shape III is dilated by a scale factor of 2 to get Shape II. Thus, the sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.

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The chance that it will not rain tomorrow can be found by subtracting the probability of rain from 100% or 1 in decimal form. Therefore, if there is a 70% chance of rain, there is a 30% chance it will not rain.

If there is a 70% chance of rain tomorrow, the chance it will not rain can be found by subtracting the probability of rain from 100% (or 1 in decimal form):

Chance of not raining = 100% - Chance of raining

Chance of not raining = 1 - 0.7

Chance of not raining = 0.3 or 30%

Therefore, the chance it will not rain is 30%.

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The equation of the line is shown as y = ax + p, where a and p are actual numbers. The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. The line slope-intercept form can be compared with the equation of the line given as y = ax + p.

We know that the equation of a line in slope-intercept form is given as y = mx + b. Here, we are given the equation of the line as y = ax + p, where a and p are real numbers. Thus, the following is true about a and p.The slope of the line in the slope-intercept form is m = a. Therefore, a is the slope of the given line. The y-intercept of the line in the slope-intercept form is b = p.

p is the y-intercept of the given line. Hence, we conclude that in the equation of the line, y = ax + p, where a and p are real numbers, a is the slope of the line and p is the y-intercept of the line.

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The true statement is Statement 1: The width of the sidewalk is equal to one-third of its length.

The true statement can be found by examining the relationship between the length of the sidewalk (l) and its width, which is given as l ÷ 3.

Let's consider two possible statements:

Statement 1: The width of the sidewalk is equal to one-third of its length.

Statement 2: The width of the sidewalk is three times its length.

To determine which statement is true, we can substitute a numerical value for the length of the sidewalk (l) and compare the resulting width to the statement.

Let's assume the length of the sidewalk (l) is 9 units.

Statement 1: The width of the sidewalk is 9 ÷ 3 = 3 units.

Statement 2: The width of the sidewalk is 3 × 9 = 27 units.

Comparing the width obtained from the calculation (3 units) with Statement 1 (The width of the sidewalk is equal to one-third of its length), we find that they are equal.

It's important to note that this conclusion is based on the assumption that the relationship between the length and width provided in the question is accurate and consistent.

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The time it takes for the rock to hit the ground can be determined using the equation h(t) = -4.9t^2 + 150, where h(t) represents the height of the rock in meters and t represents time in seconds. By setting h(t) to 0 and solving for t, we can find the time it takes for the rock to hit the ground.

Set the equation h(t) = -4.9t^2 + 150 to 0, since the rock hits the ground when the height is 0.

-4.9t^2 + 150 = 0

Solve the quadratic equation for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c:

t = (-0 ± √(0^2 - 4(-4.9)(150))) / (2(-4.9))

Simplify and calculate the value of t:

t = (√(2940)) / (-9.8) ≈ ±7.23

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To find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d, we can use the equation W = Fd.

Rearranging the equation, we can solve for F by dividing both sides of the equation by d.

The equation W = Fd represents the relationship between work (W), force (F), and distance (d).

In this case, we are given the values of W and d and need to find F.

To isolate F, we can rearrange the equation as F = W/d.

By dividing the work (W) by the distance (d), we obtain the force (F) required to move the piano. The unit of force is typically measured in newtons (N), work in joules (J), and distance in meters (m).

It's important to note that this equation assumes a linear motion, where the force applied remains constant throughout the displacement of the piano. In practical situations, however, additional factors such as friction and the piano's weight distribution may affect the force required to move it.

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The length of DE is approximately 4.8 units, and the length of EF is approximately 5.6 units.

In similar triangles, corresponding sides are in proportion. We can set up the following ratios based on the given information:

AB/DE = BC/EF = AC/DF

Substituting the given values, we have:

6/DE = 7/EF = 8/(6.4)

Cross-multiplying, we get:

6EF = 7DE

8EF = 48

Simplifying the second equation, we find that EF = 6.

Substituting EF = 6 into the first equation, we can solve for DE:

6(6) = 7DE

36 = 7DE

DE ≈ 36/7 ≈ 4.8

Therefore, DE is approximately 4.8 units and EF is 6 units.

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Trigonometric function cos(x - π/6) in terms of sin(x) and cos(x) is (√3/2)cos(x) + (1/2)sin(x).

