Archive invested an amount of money in a savings account that pays compound interest at a rate of 6% per annum. After 11 years there is £13,288.09 in the savings account (rounded to the nearest 1p). How much did Archive initially invest?

G(2, -6) is reflected in the line y=-2, the image is located at G' is (2, 2).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, G(2, -6) is reflected in the line y=-2.

Since y=-2 is a horizontal line, the reflection will be vertical

So (2,-6) will reflect down 6 spaces vertically.

-6 + (4×2) = (-6 + 8) = 2  

Therefore, when we establish 4 below the line we just apply ×2 as a double as its across the line each side of the line to find that below the line = 4 = 4×2 and add it to -6

Therefore, G(2, -6) is reflected in the line y=-2, the image is located at G' is (2, 2).

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No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.

Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:

SS = Σ (X - μ)^2

Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:

Variance = SS / (n - 1)

Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:

Standard deviation = √Variance

Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.

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The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

Given that;

Nelly owns farm land that has an area of 4.2 × 10² acres. Each year, the farm produces 6.72 × 10⁴ bushels of corn.

Hence, The average amount of corn produced per acre is,

⇒ 6.72 × 10⁴ ÷ 4.2 × 10²

⇒ 6.72 × 10⁴ / 4.2 × 10²

⇒ 1.6 × 10²

Thus, The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.

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Malik's mixed number is not correct and he needs to revise it to match the correct answer of 3 3/5.

A mixed number is a combination of a whole number and a fraction. It is written as a whole number followed by a fraction.

In Malik's case, the answer he found was 3 3/5, which means three and three fifths. However, he wrote the answer as 6 3/5, which means six and three fifths.

When adding a whole number and a fraction, the final result must still be a mixed number, with the whole number part representing the sum of the whole numbers and the fraction part representing the sum of the fractions.

In this case, adding 3 and 3/5 does not result in 6 and 3/5. To see this, we need to simplify the fractional part.

Dividing 5 by 5 gives us 1, so the fractional part of 3 3/5 is 1 3/5.

Adding 3 to the whole number part and 1 3/5 to the fractional part, we get 4 1/5, not 6 3/5.

Complete Question:

Malik solved a problem that had an answer of 3 3/5. He wrote his answer as the mixed number 6 3/5. Is his mixed number correct? Explain

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Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.

An algebraic progression is when there is a continual difference between terms that follow each other in an series. For illustration, the decimal number 5, 7, 9, 11, 13, and 15 is an example of an algebraic expression with a tolerance of two. A advance with a set tolerance among any two consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of algebraic progression are plausible: series in mathematics with a finite length A finite geometric evolution is a series with just a finite number of terms. The early, late, allowance, and frequency of terms may all be calculated using the terms in the series.

given

a1 = 3

a2 = 5 * 3 + 1 = 16

a3 = 5 * 16 + 1  = 81

a4 = 5* 81 + 1 = 406

a5 = 5* 406 + 1 = 2031

Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.

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Answer: 5

Step-by-step explanation:

Using order of operations, you multiply 1 and 3 first to get 3. Then you add 1 to it to get 4. Then add 4 to get 8 and subtract 3 to get 5.

Answer: 5

To solve this equation we must do PEMDAS.

Parentheses, Exponents, Multiply, Divide, Addition, Subtract.

There is no Paratheses, or Expenonets so first we divide 1 by 3.

Our equation would now be

1+3+4-3.

Next we Divide, once again there is no division so we move on to addition. The firs thing we add is 1+3, which is 4. Then 4 plus 4 which 8.

Our eqatuion would now be

8-3

Lastly we subtract 8-3 is 5

This means our answer is 5.

I hope this helps & Good Luck <3!!!

