Katy invests £200 000 in a savings account for 4 years. The account pays compound interest
at a rate of 1.5 % per annum.
Calculate the total amount of interest Katy will get at the end of 4 years

Answer:

Step-by-step explanation:

The number of meals that Boris can feed his dog will be 50 meals.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Boris takes care of his canine with 3/5 pounds of canine nourishment for every dinner. Boris has quite recently purchased 30 pounds of canine food.

The number of meals that Boris can feed his dog will be calculated as,

⇒ 30 ÷ (3/5)

Simplify the expression, then we have

⇒ 30 ÷ (3/5)

⇒ 30 / (3/5)

⇒ 30 x 5 / 3

⇒ 10 x 5

⇒ 50

The number of feasts that Boris can take care of his canine will be 50 dinners.

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Answer:

Answer:

1.11111=111111100000

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

1.11111=1.111111

Multiply to remove 5 decimal places. Here, you multiply top and bottom by 105 = 100000

1.111111×100000100000=111111100000

Simplify the improper fraction,

=111111100000

In conclusion,

1.11111=111111100000

Step-by-step explanation:

The fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

To express the decimal 1.11111 as a fraction, we can use algebraic manipulation. Let's denote the repeating decimal as x:

x = 1.11111...

To eliminate the repeating part, we can multiply x by 10:

10x = 11.11111...

Now, we can subtract the original equation from the multiplied equation to eliminate the repeating part:

10x - x = 11.11111... - 1.11111...

Simplifying the equation:

9x = 10

Dividing both sides by 9:

x = 10/9

Therefore, the fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

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No, the sides of a triangle cannot have lengths 7, 15, and 20.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees.

No, the sides of a triangle cannot have lengths 7, 15, and 20.

This is because of the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

In this case, if we add the two smaller sides, 7 and 15, we get 22, which is less than the length of the longest side, 20. Therefore, it is impossible to form a triangle with these side lengths.

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The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.

We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.

The total distance that the student travelled can be obtained from;

5000 m + 5000 m + 5000 m

= 15000 m

The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds

= 5220 second

Speed = Distance/ Time

= 15000 m/5220 second

= 2.87 m/s

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Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

Answer:

  14

Step-by-step explanation:

Look for 10 in the f(x) column. This is the output value.

Find the corresponding value in the x-column. This is the input for that output value.

The input that corresponds to an output of 10 is x=14.

Answer:

the answer is (3, 6)

happy to help!

For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:To find the value of k such that 156k is a perfect square, we need to determine the factors of 156 and look for a common factor that can be squared to obtain a perfect square.

The prime factorization of 156 is \(2^2\) * 3 * 13. A perfect square must have an even exponent for each prime factor in its prime factorization. Thus, for 156k to be a perfect square, k must have an even exponent for each prime factor in the prime factorization of 156.

Analyzing the prime factorization, we can see that the exponent of 2 in 156 is 2, the exponent of 3 is 1, and the exponent of 13 is 1. To make each exponent even, we need to multiply 156 by another 2. Therefore, k should be equal to 2.

Let's verify this by calculating 156 * \(2^2:\)

156 * \(2^2\) = 156 * 4 = 624

624 is a perfect square since it can be expressed as \(24^2.\) Hence, the value of k that makes 156k a perfect square is 2.

In summary, the value of k that makes 156k a perfect square is 2.

Step-by-step explanation:

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The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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Answer:

Chen family used the sprinklers for 25 hours

Aoki family used the sprinklers for 40 hours

Step-by-step explanation:

Let C be the number of hours the Chen family used the sprinklers and let A be the number of hours the Aoki family used the sprinklers

Total hours used

=> C + A = 65 (1)

Total water usage for Chen family = 40C  (40 L per hour x no. hour)
Total water usage for Aoki family = 25C    (25 L per hour x no. hours)

Total used by both families = 2000 L

So
40C + 25A = 2000           (2)

Therefore we have two equations in 2 variables which can be solved simultaneously

Multiply (1) by 25:
==> 25C + 25A = 25 x 65
==> 25C + 25A = 1,625   (3)

Subtract (3) from (2) to eliminate the A term:
(2) - (3) ==>
40C + 25A - (25C + 25A ) = 2000 - 1625

40C + 25A - 25C - 25A = 375
40C - 25C = 375
15C = 375
C = 375/15

C = 25
So the Chen family used the sprinklers for 25 hours

Since C + A = 65
A = 65 - C
==> A = 65 - 25
A = 40
The Aoki family used the sprinklers for 40 hours

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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The image of A about O after 90 degrees rotation is C

Rotation refers to the movement of an object around an axis or center point.

In the problem, the rotation of A 90 degrees about O in the clockwise direction of rotation involves moving in the said direction to make the angle 90 degrees

In an octagon, each angle in the center is solved by

= 360 / 8

= 45

Hence each step in the clockwise rotation covers angle 45 degrees> In the figure from A to B is 45 degrees.

