Find the circumference of a circle with radius, r = 4.8m.
Give your answer rounded to 1 DP.

Answers please

The ladder will reach 24.27m far from the base of the wall.

The relationship between a right-angled triangle's three sides is described by Pythagoras' theorem, also referred to as the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the hypotenuse's square is equal to the sum of its two other sides' squares. The angles of a right-angled triangle are referred to as Pythagorean triplets.

The length of the wall can be determined by using the Pythagoras theorem.

c² = a² + b²

c = hypotenuse = ladder = 25ft

a = altitude = wall = ?

b = base = 6ft

Putting the values

25² = a² + 6²

625 - 36 =  a²

a² = 589

a = √589

a = 24.27m

Thus, the ladder will reach 24.27m far from the base of the wall.

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If the perimeter and area of the hexagon are $p$ and $a$, respectively, the value of $\frac{p^4}{a^2}$ is 192.

Regular hexagon has side length of 6

Perimeter of regular hexagon is given by 6*(side)

∴Perimeter = 6*(6) = 36

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

Area of Regular hexagon is composed of 6 equilateral triangles and is given by,

= 6* (1/2)*6² * √3/2

= 3√3/2 * 36

= 54√3

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

So fraction [tex]\frac{p^4}{a^2}[/tex] = [tex]\frac{36^4}{(54\sqrt{3})^2 } = \frac{36*36*36*36}{54*54*3}[/tex]  =192.

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The ratio of the area of circle A to the area of circle B expressed in the common fraction is 4/9.

An arc is a portion of the circumference of a circle. The length of an arc is proportional to the radius of the circle and the measure of the angle formed by the arc and the center of the circle. The formula for the length of an arc is:

Arc Length = (Angle Measure / 360) x (Circumference)

In this problem, we are given that the arc of 55 degrees on circle A has the same length as the arc of 40 degrees on circle B. So we can set up the following equation:

(55/360) x (Circumference of A) = (40/360) x (Circumference of B)

We can simplify this equation by canceling out the common factor of 360:

(5/12) x (Circumference of A) = (2/9) x (Circumference of B)

Now we can use the fact that the circumference of a circle is equal to 2π times the radius:

(5/12) x (2π x radius of A) = (2/9) x (2π x radius of B)

We can cross-multiply and divide by 2π to find the ratio of the radii of the two circles:

(5/12) x (radius of A) = (2/9) x (radius of B)

radius of A / radius of B = (2/9) / (5/12) = 12/18 = 2/3

Since the ratio of the areas of two circles is equal to the square of the ratio of their radii, the ratio of the area of circle A to the area of circle B is:

Area of A / Area of B = (radius of A / radius of B)^2 = (2/3)^2 = 4/9

So the ratio of the area of circle A to the area of circle B is 4/9.

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Properties of operations that can be used to decide whether or not expressions are equivalent is the use of commutative property of addition.

An equivalent expression is defined as the expression that gives the same value of result even though they look different.

One of the properties of operations that can be used to show whether or not expressions are equivalent is the use of commutative property of addition.

The commutative property of addition show that when the order of addends are changed, the result of the total summation doesn't change.

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The size of each exterior angle is given by β = 180° - θ.

To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first.

If the number of sides is n, then the sum of the interior angles is:

S = 180 (n-2)

This formula derives from the fact that if you draw diagonals from one vertex in the polygon, the number of triangles formed will be 2 less than the number of sides. Each triangle has 180°.

This form of the formula derives from drawing triangles in the polygon by drawing lines from a central point to each vertex. In this way the number of triangles is the same as the number of sides, but the angles at the centre are not required, so 360° is subtracted.

Once you have the sum of all the interior angles you divide by the number of sides to find the size of each interior angle.

Each interior angle of a regular polygon with n sides:

θ = 180°(n-2)/n

Each exterior angle of a regular polygon with n sides:

β = 180° - θ

Thus, the size of each exterior angle is given by β = 180° - θ.

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Answer:

8x+7

Step-by-step explanation:

The reason why I say this is because I subtracted 10x from 2x and then you get left with +7 so in conclusion I think the answer would be 8x+7

The smallest value of 'n' that can be obtained by adding three consecutive numbers is 48.