The volume of cuboid with dimensions 9cm × 4cm × 5cm is 180 cm³

We know that the formula for the volume of the cuboid is:

V = l × w × h

where, V is the volume of the cuboid

l is the length of the cuboid

w is the  width of the cuboid

and h is the height of the cuboid

Here, the length of the cuboid is l = 9 cm,

the width of the cuboid is w = 4 cm

and the height of the cuboid is h = 5 cm

Using above formula,

V = l × w × h

V = 9 × 4 × 5

V = 180 cubic cm

Therefore, the required volume is 180 cubic centimeters

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The solution to the perimeter is 6.4 feet

From the question, we have the following parameters that can be used in our computation:

Side length = 1.6 ft

Shape = Square

Using the above as a guide, we have the following:

Perimeter = 4 * Side length

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 4 * 1.6 ft

Evaluate

Perimeter = 6.4 ft

Hence, the perimeter is 6.4 ft

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Complete question

2) Determine the perimeter of a square with side length 1.6 ft

what is the answer​

According to the information, it can be inferred that the F bacterium had a greater growth over time. Additionally, the population of G si will exceed the population of F because it has an x exponent.

The functions express the relationship between the number of bacteria and time. In accordance with the above, the function of the bacterium A, expresses that the number of bacteria grows 36 individuals every hour.

On the other hand, the function of B expresses that the individuals grow exponentially in 3. According to the above, at some point the exponent of 3 will be so great that it will be able to exceed the number of individuals of A. (not in the first four hours).

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The nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

Given that, an arithmetic sequence has a common difference of 125,000. A geometric sequence has a common ratio of 4. In both sequences, a(1) = 10.  We asked to compare the sequences,

The formula for AP =

aₙ = a + (n-1)d, d = common difference, a = first term, n = number of terms and aₙ = nth term

The formula for GP =

aₙ = arⁿ⁻¹, r = common ratio, a = first term, n = number of terms and aₙ = nth term

The common difference and first term are, 125000 and 10 respectively,

aₙ = 10 + (n-1)125000

aₙ = 10+1245000n-125000

aₙ = 125000n - 124990

Therefore, nth term in the given AP is given by aₙ = 125000n - 124990

The common ratio and the first term are, 4 and 10 respectively,

aₙ = 10×4ⁿ⁻¹

aₙ = 10×4ⁿ / 4

aₙ = 5×4ⁿ/2

Therefore, nth term in the given GP is given by aₙ = 5×4ⁿ/2

In the AP, nth term will be multiplied to 125000 and the product will be subtracted from 124990, and GP nth term will increase by product of 2.5 and 4ⁿ,

Hence, the nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2

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Answer:

Graph of polynomial of 2nd degree,i.e,X^2

Step-by-step explanation:

We can solve the inequality |8x - 7| < 9 to get the compound inequality:

-1/4 < x < 2

Here we have an absolute value inequality:

|8x - 7| < 9

The absolute value part can be "broken" into two parts, these are:

(8x - 7) < 9

(8x - 7) > -9

Now we need to solve these two.

The first one gives:

8x - 7 < 9

8x < 9 + 7

8x < 16

x < 16/8

x < 2

The other gives:

(8x - 7) > -9

8x > -9 + 7

8x > -2

x > -2/8

x > -1/4

Then we have the compound inequality:

-1/4 < x < 2

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Step-by-step explanation:

To determine the missing values in the Venn diagram, we can use the information from the problem to set up a system of equations. Let's assign variables to each section of the diagram:

X = number of students who play tennis only

Y = number of students who play soccer only

Z = number of students who play volleyball only

W = number of students who play tennis and soccer only

y = number of students who play tennis and volleyball only

Using the information from the problem, we can set up the following equations:

X + W + 3 = 21 (21 students play tennis)

Y + W + 4 = 16 (16 students play soccer)

Z + y + 5 = 19 (19 students play volleyball)

W + 3 = 3 (3 students play soccer and tennis)

y + 5 = 5 (5 students play volleyball and tennis)

Solving for one variable in terms of the others, we can substitute into the other equations:

X = 21 - W - 3

Y = 16 - W - 4

Z = 19 - y - 5

Substituting into the equation for W, we find:

W + 3 = 3

W = 0

Substituting W = 0 into the equations for X and Y:

X = 21 - 0 - 3 = 18

Y = 16 - 0 - 4 = 12

Finally, we can substitute X, Y, and W into the equation for Z to find:

Z = 19 - y - 5

Z = 19 - 5 - 5 = 9

So the missing values in the Venn diagram are:

