A bank account starts with a balance of £8000 and pays compound interest of 5% per year. Work out the balance of the account after 1 year and after 2 years.

Six pounds is the cost of both shipping companies the same.

An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign.

An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.

company A:

shipping fee is  12 and $1.50 per pound

Let p be the variable  for the pounds of the package.

Liner Equation :

shipping fee = [tex]12+ 1.5p[/tex]

For company B :

shipping fee = 15 + p

if the cost of both shipping companies the same then,

12+1.5p = 15+p

ie. P = 6.

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Answer:

96%

Step-by-step explanation:

48 ÷ 50 × 100

Ignacio should use 3 fish tanks, number of guppies in each tank is 4, number of mollies in each tank is 3 and number of swordtails in each tank is 5.

The largest positive integer that divides each of the two or more integers is referred to as the greatest common divisor. The greatest common divisor of two integers x and y is shown by the symbol gcd (x, y).

Ignacio purchases 15 swordtails, 12 guppies, and 9 mollies.

He desires to divide the fish across several tanks and to place an equal number of each variety of fish in each tank.

The gcd of 12,9 and 15 will be used for the number of fish tanks.

Factors of the numbers are

12= 2x 2 x 3

9=3 x 3

15= 5 x 3

The common factor among all the numbers is 3.

The gcd of 12, 9, and 15 is therefore 3. Ignacio must therefore utilize three fish tanks.

Each type of fish in each tank is,

number of fish of each kind/ gcd(12,9,15)

Number of guppies in each tank= 12/3=4

Number of mollies in each tank= 9/3=3

Number of swordtails in each tank= 15/3=5

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The candy bar A contains 261 calories and candy bar B contains 254 amount of calories.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let candy bar A contains 'x' calories and candy bar B contains 'y' amount of calories.

Then by using the given data, we can prepare the equations as

                    x + 2y = 769 -----(I)

                  2x + y = 776 -------(II)

 Multiplying equation (II) by '2' and then taking subtraction, we get

                     -3x = -783

                        x = 261

Now put x = 261 in equation (I), we get

            261 + 2y = 769

                   2y = 508

                     y = 254.

Hence, the candy bar A contains 261 calories and candy bar B contains 254 amount of calories.

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The statement that could be true for function g is g(-13) = 20

The correct answer is an option (C)

In this question we have been given a function g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

Also, g(0) = -2

g(-9) = 6,

We need to select the statement that could be true for g.

A. g(0) = 2

As we have been given g(0) = -2, above statement is false.

B. g(-4) = -11

the range of function is  -5 ≤ g(x) ≤ 45 but -11 < -5

this means, above statement is false.

C. g(-13) = 20

here the values of x and g(x) fall within given intervals of domain and range

so, this statement is true.

D. g(7) = -1

since the domain of g is -20 ≤ x ≤ 5 but here x has value 7 which is false.

Therefore, the statement that could be true for function g is g(-13) = 20

The correct answer is an option (C)

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The solution to the system of equations y=-5x+3 and y=1 is given by coordinates  (x,y)=(0.4,1)

Define the system of equations ?

System of equations, or simultaneous equations, in algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

What is a subsitution method ?

The substitution method is the algebraic method to solve simultaneous linear equations.

Given:

y=-5x+3

and

y=1

On subsituting y=1 ,we get

⇒[tex]y=-5x+3[/tex]

⇒[tex]1 = -5x+3[/tex]

⇒[tex](1-3)=(-5)x[/tex]

⇒[tex]-2=-5x[/tex]

⇒[tex]2=5x[/tex]

⇒[tex]5x=2[/tex]

⇒[tex]x=\frac{2}{5} =0.4[/tex]

Hence ,x=0.4 and y=1

So, the coordinates of (x,y) are (0.4,1)

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There were total 11 birds and 7 cats on Thursday.