Moving from A to C in clockwise direction is equal to 90 degrees

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Answer:

20

Step-by-step explanation:

lol

The time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

For this case, we're provided that:

Let the time be 'T' years after which this investment becomes $2310

Then, by the formula stated above, we get:

\(A = P\left(1 +\dfrac{R}{100}\right)^T\\\\2310 = 920\left(1 +\dfrac{4.7}{100}\right)^T\\\\\\2310 = 920\times(1.047)^T\\\\(1.047)^T = \dfrac{2310}{920}\\\\\\T = \log_{1.047}\left( \dfrac{2310}{920} \right)\\\)

Using calculator, we get:

\(T \approx 20.0446 \approx 20 \: \rm years\) (as unit of time in rate of interest was assumed to be yearly)

Thus, the time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

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Answer:

8

Step-by-step explanation:

120/15

Answer:

Step-by-step explanation:

Danielle has :

Principal = $125

Time = 2 years

Rate = ?

Interest =

\(\frac{Principal \times Rate \times Time}{100}\)

Answer:

its D

Step-by-step explanation:

trust

Answer:

Just calculate

3×2×4 ÷ (2×5)

24÷10

=2.4

Step-by-step explanation:

work he in a department store

Answer:

Step-by-step explanation:

A productive approach to identifying a research topic and subsequent research question can involve utilizing multiple sources, including:

Literature review: Reviewing existing research in the field can help identify gaps in knowledge and areas that need further investigation.

Personal interests and experiences: Consider your own experiences, interests, and expertise to identify a topic that you are passionate about and can contribute to.

News articles and current events: Stay up-to-date on current events and identify topics that are relevant and pressing in your field.

Professional associations and organizations: These organizations often have conferences and publications that highlight current research trends and topics.

Government reports and data sources: These sources can provide data and information on a wide range of topics and can serve as a starting point for identifying a research question.

Ultimately, a combination of these sources can be useful in identifying a research topic and subsequent research question. It's important to consider the feasibility, importance, and originality of the research topic, and to choose a topic that you can research thoroughly and effectively.

5. The missing length = D. 91

6. The missing length = C. 5

7. The missing length = B. 121

8. The missing length = D. 30

Similar triangles are triangles that have the same shape but possibly different sizes. In other words, they have the same angles but different side lengths.

The corresponding sides of similar triangles are proportional to each other, meaning that if you were to multiply all the sides of one triangle by a certain factor, you would get the corresponding sides of the other triangle.

5. In order to find the missing length:

WU/FU = UV/UG  = 130/60 = UV/42

Cross-multiplying, we have:

60UV = 130 x 42

UV = 5 460/60 = 91.

6. To find the missing length, we have:

PQ/DE = PR/DF = PQ/20 = 10/40

Cross-multiplying, we have:

40PQ = 20 x 10

PQ = 200/40 = 5.

7.  To find the missing length, we have:

CE/EW = DE/EV = CE/55 = 110/50

Cross-multiplying, we have:

50CE = 110 x 55

CE = 6 050/50 = 121.

8.  To find the missing length, we have:

DE/LM = CE/LN = 42/36 = 35/LN

Cross-multiplying, we have:

42LN = 35 x 36 = 1 260

LN = 1 260/42 = 30.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

Answer:

cool

Step-by-step explanation:

Answer:

what?

Step-by-step explanation:

vfgchgcbgjvygfcb

Answer:

There are 12

Step-by-step explanation:

hope this helps.

answer-

577468-64753=57623546

the relationship between two expressions on opposite side of a sign expressed by an equation. It typically has one variable and an equal sign. for instance: 2x - 4 = 2.

Let's denote the cost of each pen as "p", and the cost of each file as "4p" (as per the given information).

(a) Let's assume that Rebecca had a total of "x" dollars. She spent 1/2 of her money on 8 files and 13 pens, so we can set up the following equation:

1/2 x = 8(4p) + 13p

1/2 x = 45p

x = 90p

After buying the 8 files and 13 pens, Rebecca had 1/2 of her money remaining. She then used 2/5 of her remaining money to buy more files. So, the amount of money she spent on additional files is:

(1/2)x - (2/5)(1/2)x = (3/10)x

We can substitute the value of x we found earlier to get:

(3/10)(90p) = 27p

Rebecca used this amount of money to buy more files. Since each file costs 4p, the number of additional files she bought is:

27p / (4p) = 6.75

Since we cannot buy fractional files, we round up to the nearest whole number. Therefore, Rebecca bought a total of:

8 + 7 = 15 files altogether

(b) We know that Rebecca spent $91.80 on all the files. We can set up the following equation to find the cost of each pen:

8(4p) + 13p + 15(4p) = 91.8

32p + 13p + 60p = 91.8

105p = 91.8

p = 0.87

Therefore, each pen costs $0.87.

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(a) Rebecca bought 24 files altogether.

(b) Each pen cost $1.80.

What is an equation?

An equation is a mathematical statement that uses an equal sign (=) to show that two expressions are equivalent. It can also be seen as a representation of a relationship between two or more variables or quantities.

Let's start by assigning variables to the unknowns:

Let's say the cost of each pen is x, then the cost of each file is 4x.

(a) Rebecca spent 1/2 of her money on 8 files and 13 pens, which means she spent the other half on more files. Therefore, the total number of files she bought is:

number of files = 8 + 2/5 * (1/2) = 8.8

Since she cannot buy a fraction of a file, we round up to the nearest integer, and we get that Rebecca bought 9 files altogether.

(b) We know that the total cost of all the files is $91.80. We can set up an equation:

Total cost of files = 9(4x) = 36x

36x = $91.80

x = $2.55

Therefore, each pen costs $2.55.

Hence,

(a) Rebecca bought 24 files altogether.

(b) Each pen cost $1.80.

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