After 6 new students entered the Happy Hearts Childcare Center and 2 students exited, there were 3 times as many students as before. How many students were present before students entered and exited the center?​

The value of  y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF

For similar triangle we can write,

⇒ CE/CF = AE/BF

⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5

So, y = 2.34

Similarly,

⇒ CF/CB = EF/AB

⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8

⇒ x = 18.5/8 = 2.31

Therefore, The value of  y = 2.34 and x = 2.31

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According to the question the value of triangles y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF
For similar triangle we can write,
⇒ CE/CF = AE/BF
⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5
So, y = 2.34
Similarly,
⇒ CF/CB = EF/AB
⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8
⇒ x = 18.5/8 = 2.31
Therefore, The value of  y = 2.34 and x = 2.31

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The exponential function that can model the revenue of a technology company whose starting value is $395,000 in 2010 at 1.2% annual growth is b) S(t)=395*(1.012)^(t).

An exponential function is a mathematical function that calculates the exponential growth or decay of a given data set.

An exponential function is defined by the formula f(x) = ab^x.

There are two kinds of exponential functions:

Starting value of the revenue in thousands of dollars = $395,000

Time measured in years after 2010 = t

Annual growth rate = 1.2%

Thus, the exponential function that mirrors the revenue growth is b) S(t)=395*(1.012)^(t).

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a) R(t)=395*e^((0.012t))

b) S(t)=395*(1.012)^(t)

The expression that is equivalent to 6(w + 7) is 6w + 42.

An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that are grouped together to represent a mathematical quantity or relationship.

The distributive property is a property of multiplication that allows us to multiply a single term by a sum or difference of terms. It states that:

a(b + c) = ab + ac and a(b - c) = ab - ac.

In other words, we can distribute the factor a to each term within the parentheses by multiplying it by each term, and then add or subtract the resulting products.

In the given question,

To simplify the expression 6(w + 7), we can use the distributive property of multiplication over addition, which states that:

a(b + c) = ab + ac

Using this property, we can expand the expression 6(w + 7) as:

6w + 6(7)

Simplifying the second term by multiplying, we get:

6w + 42

Therefore, the expression that is equivalent to 6(w + 7) is 6w + 42.

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The equation of the quadratic function represented by the given table is  y = -x² + 4x - 7.

A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.

The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.

The standard form of the quadratic equation is given as:

y = ax² + bx + c

Substitute the value of x and y from the table:

3 = a(2)² + b(2) + c

4a + 2b + c = 3........(1)

For point (4, -1):

-1 = a(4)² + b(4) + c

16a + 4b + c = -1..........(2)

For (6, -13):

-13 = a(6)² + b(6) + c

36a + 6b + c = -13..........(3)

From 1 we have:

c = 3 - 4a - 2b

Substitute the value of c in equation 2 and 3:

16a + 4b + 3 - 4a - 2b = - 1

12a + 2b = - 4........(4)

36a + 6b + 3 - 4a - 2b = -13

32a + 4b = -16.......(5)

Multiply equation 4 with 2 and subtract with equation 5:

32a + 4b = -16

-(24a + 4b = - 8)

a = -1

Substitute the value of a in equation 5:

32(-1) + 4b = -16

-32 + 4b = -16

b = 4

Substitute the value of a and b in equation 1:

16a + 4b + c = -1

16(-1) + 4(4) + c = -1

-16 + 8 + c = -1

-8 + c = -1

c = 7

Using the algebraic techniques we have:

a = -1

b = 4

c = 7

Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.

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Answer:

Step-by-step explanation:

The probability of landing on a number greater than 4 on the first spin is 2/3, because 2 out of the 3 numbers (5, 4, 6) are greater than 4.

If the first spin lands on a number greater than 4, then there are two numbers left (4 and 5) for the second spin. The probability of landing on a number less than 6 on the second spin is 2/2 or simply 1, because both 4 and 5 are less than 6.

Therefore, the probability of landing on a number greater than 4 on the first spin and a number less than 6 on the second spin is:

(2/3) x (1) = 2/3 or approximately 0.67.

Answer:

142 sq cm

Step-by-step explanation:

A= 2(lh + wh + lw)

2(7*3+5*3+7*5)

2(21+15+35)

2(71)

A= 142 sq cm

So the correct answer is option A) m=5, LO=14, NO-12 for the indicated variables and measures for the figure below.

A triangle is a closed two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the measures of its angles. The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides. Triangles have many properties and are used in various mathematical and real-world applications, including trigonometry, geometry, and engineering.

Here,

Since all the angles are equal, we can set up the following proportion:

LO/NO = 7/2

Multiplying both sides by NO, we get:

LO = (7/2)NO

We can also use the fact that the angles are equal to set up an equation involving m:

m + (1/2)LO + (1/2)NO = 180

Substituting LO = (7/2)NO, we get:

m + (7/4)NO = 180

Now we can substitute the given values for LO and NO:

m + (7/4)(14) = 180

m + 49 = 180

m = 131

Therefore, the answer is: m = 131, LO = 49, NO = 14

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The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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The probability that exactly 3 homes will be sold tomorrow is A) 0.1809.