Make the cats = 'x'

and the birds = 'y'

x + y = 18.......(1)

500x + 650y = 10000......(20

Multiply (1) by 50

500x + 500y = 9000.....(1)

500x + 650y = 10050.....(2)

Subtract (2) from (1)

.......150y = 1050

y = 1050/150

y=7

Substitute y =7 into (1)

x + 7 = 18.......(1)

x = 18 - 7

x = 11

11 birds and 7 cats were in on Thursday.

Hence we get the required answer.

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The measure of angle h is  19° angle measure of angle c is 132°

In this question, we need to find the value of h and c.

We can observe that the opposite angle to angle (h + g) measures 48 degrees.

So, angle (h + g) = 48°                ..........(1)

We know that sum of linear angles is 180°

So, 151° + e = 180°

e = 180 - 151

e = 29°

As angle d and angle e are opposite angles, angle d = 29°

Consider given parallel lines and a transversal passing through points a and f

then angle g and angle d are alternate interior angles.

So, angle g = angle d = 29°

from (1),

∠h + ∠g = 48°

∠h = 48° - 29°

∠h = 19°

Consider a triangle with angles h, c and d.

∠h + ∠c + ∠d = 180°

19° + ∠c + 29° = 180°

∠c = 180° - (19 + 29)°

∠c = 132°

Therefore, the measure of angle h is  19° angle measure of angle c is 132°

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The steps for using a compass and straightedge to construct a square is:

Given:

Let AB the length of one side given.

Steps:

a. Using your straightedge, draw a reference line, if one is not provided.

b. Copy the side of the square onto the reference line, starting at a point labeled A'.

c. Construct a perpendicular at point B' to the line through [tex]AB[/tex].

d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.

e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.

f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.

g. Connect points A' to D, D to C, and C to B' to form a square.

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The value of the y-coordinate as calculated from the equation 10+10y=-20 is -3

The given equation is  10+10y=-20

We will solve this linear equation by taking the y coordinate of the function.

Subtracting 10 from both sides of the equation:

or ,10+10y -10 = -20 -10

or, 10y = -30

Dividing both sides by 10 we get:

or, 10y ÷10  = -30 ÷ 10

or, y = -3

In mathematical formulas, the equals sign is used to indicate that two expressions are equal. It's possible that the definitions of words like "equation" or their cognates vary slightly between languages. For instance, an equation is defined as having one or more variables, whereas an equation is any well-formed formula that consists of two expressions connected by the equals sign.

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There are 132 different ways  this is possible(given situation).

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

let[tex]$AB, BJ$, and $AJ$[/tex] denote a song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), respectively. Similarly, let[tex]$A, B, J,$ and $N$[/tex] denote a song that is liked by only Amy, only Beth, only Jo, and none of them, respectively. Since we know that there is at least[tex]$1\: AB, BJ$, and $AJ$[/tex], they must be[tex]$3$[/tex] songs out of the [tex]$4$[/tex] that Amy, Beth, and Jo listened to. The fourth song can be of any type

[tex]$N, A, B, J, AB, BJ$, and $AJ$ (there is no $ABJ$[/tex]

because no song is liked by all three, as stated in the problem.) Therefore, we must find the number of ways to rearrangeand a song [tex]$AB, BJ, AJ$,[/tex]from the se[tex]t $\{N, A, B, J, AB, BJ, AJ\}$.[/tex]

Case 1: Fourth song =[tex]$N, A, B, J$[/tex]

Note that in Case 1, all four of the choices for the fourth song are different from the first three songs.

Number of ways to rearrange =[tex]$(4!)$[/tex] rearrangements for each choice[tex]$*\: 4$ choices = $96$.[/tex]

Case 2: Fourth song =[tex]$AB, BJ, AJ$\\[/tex]

Note that in Case 2 all three of the choices for the fourth song repeat somewhere in the first three songs.

Number of ways to rearrange = [tex]$(4!/2!)$[/tex]rearrangements for each choice [tex]$*\: 3$ choices = $36$.[/tex]

[tex]$96 + 36 = \boxed{\textbf{(B)} \: 132}$.[/tex]

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The surface area of the regular pyramid is 131.15 cm.