Soccer: 12 students

Volleyball: 9 students

Tennis: 18 students

Soccer & Tennis: 0 students

Volleyball & Tennis: 5 students

Volleyball & Soccer: 4 students

Note that the number of students who play none of the three sports is not explicitly stated in the problem, but it can be calculated as:

13 = total number of students - (X + Y + Z + W + y)

13 = total number of students - (18 + 12 + 9 + 0 + 5)

13 = total number of students - 44

So there are 57 total middle school students

Answer:

*diameter=radius ×2

6cm×2=12cm

*diameter=10 ×2=30cm

*radius=diameter÷2

140cm÷2=70cm

*radius

250cm÷2=125cm

*diameter

2.5m×2=5m

*radius

3.6m÷2=1.8m

Answer:

44%

Step-by-step explanation:

33 first-year teachers

42 experienced teachers

What %  of the teachers in the meeting were Trst-year teachers?

33/(33+42)= 44%

The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%

To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.

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Answer:

Step-by-step explanation:

[tex]5\frac{1}{2}=\frac{11}{2}\\\mathrm{So\:this\:becomes}\\2x-\frac{1}{2}=\frac{11}{2}\\\mathrm{Then,}\\(2x+\frac{-1}{2})+\frac{1}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{(-1+1)}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{0}{2}=(\frac{11}{2})+\frac{1}{2}\\\mathrm{Reduce}\\2x+0=(\frac{11}{2})+\frac{1}{2}\\2x=(\frac{11}{2})+\frac{1}{2}\\2x=\frac{(11+1)}{2}\\\mathrm{11+1=12,\:so}\\2x=\frac{12}{2}\\\mathrm{Prime-factorization}\\2x=\frac{(6\times 2)}{(1\times 2)}[/tex]

[tex]\mathrm{6\times2=12\:and\:1\times2=2\:so\:\frac{12}{2}\:equals\:6,}\\2x=6\\\mathrm{Now,\:divide\:by\:the\:leading\:term,\:2}\\\frac{(2x)}{2}=\frac{6}{2}\\\mathrm{Factorization}\\x=\frac{(3\times 2)}{(1\times 2)}\\\mathrm{3\times2=6\:and\:1\times2=2\:so\:\frac{6}{2}\:equals\:3,}\\x=3[/tex]

Hope this helps.

The solution to the equation 2x - 1/2 = 5 1/2 is x = 3.

Given Equation: 2x - 1/2 = 5 1/2

Step 1: Let's simplify the mixed number 5 1/2 to an improper fraction. 5 1/2 can be written as (11/2).

2x - 1/2 = 11/2

Step 2: To eliminate the fraction, multiply the entire equation by 2 to clear the denominators:

2  (2x - 1/2) = 2 (11/2)

This simplifies to:

4x - 1 = 11

Step 3: Add 1 to both sides of the equation to isolate the variable:

4x - 1 + 1 = 11 + 1

4x = 12

Step 4: Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 12/4

x = 3

Therefore, the solution is x = 3.

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The probability of winning a prize worth more than the price of playing the game is 38%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that the percentage of the winning price is:-

Toy = 25%

Soda = 25%

Candy = 37%

Mega win = 13%

The probability of winning a prize worth more than the price of playing the game is calculated as:-

P = ( 25 + 13 ) x 100 / 100

P = 0.38 x 100

P = 38%

Therefore, the probability will be 38%.

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The width of the rectangle is 7.2 cm because if you divide 93.6 cm by 13 cm you will get 7.2 cm.

Brainliest please that would be nice of you(:

Answer:

x = 48.6°

Step-by-step explanation:

see photo for explanation

Answer:

Step-by-step explanation:

[tex]y=\left \{ {({1/2)x+6, x > 4} \atop {6x,} x\geq 1} \right.[/tex]

Table A of conditional percentages answers the question of whether the region where one lives affects whether or not one has health insurance.

Table A is the appropriate table of conditional percentages to discover if one's region of residence influences if they have health insurance.

Table A provides the overall percentage of individuals who are insured and uninsured in each region of the country. It gives a clear picture of the proportion of people in each region who have health insurance coverage. The data in this table allows us to compare the percentage of uninsured individuals across different regions.