To rewrite cos(x - π/6) in terms of sin(x) and cos(x), we can use the trigonometric identity known as the cosine of a difference formula:

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

In this case, let's substitute a = x and b = π/6:

cos(x - π/6) = cos(x)cos(π/6) + sin(x)sin(π/6)

Now, we can simplify further using the values of cos(π/6) and sin(π/6):

cos(x - π/6) = cos(x)(√3/2) + sin(x)(1/2)

Therefore, cos(x - π/6) can be expressed in terms of sin(x) and cos(x) as:

cos(x - π/6) = (√3/2)cos(x) + (1/2)sin(x)

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The equation Y = 9x + 4 has a rate of change of 9, indicating that for every unit increase in x, y increases by 9. The initial value is 4, representing the y-value when x is zero.



To identify the rate of change and initial value from one of the given equations, let's analyze equation C: Y = 9x + 4.

In this equation, the coefficient of x, which is 9, represents the rate of change. This means that for every unit increase in x, the corresponding value of y will increase by 9 units. Therefore, the rate of change is 9.

To find the initial value, we need to determine the value of y when x is equal to zero. Plugging in x = 0 into the equation, we get:

Y = 9(0) + 4

Y = 0 + 4

Y = 4

Hence, the initial value or y-intercept is 4.

In summary, for the equation Y = 9x + 4, the rate of change is 9, indicating that y increases by 9 units for each unit increase in x, and the initial value is 4, representing the y-value when x is equal to zero.

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To simplify the given expression, we can first simplify the height and width separately.

The height is 4w^3 - 4w. This expression does not have any common factors, so it cannot be simplified further.

The width is 5w^2 - 3w - 4. This expression can be factored as (5w + 1)(w - 4).

Now we can substitute these simplified expressions into the formula for the area of a rectangle, which is A = length × width. The length in this case is the height.

Area = (4w^3 - 4w) × (5w^2 - 3w - 4)

To multiply these expressions, we can use the distributive property:

Area = 4w^3(5w^2 - 3w - 4) - 4w(5w^2 - 3w - 4)

Expanding the multiplication:

Area = 20w^5 - 12w^4 - 16w^3 - 20w^3 + 12w^2 + 16w

Combining like terms:

Area = 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w

Therefore, the simplified expression for the area of the rectangle is 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w.

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The employee's gross pay is $816.08.

None of the answer choices provided matches the result obtained.

To determine the employee's gross pay, we have to use the information given. We'll multiply the employee's regular hourly rate by the hours worked in a week, then add any overtime earnings. Here's the given information:

- Regular hourly rate: $12.75
- Overtime hourly rate: $19.13
- Hours worked in a week: 56

First, we'll calculate the employee's earnings for regular time:

$12.75/hour × 40 regular hours worked = $510.00

Next, we'll calculate the employee's earnings for overtime:

$19.13/hour × 16 overtime hours worked = $306.08

Now we'll add the employee's earnings for regular time and overtime together to find the gross pay:

$510.00 (regular earnings) + $306.08 (overtime earnings) = $816.08

Therefore, the employee's gross pay is $816.08.

None of the answer choices provided matches the result obtained.

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Given that the cost to upgrade from a standard seat to a seat with more legroom is £25. The standard seat costs s and the upgraded seat costs £370.

We are to find how much the standard seat cost. Let's solve for s Standard seat cost is what we need to find. Let us represent standard seat cost by s.

The cost to upgrade from a standard seat to a seat with more legroom is £25. Hence the cost of the upgraded seat is the cost of the standard seat plus the cost of upgrading.

So the cost of the upgraded seat is s + 25.And, we know the cost of the upgraded seat is £370.

So we can write the equation as:

s + 25 = 370 Subtracting 25 from both sides, we get:s = 345 Therefore, the standard seat costs £345. Answer: £345

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The given system of equations can be solved using the elimination method. The possible solutions to the system are: the only solution is (-32, 4), the only solution is (0, 2), there are an infinite number of solutions, or there is no solution.

To solve the system using the elimination method, we can multiply the first equation by 2 and the second equation by 3 to eliminate the variable x. This gives us the following system:

8x + 6y = 124

6x + 6y = 15

Subtracting the second equation from the first equation, we get:

2x = 109

Dividing both sides by 2, we find:

x = 54.5

Substituting this value of x into either of the original equations, we can solve for y. However, when we substitute x = 54.5 into the second equation, we get a contradiction. The equation becomes:

2(54.5) + 2y = 5

109 + 2y = 5

2y = -104

y = -52

Therefore, the system has no solution. The only solution option that matches this result is "There is no solution."

