Mathematics College

£850 is invested for 2 years at 6% per annum compound interest. a) Work out the total interest earned over the first 2 years.

Answers

Answer 1

The correct answer to 850 for 2 years at 6% interest is 955

Answer 2

Answer:

6% annum for 850 would be 955

Related Questions

Find a1 for the arithmetic series with s20 = 80 And d = 2

Answers

we know that
the formula of the arithmetic series is
Sn=n[2(a1) + (n - 1)d]/2
where
Sn=80
n=20
d=2
a1=?
then
80=20*[2*a1+19*2]/2----------------> 160=[40*a1+760]
160=[40*a1+760]----------> a1=(160-760)/40------------> a1=-15

the answer is
a1=-15

To solve this, we are going to use the standard formula for arithmetic series [tex]S _{n} = \frac{n}{2} [2a_{1} +(n-1)d][/tex]
where:
[tex]S_{n} [/tex] is the sum of the arithmetic sequence
[tex]n[/tex] is the number of terms
[tex]d[/tex] is the difference
[tex]a_{1} [/tex] is the first term
From our problem we know that [tex]S_{n} =80[/tex], [tex]n=20[/tex], and [tex]d=2[/tex]. Lets replace those values in our formula to find [tex]a_{1} [/tex]:
[tex]80= \frac{20}{2} [2a_{1} +(20-1)2][/tex]
[tex]80=10(2a_{1} +38)[/tex]
[tex]80=20a_{1} +380[/tex]
[tex]20a_{1} =-300[/tex]
[tex]a_{1} = \frac{-300}{20} [/tex]
[tex]a_{1} =-15[/tex]

We can conclude that the first term [tex]a_{1} [/tex] of the arithmetic series is [tex]-15[/tex]

If the asymptotes of a hyperbola are the x- and y-axes, it is known as a rectangular hyperbola?

Answers

Yes, This is true. If the asymptotes of a hyperbola are the x- and y- axes, it IS known as a rectangular hyperbola.

Final answer:

A rectangular hyperbola is defined by the angle between its asymptotes being 90°, with its Equation represented as x'y' = a².

Explanation:

Rectangular Hyperbola: When the angle between the asymptotes of a hyperbola is 90°, it is called a rectangular hyperbola. In this case, b = a and the eccentricity is √2. The Equation to a rectangular hyperbola is x'y' = a².

what is the average of -10.25 and 125.75

Answers

add them together and divide it by 2 since there are two numbers
125.75+(-10.25)=115.5
115.5/2= 57.75

the mean is 57.75

122% in simplest form

Answers

For this case we have the following decimal expression:
122%
To write it in a simple numerical value, we must divide the given value by 100.
We have then:
[tex](122/100) [/tex]
Simplifying we have:
[tex]61/50 [/tex]
In decimal form we have:
1.22
Answer:
Two options:
1) as a decimal: 1.22
2) as a fraction: 61/50
Both answers are equivalent.

Answer: The simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.

Step-by-step explanation:

We know that to simplify percentage into fractions or decimals, we need to divide it by 100.

The percent value = 122%

Therefore , to simplify it into the simplest form we divide it by 100, we get

[tex]122\%=\frac{122}{100}=\frac{61}{50}[/tex]

In decimal , [tex]122\%=\frac{122}{100}=1.22[/tex]

Hence, the simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.

In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram

Answers

Your area would be 32, 8 by 4 is what the formula is

The area of the parallelogram is 32 square units.

What is a parallelogram?

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:

| (3,6) (11,6)

| *-----------*

| / /

| *-----------*

| (0,2) (8,2)

Now,

We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.

To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.

Therefore,

The height of the parallelogram is 4 units.

Now,

The area of a parallelogram is given by the formula:

Area = base x height

Plugging in the values we found, we get:

Area = 8 x 4

Area = 32

Therefore,

The area of the parallelogram is 32 square units.