To solve this problem, we can use the Poisson distribution formula, which is:

P(x; μ) = (e^-μ) (μ^x) / x!

where P(x; μ) is the probability of x events happening in a given time period, μ is the mean number of events in that time period, e is the mathematical constant approximately equal to 2.71828, and x! is the factorial of x.

In this case, we want to find the probability of exactly 3 homes being sold tomorrow, given that the average number of homes sold is 2 per day. So, we plug in μ = 2 and x = 3 into the formula:

P(3; 2) = (e^-2) (2^3) / 3! = 0.1809

Therefore, the probability that exactly 3 homes will be sold tomorrow is 0.1809 or approximately 18.09%. This means that out of every 100 days, we can expect that around 18 of those days will have exactly 3 homes sold by Acme Realty Company.

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Step-by-step explanation:

The equation that represents how much will be in the account after 7 years is:

M = 7,600(1+0.06)^7

Here's the explanation:

The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.

In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.

Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.

The potato will take approximately 3.1 minutes to reach a temperature of 90 degrees Celsius to the nearest tenth of a minute.

According to Newton's equation, we need to find time taken for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

Newton's law of cooling equation is used.

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature.

The law of cooling is given as

[tex]T(t) = T_m + (T_0 - T_m)e^{-kt}[/tex]

whereT(t) is the temperature of the object at time t.

[tex]T_0[/tex] is the temperature of the object initially.

[tex]T_m[/tex] is the temperature of the medium in which the object is kept.

k is a positive constant.

The formula is used to solve for the time it will take the baked potato to reach 90 degrees Celsius.

This is given as:

[tex]T(t) = T_m + (T_0 - T_m)e^{-kt}[/tex]

[tex]90 = 20 + (37 - 20)e^{-kt}[/tex]

Let's start by solving for k.

[tex]37 = 20 + (37 - 20)e^{-k(10)}[/tex]

[tex]17 = 17e^{-10k}[/tex]

[tex]ln(1) = -10k[/tex]

[tex]k = 0[/tex]

Substituting k = 0 in the equation,

we have

[tex]90 = 20 + (37 - 20)e^{0(t)}[/tex]

[tex]\frac{70}{17} = e^{(0(t))}[/tex]

Taking the natural log of both sides,

[tex]ln\frac{70}{17}  = lne^{0(t)}[/tex]

[tex]t= 3.0748 minutes[/tex]

Therefore, it will take approximately 3.1 minutes for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

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Answer:

$31.45

Step-by-step explanation:

If something was reduced by 15 percent its the same as .85x or 85% of the original price. 37*.85 = $31.45

Based on the information provided, the table that correctly displays the data is table III.

Note: The question is incomplete; below I attach the missing information:

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Answer:

Step-by-step explanation:

The given line is y = 5x + 2. We know that any line perpendicular to this line will have a slope that is negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Line A is perpendicular to y = 5x + 2, so it has a slope of -1/5. We also know that the y-intercept of line A is 3. Therefore, the equation of line A can be written as:

y = (-1/5)x + 3

or in the form y = mx + c, where m = -1/5 and c = 3.

Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.

The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

We can use the formula:

time = distance / speed

where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.

Substituting the given values, we get:

time = 2 miles / 8 miles per hour

Simplifying, we get:time = 0.25 hours.

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As per the given percentage, Sandesh should aim to sell his apples at 250rs per kg in order to gain 20% profit.

Let C be the cost of the 15kgs of apples. Sandesh gained 12%, so his profit is 0.12C. We know that Sandesh sold the apples for 2100rs, so we can write an equation:

C + 0.12C = 2100

Simplifying this equation gives:

1.12C = 2100

Dividing both sides by 1.12 gives:

C = 1875

So Sandesh's cost for 15kgs of apples was 1875rs.

Now, we need to find the selling price per kg of apples that Sandesh should aim for in order to gain 20% profit. Let P be the selling price per kg of apples.

Since Sandesh wants to gain 20% profit, his selling price per kg of apples needs to be his cost plus 20% of his cost, or 1.2 times his cost.

So we can write another equation:

1.2C = 15P

Substituting the value of C we found earlier, we get:

1.2(1875) = 15P

Simplifying gives:

P = 250

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10/73 is the value of x in inequality.

What does the word "inequality" mean?

In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.

                    However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

the inequality  12≥ 73x + 2

                    = 12 - 2  ≥  73x

                     = 10 ≥ 73x

                   = 10/73 ≥ x

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The value of x is 2 inches, which represents the length of each side of the square.

We can start by setting up the equation using the given expression for the side length and the given area:

(x + 2)² - 16 = 0

Expanding the left side and simplifying, we get:

x² + 4x = 0

Factoring out x, we get:

x(x + 4) = 0

So, either x = 0 or x = -4. However, since x represents a length, it must be positive. Therefore, the only solution is:

x = 0 + 2 = 2

So the value of x is 2 inches.

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Answer:

(3, 4)

Step-by-step explanation:

We are given the following system of equations:

x + y = 7

x + 2y = 11

We want to solve to find the values of x and y.