The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The whole area of the surface of the specified solid item is referred to as surface area. We should add the areas of the surfaces to determine the object's surface area because the faces of three-dimensional objects are essentially 2D shapes.

Given,

Surface area = 1/2(a× b) + 3/2(b ×s)

Where b is a pyramid's side, a is a triangle's base height, and s is a pyramid's slant height.

Side = 6.1

Base = 7

Slant height = 12

Equating in formula:

1/2(6.1 × 7) + 3/2(6.1 × 12)

1/2(42.7) + 3/2(73.2)

21.35 + 109.8

131.15

The surface area of the regular pyramid is 131.15 cm.

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Answer:

35

Step-by-step explanation:

if x/y is 70

then x/2y is half 70

so it's. 70÷2

x/2y=35

The value for x/2y is 1/140.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

x/y= 70

So, for x/2y we have multiply the quantity y by 2.

Then x/2y= 1/70 x 1/2

x/2y = 1/140

Hence, the value for x/2y is 1/140.

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According to the division methods, the quotient is 2037 and the remainder is 433.

Division method:

Division is the method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.

There are four parts in the division operation. They are quotient, remainder, divisor and the dividend.

Given,

Here we have the expression 998563÷73.

Now, we have to divide the numbers and then we have to find the quotient and the remainder for the numbers.

In order to do the division, we have to perform the following steps,

Based on these steps we have divided the given number, then we get the quotient as 2037 and the remainder as 433.

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A road's grade can be thought of as its slope. In the US, grades are frequently reported as percentages by dividing the result by 100. (slope). A road with a rise of 950 feet over three miles is roughly 3% grade.

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Slope is usually represented with the letter m; the rationale for this is unclear, although O'Brien (1844) stated the equation for a straight line as "y = mx + b," which is the first recorded use of the letter in English. It was also written as "y = mx + c" by Todhunter in 1888. The ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line is used to calculate slope.

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The sum of the measures of the interior angles of a convex 27-gon is 4,500°.

The angles located inside a polygon are referred to as its interior angles. The number of interior angles in a polygon is equal to the number of sides.

According to the polygon sum formula, the internal angles of any n-polygon add up to (n - 2)x180°.

=(27-2)×180°

=25×180°

=4,500°

Each side of a regular convex polygon must be the same length, and all interior angles must be equal and less than 180 degrees.

Therefore, the sum of the measures of the interior angles of a convex 27-gon is [tex]4500^{\circ}[/tex].

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The average of the positive numbers from 1 to 100= 50.5

According to our question-

the median of all positive values between 1 and 100.

Since there are 100 whole numbers in this range, we know that adding up all of the whole numbers in this range equals 5050.

The sum of all whole numbers from 1 to 100 divided by 100 is the average of all whole numbers from 1 to 100.

Hence, 50.5 is the average of all whole numbers between 1 and 100.

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It will take 18 years to reach an amount of $ 27200

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = PRT / 100

where P = Principal

R = rate of interest

T = time period

Given data ,

The principal amount = $ 8400

Interest rate = 6.75 %

                    = 0.0675

Let the time period be = n

The Amount in n years = $ 27200

Now ,

The Amount is calculated by the formula ,

A = P ( R+1 )ⁿ

where n = time period

Substituting the values of A , P , and R , we get

27200 = 8400 x ( 1.0675 )ⁿ

Dividing by 8400 on both sides , we get

( 1.0675 )ⁿ = 68 / 21

Taking logarithm on both sides , we get

[tex]n=log_{1. 0625} \frac{68}{21}[/tex]

On solving the equation , we get

n ≈ 18 years

Hence , it will take 18 years to reach an account value of $ 27200

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============================================================

Explanation:

If his father saves 18%, then he pays the remaining 82% since 100-18 = 82.

The 82% then converts to 0.82 which is one of the multipliers we'll use to get the answer.

The other multiplier is 1.10 to represent an increase of 10%

The net multiplier is 0.82*1.10 = 0.902

Therefore, his father pays 0.902*60 = 54.12 dollars after the discount and maintenance fee are applied.

The pair of ratios that will make a proportion include:

A. 1/3 and 12/36

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.