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GIVEN circle P with arc AE = 53 , arc BA =68 and arc CB =72

match the following angles with their corresponding measurements

Answers

the theory that is mainly used to find out the angles of the above diagram is that;
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°

the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7

m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°

next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°

m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°

consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°

finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°

All the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8 = 90°

The theory that is mainly used to find out the angles of the above diagram is that;

the sum of the internal angles of a triangle is 180°.

when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.

Next from point A to point E, the angle rotated is 68°

the addition of these 2 angles give the angle rotated from point B to point E,

that is angle no.7

m∠7 = 53° + 68° = 121°

consider ΔPBE,

PB and PE are radii therefore isosceles triangles

In isosceles triangles the angles opposite equal sides are equal

if the angle is x°, then there are 2 angles with values x each

x° +x° + 121° = 180°

2x° = 59°

x = 29.5°

therefore m∠3 = 29.5°

next connect PC and consider ΔPCB,

according to given information, C∠PB = 72°

as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal

2y° + 72° = 180°

y° = 54°

then consider ΔPCD, again an isosceles triangle

as a straight line has an angle of 180°

B∠PC + C∠PD = 180°

72° + C∠PD = 180°

C∠PD = 108°

as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)

2z° + 108° = 180°

z° = 36°

B∠CD is a sum of y and z angles

therefore m∠8 = y + z

m∠8 = 54° + 36° = 90°

there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius

this indicates that lines PD and HD are perpendicular to each other

hence, forms a right angle where it cuts each other.

therefore H∠DP / m∠4 = 90°

C∠DH /m∠5 is the difference between P∠DH and P∠DC

m∠5 = 90° - 36° = 54°

m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°

by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.

m∠1 is the acute angle therefore m∠1 = 63.5°

m∠6 is the obtuse angle therefore m∠6 = 116.5°

consider ΔDFB

D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°

D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°

116.5 + w° + 29.5° = 180°

w° = 34°

m∠2 = m∠4 + w°

= 90° + 34°

= 124°

finally all the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8 = 90°

Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2

Answers

Answer:

[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]

Step-by-step explanation:

The given expresion is:

(−2x + 4y)(3x − 7y)

We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]

We expand further to obtain:

[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]

[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]

Answer:

[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]

Step-by-step explanation:

We multiply each term in the parentheses, by those of the other parenthesis:

[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]

Now, we simplify.

We have two terms that contain xy:

[tex]=-6x^2+26xy-28y^2[/tex]

Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]

Sierra sawed 10 1/2 inches off the end of a board. the remaining board was 37 1/2 inches long. how long was the boared that sierra started with? please explain answer

Answers

37 1/2 +10 1/2 = 48 inches
48 inches is your answer ;)

Write the time another way 23 minutes after 4

Answers

23 minutes after 4 o'clock is the same as 4:23.

4:23

Would be the answer

An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.

What is the explicit rule for this situation, and how many marbles will be in the 10th row?

Drag and drop the answers into the boxes to match the situation.

Explicit rule

Number of marbles in the 10th row

An = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,

Answers

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

The explicit rule for this situation is An = 12 + n, where "n" represents the row number.

To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:

A10 = 12 + 10

A10 = 22

So, there will be 22 marbles in the 10th row.

Matching the answers:

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

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During each minute of a comedy show, Carlin laughs 555 times. Carlin watches 333 comedy shows every day, and each show is 404040 minutes long. How many times does Carlin laugh every day due to the comedy shows?

Answers

74,672,652,600. Take the time of the show and multiply it by the number of times she laughs in a minute. Then multiply that by the number of shows she watches in a day. That number seems pretty large though so you may want to make sure you have the right numbers and that it's not just 5 times, 3 shows, and 40 minutes.

Answer: 600

Step-by-step explanation:

Given : The number of times Carlin laughs in each minute = 5

The number of comedy show Carlin watched = 3

The length of each comedy show = 40 minutes

Total minute she watched Comedy show will be :-

[tex]40\times3=120\text{ minutes}[/tex]

Then , the total number of times Carlin will be :-

[tex]120\times5=600[/tex]

Hence,Carlin laughs 600 times every day due to the comedy shows.

Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -

Answers

Answer:

A. 12

B. 3

C. -2

D. -5

Step-by-step explanation:

Verified on edge, just finished it

The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.

What is Vertex Form?

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.

Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.

Given:

y = 3x² + 12x + 7

Now writing the equation in vertex form

y = 3x² + 12x + 7

y = 3x(x + 4) + 7

Adding and subtracting 12 on both side

y= 3(x²+ 4x) + 7 -12 + 12

y= 3(x² + 4x + 4) + 7- 12

y= 3(x+ 2)² -5

Now, Comparing it with y = a(x - h)² + k we get

a= 3

h= -2

and, k= -12

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The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. answer General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
I think it is 34 general and 61 youth

Answers

i just answered this question few minutes ago
yes, you are right

The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall. What is the length of the diagonal of this monitor, to the nearest tenth of an inch? Enter your answer, as a decimal, in the box.

Answers

14.

a^2 + b^2 = c^2
12^2 + 7^2 = c^2
144 + 49 =c^2
193 = c^2
c= 13.89
14

The length of the diagonal of this monitor, to the nearest tenth of an inch, would be 14.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall.

[tex]a^2 + b^2 = c^2\\12^2 + 7^2 = c^2\\144 + 49 =c^2\\193 = c^2\\c= 13.89 14[/tex]

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By connecting two non-intersecting vertices of a regular pentagon, the figure can be split into a triangle and a quadrilateral. Always Sometimes Never

Answers

A triangle has three sides.
A quadrilateral has four sides.
See attached figure.
If you cannot find another way of subdividing the pentagon, then you have found that the pentagon is always split into a triangle and a quad.

Natasha had d dollars. She bought two ice creams which cost x dollars each. How much money does she have left?

Answers

the answer is (d-x)-x

d-2x because x is the ice cream and she got two of them

PLEASE HELP BABES!!

Heather is trying to decide what classes to take next year. She must take one of each and can choose from 3 math classes, 2 science classes, 4 history classes, and 3 English classes. How many different schedules can she have?
A) 4
B) 12
C) 48
D) 72

Answers

d)72 is the answer. It might also be c)48 but im not sure.

Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use

Answers

3 is the greatest number of book shelves Andy can use. I solved this by finding the greatest comment factor of 9 and 6, which turned out to be 3.
6/3=2(reading books per shelf)
9/3=3(math books per shelf)
Every shelf there are two reading books and 3 math books

9 math books
6 reading books
First we need to find the greatest common factor.
in this case it would be 3.
9 ÷ 3 = 3
6 ÷ 3 = 2
Here we have our answer
since 3 is not an even number it cannot be split evenly which means each bookcase will have at least 3 math books on it - and 2 reading books as well

*bookcase 1:
3 (math)
2(reading
*bookcase 2:
3 (math)
2 (reading)
*bookcase 3:
3 (math)
2 (reading

If an object is dropped from a height of 55 feet, the function d=-16t^2+55 gives the height of the object after t seconds. Graph this function. Approximately how long does it take the object to reach the ground (d=0)

Answers

notice, it hits the ground when d = 0, thus

[tex]\bf \stackrel{d}{0}=-16t^2+55\implies 16t^2=55\implies t^2=\cfrac{55}{16}\implies t=\sqrt{\cfrac{55}{16}}[/tex]

that's when.

as far as its graph, is more or less like the picture below, now, notice that if we put the quadratic in "vertex form", it'd look like

[tex]\bf d=-16t^2+55\implies d=-16(t-\stackrel{h}{0})^2+\stackrel{k}{55}\qquad vertex~(h,k)[/tex]

so its vertex is at (0, 55), so just pick one point to the left of the vertex, and one to the right of the vertex, and draw it away

convert 39/5 to a mixed number written in lowest terms

Answers

Hello!