In contrast, Table B provides the percentage of uninsured individuals among the total number of insured and uninsured individuals in each region. This type of table does not give us a clear understanding of the overall proportion of insured and uninsured individuals in each region.

Table C provides the percentage of uninsured individuals among the total population in each region. However, it does not provide a clear picture of the proportion of insured individuals in each region, which is crucial information to determine if the region where one lives affects whether or not one has health insurance.

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Complete Question: Table image has been uploaded.

The equation be x²(x + y)³ - 2xy²(x + y)² then the factorization be x(x + y)²(x - y)(x + 2y).

In mathematics, the term "factorization" or "factoring" refers to the splitting apart or "factoring" of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together yield the original number, matrix, etc.

Factoring is a useful skill in real life. Examples of typical uses include splitting something into equal portions, exchanging money, comparing costs, understanding time, and performing calculations while traveling.

Let the equation be x²(x + y)³ - 2xy²(x + y)²

Factor out common term [tex]$x(x+y)^2= x(x+y)^2\left(x(x+y)-2 y^2\right)$[/tex]

[tex]$=x(x+y)^2\left(x(x+y)-2 y^2\right)$$[/tex]

Expand [tex]$x(x+y)-2 y^2= x^2+x y-2 y^2$[/tex]

simplifying the above equation, we get

[tex]$=x(x+y)^2\left(x^2+x y-2 y^2\right)$$[/tex]

Factor [tex]$x^2+x y-2 y^2=(x-y)(x+2 y)$[/tex]

= x(x + y)²(x - y)(x + 2y)

Therefore, the factorization be x(x + y)²(x - y)(x + 2y).

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Answer:

Let's call the two numbers x and 5x. We know that their difference is 1016:

5x - x = 1016

Expanding and solving for x:

4x = 1016

x = 254

So, the two numbers are 254 and 5 * 254 = 1270. These are the two numbers that have a difference of 1016 and satisfy the given condition.

Step-by-step explanation:

Answer:

1+5x=1016

Step-by-step explanation:

The given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².

Given is the expression as -

[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]

The given expression is -

[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]

We can solve further as -

{(x² - xy)/9y²} x {3y/2x}

{x(x - y)/9y²} x {3y/2x}

(x - y)/18y²

Therefore, the given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².

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The inequality equations of each an one described briefly with graphs.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. The characters >, < , ≥ , or ≤ are used to denote an inequality, when the two expressions aren't always equal.

1.

y > 3x - 17

y ≤ - 4x + 11

The graph of the above inequality equations shown below:

2.

4x + 4y > - 40

-5x + 5y < 10

The graph of the above inequality equations shown below:

3.

x + 3y ≥ 31

4x - 2y > -2

The graph of the above inequality equations shown below:

4.

5x + y < 3

5x + y > 37

The graph of the above inequality equations shown below:

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The inverse function of g(x) is:

f(x) =  (x - 2)^(2/3) + 3

Two functions are inverses if their composition is equal to the identity, then if f(x) is the inverse of our function, we must have that:

g( f(x) ) = x

Here we know that:

g(x) = (x - 3)^(3/2) + 2

Evaluating this in f(x) we should get:

g( f(x) = (f(x) - 3)^(3/2) + 2  = x

Now we can solve that for f(x).

(f(x) - 3)^(3/2) + 2  = x

( (f(x) - 3)^(3/2) =  x - 2

f(x) - 3 = (x - 2)^(2/3)

f(x) =  (x - 2)^(2/3) + 3

That is the inverse function.

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Answer:

two plus two equals five

Step-by-step explanation:

On solving the provided question, we can say that the equation, we have is [tex]t^2 +5t +6.[/tex]

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.

the equation, we have is V = P/I

[tex]V = \frac{t^3 +9t^2 +26t +24}{t + 4}[/tex]

on dividing

the answer will be [tex]x^3+9x^2+26x +24=t^2 + 5t + 6[/tex]

x = -4

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See the attached image for the plotted graph

The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

4x -4y = 24

x - y= 6

y= x-6

Slope= 1, pass through (6,0), (0, -6)

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