Colin invests £3300 into his bank account. He receives 3% per year compound interest. How much will Colin have after 4 years? Give your answer to the nearest penny where appropriate

Answer: I think it's 6816606.576

Step-by-step explanation: Hope this helps?

By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).

Here we have the following system of equations:

y = x + 8

y = -(1/2)x+5

And we want to solve it graphically.

To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.

The graph of the system of equations can be seen in the image below:

There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.

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The formula for vector direction is: Direction = arctan (y/x) , Where x is the x component of the vector and y is the y component of the vector.

1. Find the x and y components of the vector

2. Divide the y component by the x component

3. Calculate the arctan (inverse tangent) of the result

4. The result is the direction of the vector in radians (or degrees if you prefer).

If you want to convert the result from radians to degrees, you can use the following formula:

(in degrees) = arctan (y/x) * (180/π)

Where π (pi) is approximately equal to 3.14.

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Answer:

The angle in the sector is 180°.

Because the area of circle is 36 pie cm². So the angle is the half of 360°.

[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]

Answer:

the equation of line parallel to y=-3x+2

is y=-3x+k---(1)

Since,line(1) passes through point (4,3).

3=-3(4)+k

or,3=-12+k

or,k=3+12

:.k=15

Putting value of k in line (1), we get

y=-3x+15,which is the required eqn.

*mark me brainliest

Answer: for A it is: 3 and 4 represent the number values for X and Y.

Step-by-step explanation:

Sorry, but you B and C you did not give enough information

Answer:

55 miles per hour

Step-by-step explanation:

The equation is:

R = d / s

We know

d = 495 miles

s = 9 hours

Let's solve

R = 495 / 9

R = 55 miles per hour

So, their driving rate is 55 miles per hour

In a reaction the amount f a substance which react with another substance is known as it's equivalent.

The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."

It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.

The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.

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The area of square 1 is 180 sq cm

The area of a square is calculated with the help of the formula: Area = s × s, where, 's' is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units

Square 1 formed on hypotenuse of the triangle, squares 2 and 3 are formed on the perpendicular legs of the triangle. Thus, by Pythagoras Theorem, A(square 1) will be equal to the sum of the areas of (square 2) and (square 3).

Area of square 1 = Area of square 2 + Area of square 3

Area of square 1 = 100 + 80

Area of square 1 = 180cm^2

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To solve for x, we need to get x by itself on one side of the equation. To do this, we can start by subtracting 1.4x from both sides of the equation. This gives us:

3 1/2 - 1.4x ≥ 0

Next, we can simplify the left side of the equation to get:

7/2 - 7/5x ≥ 0

Now we can divide both sides of the equation by -7/5 to get:

-5/2x ≤ -7/2

Finally, we can multiply both sides of the equation by -2/5 to get:

x ≥ 4 9/10

Therefore, the solution is x ≥ 4 9/10, which corresponds to answer choice C.

Answer:
x ≥ 4 9/10 C:)

Step-by-step explanation:

We have proved that △BCD≅△CBE.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.

By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.

It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC

So, In right triangles BCD and CBE

BC=CB=common side⋯⋯[hypotenuse]

And BD=CE=given⋯⋯[sides of right triangles]

So, by RHS condition

△BCD≅△CBE.

Hence, we have proved that △BCD≅△CBE.

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We have proved that △BCD≅△CBE.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.

By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.

It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC

So, In right triangles BCD and CBE

BC=CB=common side⋯⋯[hypotenuse]

And BD=CE=given⋯⋯[sides of right triangles]

So, by RHS condition

△BCD≅△CBE.

Hence, we have proved that △BCD≅△CBE.

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Answer:

Step-by-step explanation:

Answer:

6,532

Step-by-step explanation:

ixl

The largest side of the length is 26cm.

Now, According to the question:

Three consecutive even numbers can be expressed in terms of n. If n is an even number then,

(n -2), (n), (n + 2)

are three consecutive even numbers.

Therefore,

(n -2)+ (n)+ (n + 2) = 72cm.

We can simplify so...

3n + 2 - 2 = 72 cm.

3n + 0 = 72 cm.

3n = 72cm.

Divide both sides by 3 to solve for n

n = 24 cm.

24 is an even integer. Input 24 into the original equation.

(n -2)+ (n)+ (n + 2) = 72cm.

(24 - 2) + 24 + (24 + 2) = 72cm

22 + 24 + 26 = 72

72 = 72

Hence, The largest side of the length is 26cm.

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Answer:

Step-by-step explanation:6

Answer:

Option 2

Step-by-step explanation:

Hello!

We can solve the equation for n by isolating the variable.

The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."

The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

What is an apothem of a polygon?

A line segment from a regular polygon's centre to one of its sides is known as the apothem.

The given options are the following:

a)The apothem can be found using the Pythagorean theorem.

b)The apothem can be found using the tangent ratio.

c)The perimeter of the equilateral triangle is 15 cm.

d)The length of the apothem is approximately 2. 5 cm.

e)The area of the equilateral triangle is approximately 65 cm².

Now we will see if each option is true or not

a) From below figure,

      b = 8.7 / 2 = 4.35 cm

      From right angled triangle ΔABD,

    Using Pythagorus Theorem,

       a² + b² = 5²

       a² + 4.35² = 5²

       a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm

Apothem can be found using Pythagorus Theorem.

b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.

So from ΔABD,

tan 30° = a / 4.35

0.577 = a / 4.35

a = 2.5 cm

The apothem can be found using tangent ratio.

c) Perimeter of given equilateral triangle = 3 × side length

                                                                    = 3 × 8.7 = 26.1 cm

   This option is false.

d) From options (a) and (b) we found that length of apothem a = 2.5 cm

Therefore this option is true.

e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]

                                                                       = 32.8 cm²

Therefore this option is false.

Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

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f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)

The x-intercepts are x=-5 and x=4.

The vertex of symmetry is (-1/2, -81/8).

The axis of symmetry is:  x = -1/2

A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,

f(x) = 1/2x^2+1/2x-10

=  (1/2)(x² + x - 20)

= (1/2) (x² + 5x - 4x - 20)

= (1/2) { x(x+5) -4(x+5)

= (1/2) (x+5)(x-4)

Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)

The x-intercepts will be where the factors = 0

x + 5 = 0 ⇒x = -5

x - 4 = 0  ⇒ x = 4

Therefore, the x-intercepts are x=-5 and x=4

To find the axis of symmetry, take the average of intercepts (to find the center of parabola)

(-5 + 4)/2 = -1/2

Axis of symmetry ⇒ x = -1/2

To find the vertex, put the axis of symmetry into the equation

f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8

vertex is  (-1/2, -81/8)

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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

f(x) = (1/2)x² + (1/2)x - 10

2f(x) = x² + x - 20

2f(x) = x² + x + 1/4 - 1/4 - 20

2f(x) = (x + 1/2)² - 81/4

f(x) = 1/2 (x + 0.50)² - 10.125

The x-intercepts are given as,

f(x) = 0

1/2 (x + 0.50)² - 10.125 = 0

(x + 0.50)² = 20.25

x + 0.50 = ± 4.50

x = - 0.50 ± 4.50

x = - 0.50 - 4.50, - 0.50 + 4.50

x = - 5, 4

The equation of the axis of symmetry is given as,

x + 1/2 = 0

x = - 1/2

The graph is attached below.

The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

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Answer:

9.75

Step-by-step explanation:

3/4 |1/3x+2| < 6

you can turn the < into a =

then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with

|1/3x| = 3.25

then do 3.25/(1/3) which leaves you with 9.75

:)

The stripe's area in square feet is 240 square units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base 3 and height 80.

area=3*80

=240 square units.

the area of the stripe in square feet is 240 square units.

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Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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a)  The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same =  $369,181.93.

b)  The total amount that would be paid to the lender over 25 years = $540000

To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.

Here, future value = 0

number of periods = 25 years

                                = 25 × 12 months per year

                                = 300

payment amount = -1800 dollars

interest rate = 4.25% per year

                    = 0.3542% per month

the maximum mortgage amount they could afford = $369,181.93.

And the total payments would be equal to 300 × 1800 = 540000

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The complete question is:

Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.

What if Aya and Harumi could only afford a monthly payment of $2,000?

What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?

What is the total amount that would be paid to the lender over 25 years?

Answer:

do your own work don't ask any question

The height of a triangle can be found using the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Therefore, the height of a triangle can be found by rearranging the formula to height = (2 * area) / base.

To find the height of a triangle when the base is given, first use the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Next, rearrange the formula to height = (2 * area) / base so that the height can be found by dividing the area by the given base. Once the area is known, the height can be found by plugging the area and base into the rearranged formula. For example, if the base of a triangle is 8 and the area is 12, then the height of the triangle can be found by dividing 12 by 8, which is equal to 1.5. Therefore, the height of the triangle is 1.5.

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Retail price of the product will be double its mean will have a prbability of 0.0401.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The value of the product considering = $37*2 = $74(x)

Mean = $37

Standard Deviation (SD)= $20

here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]

P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401

Retail price of the product will be double its mean will have a prbability of 0.0401.

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Answer:

2 (21a−8)

Step-by-step explanation:

Answer:

2(21a - 8)

Step-by-step explanation:

42a - 16
The gcf of 42, 16 is 2
=> 2(21a-8)

The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel method over a sequential one.

Sequential Computing: One instruction is delivered at a specific time, and the subsequent instruction must wait for the first instruction to complete before it can be executed. This is known as sequential computing. Because all the instructions are carried out in order, it is often referred to as a conventional computing technique. It has a single CPU that performs poorly and has a heavy workload. The biggest drawback of employing this computing is that it requires more time because just one instruction is being processed at a time.

Parallel Computing: A computing method known as parallel computing involves running numerous calculations or processes simultaneously in parallel. Parallel computing is a kind of computing in which multiple processes can run at once.

Due to the simultaneous execution of the operations, time is saved. It resolves more complex issues. There are many processors with high performance and little work being put on each of them.

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An equation that represents the relationship between x and y shown in the table is y = 1.5x.

In order to write an equation that represents the relationship between x and y shown in the table, we would have to find the slope from the table and then write the required equation based on the data points by using the point-slope form.

Mathematically, the point-slope form of a line is given by this mathematical equation:

y - y₁ = m(x - x₁)

Where:

By substituting the given parameters into the point-slope formula, an equation for the data points contained in this table is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 21 = (96 - 21)/(64 - 14)(x - 14)

y - 21 = 75/50(x - 14)

y - 21 = 1.5(x - 14)

y = 1.5x - 21 + 21

y = 1.5x

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Answer:

Below

Step-by-step explanation:

How many times will the colony double ?    124 / 31 = 4 times

2^4   * 100 000 = 1 600 000

Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.

There are few basic steps to be followed while solving any mathematics problem:

1. Read and understand the problem.

2. Identify what is given and what is needed to solve the problem.

3. Choose an appropriate strategy to solve the problem.

4. Carry out the strategy.

5. Check your answer to make sure it is correct.

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