39 ÷ 5 = 7.8

A N S W E R:

7.8 = 7 4/5 (This is in lowest terms)

a rectangular park is 4 miles long and 2 miles wide. how long is pedestrian route that runs diagonally across the park

Answers

you can use the Pythagorean theorem to solve this
[tex]{x}^{2} = {4}^{2} + {2}^{2} [/tex]
Now solve for x
[tex] {x}^{2} = 16 + 4 \\ {x}^{2} = 20 \\ x = \sqrt{20} [/tex]
Now you can simplify this to
[tex]x = \sqrt{5 \times 4} \\ x = \sqrt{5} \sqrt{4} \\ x = \sqrt{5 } \times 2 \\ x = 2 \sqrt{5} [/tex]
And that's your answer

Which number completes the inequality? -5.13< ?< -4.8

Answers

-5.14? Not sure if it's correct, but it's my best guess.

Anything from -5.12 to -4.7 would work

Which is a focus of the hyperbola shown? (0, −26) (0, −24) (0, 25) (0, 30) BRAINLIESTT

Answers

Answer:its (0 -26)

Step-by-step explanation:

THATS THE ANSWER NO NEED TO explain

Answer:

A (0,-26)

Step-by-step explanation:

you deposit 2800 in a savings account that earns 1% annual intrest compounded semiannually.Write a function that represents the balance after t years

Answers

Function for compound interest:

Amount = Initial amount * ( 1 + (r/n) ) ^ (nt)

where r = interest rate per year, n = period per year

n = 2, r = 0.01

Answer: F(t) = 2,800 * [ 1 + (0.01/2) ] ^ 2t

The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex]

What is Compound Interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Here, P = $2800

I = 1 % compounded semiannually = 0.5 % = 0.005

Time = t years

n = 2t semi-years

We know that,

[tex]A = P(1+i)^n[/tex]

[tex]A = 2800 ( 1 + 0.005 )^{2t}[/tex]

[tex]A = 2800 X 1.005^{2t}[/tex]

Thus, The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex].

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Sean divides 8 cups of granola into 1/4-cup servings. How many servings of granola does he have?

Answers

Think of this, 8 is a whole number right? You can put a 1 under that 8 and it will still be a whole number, You basically flip 1/4 as a fraction, Which will make it 4/1. You can multiply the 8 and 4 which will equal 32, You can add that 1 under the 32 if that helps you but the answer, in general, is 32

1 cup makes 4 servings
8 cups make x

x = 8*4
x = 32 servings

37.5 x 10(-6) in scientific notation?

Answers

3.75*10(-7)……...space fillers

2250 i just guessed i may know the anwser but just try 2250 i may be correct

Express the complex number in trigonometric form.

-5i

A) 5(cos 270° + i sin 270°)
B) 5(cos 180° + i sin 180°)
C) 5(cos 90° + i sin 90°)
D) 5(cos 0° + i sin 0°)

Answers

-5i can be written as 0 + (-5)i
It is in the form a+bi where a = 0 and b =-5
So the point (a,b) is (0,-5)

The distance from the origin to this point is 5 units, therefore r = 5. This is the magnitude.

The angle is 270 degrees as shown in the attached image. You start on the positive x axis and rotate until you reach the point (0,-5)

This is why the answer is choice A) 5(cos(270) + i*sin(270))

56. exercise. for natural numbers a and b, give a suitable definition for "least common multiple of a and b", denoted lcm(a, b). construct and compute some examples.

Answers

LCM(a, b) ≡ a×b/GCD(a, b)

LCM(6, 9) = 6*9/3 = 18 . . . . . . . (2 [ 3 ) 3] = 18 . . . ( ) product = 6; [ ] product = 9

LCM(2,5) = 2*5/1 = 10 . . . . . . . . (2 [ 1 ) 5 ] = 10

LCM(27, 45) = 27*45/9 = 135 . . (3 [ 9 ) 5] = 135

_____
In the above LCM products, the number in [ ) brackets is the GCD.

In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1,000? Really need this I'm giving you maximum points

Answers

The shipmentof 1000 is 1000/400 = 2.5 times as large as the shipment of 400, so 2.5 * 14 = 35 defective parts can be expected.

what fractions are equivalent to 8 over 12

Answers

4/6, 16/24, 2/3 are all equivalent to 8/12.

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