In this case, it should be noted that 12 over 36 can be reduced to the lowest term. This will be:

12 / 36

= 1/3

Therefore, the correct option is A.

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The percentage of the purchase price of the sale tax is 8%

Given that,

Ahmed bought a telescope to look at the star. The final purchase price, which included the $10. 28 sales tax, was $128. 50.

To find :  The sale tax's share of the purchase price

Let PP = $128

Sales Tax = $10.28

To calculate the percentage :

Divide the Tax with purchased price and multiply with 100

By doing so we have ,

10.28/128 = 0.080 * 100 = 8%

Therefore, The percentage of the purchase price of the sale tax is 8%

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Subtraction Property of Equality

Properties of equality can help manipulate literal equations to solve for specific variables.

Subtraction Property of Equality

The subtraction PoE states:

This means if an equivalent quality is subtracted from both sides of an equation, then the equation is still true. In the equation above, 3x is subtracted from both sides of the equation. The subtraction PoE tells us that we are allowed to do this and maintain equality.

Other Properties of Equality

There is a multitude of PoEs including Addition, Multiplication, and Division. All of the properties also state that if an equal operation is done on both sides of an equation, then it is still equal. So, the subtraction PoE applies to all operations. There are also other properties of equality like Reflexive and Transitive that also help to solve literal equations.

The value of x is 25 will make ΔONM similar to ΔSRQ  by the SAS similarity theorem.

Given:

∠ONM is similar to ∠SRQ

From the figure

NM = 10

SR = 20

NO = 8

QR = x

SAS Similarity Theorem:

if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Both the triangles are similar by SAS if

NO/NM = SR/QR

substitute the values

8/10 = 20/x

cross multiplication

8x = 200

dividing both sides by 8

x = 25

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The percent of women who spend less than R190 is  0.93 .

In the question ,

it is given that ,

A survey was conducted by National Retail Federation .

the average that a women spends = R146

So , μ = 146 .

The standard deviation is R29.44  .

So , σ = 29.44

we need to find the percent of women who spend less than R190 ,

that is

P(x < 190) = P(Z < (x-μ)/σ)

= P(Z < (190-146)/29.44)

= P(Z < 44/29.44)

= P(Z < 1.49457)

By using the "Standard Normal Distribution" table ,

we get

P(x<190) = 0.93

Therefore , The percent of women who spend less than R190 is  0.93 .

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Answer:

Step-by-step explanation:

Using the Sales tax rate formula ,

The sales tax rate of an item is 8% (in percentage).

Sales tax : Sales Tax is defined as a tax on the sale, transfer, or exchange of a taxable item or service. Sales tax generally applies on the sale to the end user or ultimate consumer. Sales tax is generally added to the sales price and is charged to the purchaser.

formula :

When written out, the equation,

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate

We have given that,

An item cost price before tax = $460

sales tax = $36.80

we have to calculate sales tax rate in percentage form .

Using the above formula of sales tax rate,

Sales tax rate= sales tax /list price

=> Sales tax rate =$36.80/$460

=> Sales tax rate = $0.08

=>Sales tax rate = 8%

Hence, sales tax rate is 8% .

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Answer:

(10x - 2)° = 180°

Step-by-step explanation:

Since the sum of a triangle is always 180°,

∴ (5x - 5)° + (3x + 3)° + (5x)° = 180°

           5x - 5 + 3x + 3 + 5x = 180

                             ∴ 10x - 2 = 180

Answer:

13x - 2

Step-by-step explanation:

(5x - 5) + (3x + 3) + (5x)

5x - 5 + 3x + 3 + 5x

5x + 3x + 5x - 5 + 3

13x - 2

Answer: π * (18/2)^2

= 3.14 * 81

= 254.34 inches

Step-by-step explanation:

Formula of circle's area: πr^2, or 3.14 * radius to the power of 2

Since the radius is diameter divided by 2, the radius is 9

So, we can do 3.14 * 9 to the power of 2, which is 81.

So the formula is 3.14 * 81, and 254.32 inches.