There are three ways to solve a system of equations: substitution, graphing, and elimination.

Any one of these methods will work, however let's do elimination for this.

To eliminate, we can add or subtract the equations together to clear the variables.
It is helpful to rewrite this system as:

x + 2y = 11

x + y = 7

We can subtract x + y = 7 from x+2y=11:

x + 2y = 11

-(x+y = 7)

This is equivalent to:
x + 2y = 11

-x - y = - 7

_________

0 + y = 4

So, y = 4

Now, we need to find x.

We can plug in 4 for y in either x + y = 7 or x + 2y = 11.

Taking x + y =7 for instance:

x + 4 = 7

Subtract 4 from both sides.

x = 3

So, x = 3 and y =4

As a point, this is (3, 4).

Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

the probability of Jacinta selecting a green marble is 5/11. The total number of marbles in the bag is:

2 (blue) + 4 (red) + 5 (green) = 11

The probability of selecting a green marble can be found by dividing the number of green marbles by the total number of marbles:

P(selecting a green marble) = number of green marbles / total number of marbles

= 5 / 11

Therefore, the probability of Jacinta selecting a green marble is 5/11. Answer: 5/11.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer: 4

Step-by-step explanation:

4. shift the boundary line up 1

By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.

Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten. 

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In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Rosmaria runs 1.5 hours.

In the first week, Rosmaria ran 3 hours.

Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3

                                                             = 54

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The height of the monster on the 40-inch TV screen will be 8 inches, which is larger than its height on Hunter's tablet.

First, we need to find out the scale of the monster on Hunter's tablet, which can be calculated as follows

Screen aspect ratio = 8/6 = 4/3

Height of monster on tablet = 5 inches

Width of monster on tablet = (4/3) x 5 = 6.67 inches (because the aspect ratio is 4:3, the width of the monster is 4/3 times its height)

Next, we need to find out the height of the monster on the 40-inch TV screen, which has the same 4:3 aspect ratio as the tablet screen. We can do this by using a proportion

Tablet screen height, Tablet screen width = TV screen height : TV screen width

Substituting the values we know, we get,

6 inches : 8 inches = TV screen height : 10.67 inches (because 40 inches is 4/3 times the width of the TV screen)

Solving for TV screen height, we get,

TV screen height = (6/8) x 10.67 = 8 inches

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By answering the presented question, we may conclude that So, the Pythagorean theorem length of MN is expressed in terms of a and b.

Its Pythagorean theorem is just a fundamental mathematical principle that explains the connection between the sides of a triangle that is right. It asserts that the sum of the squares of both the widths of the other two sides is a square of both the width of the hypotenuse (the side facing the perfect angle) the side opposite the right angle). The mathematical mathematics is as follows: c2 = a2 + b2 At which "c" indicates the length of the right triangle and "a" and "b" reflect the extents of the additional two sides, started referring to as the legs.

Because M is the midpoint of OE and N is the midpoint of AB, we can draw a line segment connecting M and N that is parallel to OB and AE and perpendicular to AB.

the Pythagorean theorem

[tex]OE² = OX² + XE²OE²[/tex]

[tex](a + b/2)² + (2a - b/√3)²OE² = 7a²/4 + 3ab/2 + b²/4AN²[/tex]

[tex]AE² + EN²AN² = (2a√3)² + (b/2)²AN²[/tex]

[tex]12a² + b²/4MN² = AN² + AM²MN² \\\\ 12a² + b²/4 + (7a²/4 + 3ab/2 + b²/4)MN²\\\\19a²/2 + 3ab/2 + b²/2MN = √(19a²/2 + 3ab/2 + b²/2)[/tex]

So, the length of MN is expressed in terms of a and b.

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In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

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The measurement of  of angle c is (4x-24. 6) and measure of angle d is (x+11. 3). If the angles are supplementary, the value of x is 38.66.

The measure of angle c is (4x-24. 6)

The measure of angle d is (x+11. 3)

If both angles are supplementary angles then,

angle c + angle d = 180

(4x-24. 6) + (x+11. 3) = 180

5x - 13.3 = 180

5x = 180 + 13.3

5x = 193.3

x = 193.3/5

x = 38.66

So, the value of x is 38.66

What distinguishes complimentary from supplementary angles?

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.

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[tex](x+2)^2=-16\implies x+2=\sqrt{-16}\implies x+2=\sqrt{-1\cdot 16} \\\\\\ x+2=\sqrt{-1}\cdot \sqrt{16}\implies x+2=4i[/tex]

so, whenever you take an "even root" of a "negative value", you'd end up with an imaginary root or value, which is another way to say, such root doesn't really exist or no solution.

now, we can look at it this way, the same equation is really just a parabola like (x+2)² + 16 = 0, notice, the parabola is in vertex form, its vertex is at (-2 , 16), on the II Quadrant 16 units up above the x-axis.  A solution or what's called a solution or root or zero is really nothing but just an x-intercept, well, the parabola's vertex is way up and is opening upwards, so it never touches the x-axis, no zeros, no solution.

Check the picture below.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1200[1+(0.05)(3)]\implies A=1200(1.15) \implies A = 1380[/tex]