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Answer:

The probability is: 1/55

Step-by-step explanation:

The first sock you pick must be one of the two matching ones.

There are 2 matching socks out of 11, and all others are different.

First pick: p(one of the 2 matching socks) = 2/11

Now there are 10 socks left, and only one of them matches the first pick.

Second pick: p(the other matching sock) = 1/10

p(both matching socks) = 2/11 × 1/10 = 2/110 = 1/55

When Triangle ABC is dilated with a center of dilation at (0,0) and a scale factor of 2, the coordinates of point A' can be found by multiplying the original coordinates of point A by the scale factor.

In this case, if the coordinates of point A are (x, y), then the coordinates of A' would be (2x, 2y).

Dilation involves scaling an object by a factor while preserving its shape. When the center of dilation is at (0,0), the dilation occurs relative to the origin. By applying a scale factor of 2, the x-coordinate of point A is multiplied by 2, and the y-coordinate of point A is also multiplied by 2. This scaling operation results in the coordinates of A' being (2x, 2y).

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The equation of the given parabolic function in vertex form is: y = (x - 4)² - 4. This is because a=1.

The parabolic function going down from the left through the point zero comma twelve and through the point two comma zero and turning at the point four comma negative four and going up through the point six comma zero and continuing towards infinity can be represented by the following equation in vertex form: y = a(x - h)² + k where (h, k) is the vertex of the parabolic function.

From the graph, we can see that the vertex is (4, -4). So, the equation can be written as: y = a(x - 4)² - 4 Now, we need to find the value of a. The parabolic function passes through the point (0, 12). Substituting this point in the equation, we get:12 = a(0 - 4)² - 4 Simplifying, we get: 16a = 16a = 1 So, the equation of the given parabolic function in vertex form is: y = (x - 4)² - 4. This is because a=1.

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To find the length of the hypotenuse (c) in a right triangle, you can use the Pythagorean theorem, The length of the hypotenuse (c) is √312.

In this case, you have the lengths of the two sides, b and a, where b = 5a and[tex]a^2[/tex] = 12.

Let's go through the steps to find the length of the hypotenuse (c):

Step 1: Square the value of a

[tex]a^2[/tex] = 12

Step 2: Substitute the value of b in terms of a

b = 5a

Step 3: Square the value of b

[tex]b^2 = (5a)^2 = 25a^2[/tex]

Step 4: Apply the Pythagorean theorem

According to the Pythagorean theorem, [tex]c^2 = a^2 + b^2[/tex]

Substituting the values:

[tex]c^2 = a^2 + b^2\\c^2 = 12 + 25a^2[/tex]

Step 5: Simplify the equation

[tex]c^2 = 12 + 25a^2[/tex]

Step 6: Substitute the value of [tex]a^2[/tex]from Step 1

[tex]c^2 = 12 + 25(12)[/tex]

Step 7: Simplify further  

[tex]c^2 = 12 + 300\\c^2 = 312[/tex]

Step 8: Take the square root of both sides to find c

[tex]\sqrt{c^2} = \sqrt{312}\\c = \sqrt{312}[/tex]

The length of the hypotenuse (c) is √312.

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The total amount earned in the first 2 years of the contract is k488,400

Given that the salary is k20,000 monthly and there is an increment of k350 per month.

To find out the total amount in the first two years of contact, we need to calculate the salary for 24 months and then add the increments earned during those 24 months.

Salary for 24 months = k20,000 × 24= k480,000

Increment for 24 months = k350 × 24= k8,400

Therefore, the total amount earned in the first 2 years of the contract will be the sum of the salary for 24 months and the total increment earned during the same period= k480,000 + k8,400= k488,400

Thus, the total amount earned in the first 2 years of the contract is k488,400.

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The total amount you will have in the first 2 years of your contract is k14,000,000.

If your salary is k20,000 monthly and there is an increment of k350 per month, the total amount you will have in the first two years of your contact can be found using simple interest formula:
I = prt
where I is the interest, p is the principal amount, r is the rate of interest and t is the time in years.Therefore, using the above formula, we have;
I = (20,000)(350)(2)
= 14,000,000

Therefore, the total amount you will have in the first 2 years of your contract is k14,000,000.

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