By using Monte-Carlo simulations,

A large class of computational techniques known as "Monte Carlo procedures" or "Monte Carlo experiments" rely on repeated random sampling to get numerical results. The core idea is to leverage randomness to find solutions to issues that, in theory, may be deterministic.

16    22    10     7    28    13     1    19    25     4

7    10    25    13     4    28    16     1    19    22

16    10    22     7    13    28     1    19    25    4

(remember that the numbers are arranged in a circle, rather than the straight line shown here)

The underline number represent the smallest value for n that can be obtained by the summation of three consecutive numbers.

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Using more than 30% amount of your available credit limit can have a negative impact on your credit score, so if you have a credit limit of $5,000 and only $100 left, you should be careful with your spending.

1. Determine total credit limit: $5,000

2. Determine remaining credit before limit is reached: $100

3. Calculate the percentage of the credit limit that has been used: $100/$5,000 = 0.02 = 2%

4. Determine if the percentage of credit limit used is more than 30%: 2% < 30%

5. Conclusion: Your credit score will be affected if you max out your credit limit.

Your credit score will be affected if you max out your credit limit, meaning if you reach or exceed your credit limit. To calculate this, you will need to determine the total credit limit, the remaining credit before the limit is reached, and then calculate the percentage of the credit limit that has been used. If the percentage of credit limit used is more than 30%, then your credit score will be negatively impacted.

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The constant of proportionality from h to j is 3.

What is a constant of proportionality?

The constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

Direct Variation: The equation for direct proportionality is y = kx,  which shows as x increases, y also increases at the same rate. Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x

Inverse Variation: The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example: The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x

In both cases, k is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as the unit rate.

Now

As j=h/3 for the given table or h=3j

that means h is in Direct Variation with j

having constant of proportionality = 3.

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Answer:

$14.25

Step-by-step explanation:

5% = 0.05

15 times 0.05 = $0.75

15 - 0.75 = $14.25

So, the sale price is $14.25

Answer:

$14.25

Step-by-step explanation:

5% = 0.05

15 times 0.05 = $0.75

15 - 0.75 = $14.25

So, the sale price is $14.25

Answer:ANSWER

The function is decreasing on the interval,

Step-by-step explanation:

To determine whether the function is decreasing or increasing, we trace the graph from left to right.

If the y-values are increasing as we move towards the right, then the function is increasing.

On the other hand, if the y-values are decreasing as we move towards the right, then the function is decreasing.

We can see from the graph that, the y-values decreases as we move from the left to the right.

Therefore, the function is decreasing for all real values of x.

The bankers have made $3,125 by investing the same amount of money

at the 2014 interest rate.

In year 2013,

250000 x 4.25/100 = $10625

In year 2014 with 5.5%,

250000 x 5.5/100 = $13750

So, 13750 - 10625 = $3125 more money were made comparing to that in 2013.

Investments are financial commitments made to acquire assets in the hopes that their value would rise over time. Investment necessitates the loss of a current resource, such as time, money, or effort.

In the world of finance, investing is done in order to profit from the asset being put to use. A gain (profit) or loss realized through the sale of a home or investment, unrealized capital gain (or loss), investment income like dividends, interest, or rental income, or a mix of capital gain and income may all be included in the return. The return may also include foreign exchange profits or losses as a result of shifting exchange rates.

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a) An equation for the circle with centre (0, 0) and point B(5,-12) at circumference is (x)² + (y)² = 13².

b) The point (8,10) lies outside of the circle.

What is equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

The points that lie on the circumference is B(5,-12).

The origin is O(0,0).

The distance from O to B is the radius.

OP² = (x2-x1)² + (y2-y1)²

OP² = (5-0)² + (-12-0)²

OP² = (5)² + (-12)²

OP² = 25 + 144

OP = √169

OP = 13

The radius is 13 units.

The standard equation of a circle is given by -

(x-h)² + (y-k)² = r²

Where (h,k) is the coordinates of center of the circle and r is the radius.

So, after substituting all the values the equation will be -

(x)² + (y)² = 13²

To find if (8,10) lies inside the circle or not, substitute x = 8 and y = 10

(8)² + (10)² = 13²

8 + 10 = 13

18 ≠ 13

Therefore, the (8,10) does not lie inside the circle.

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On solving the provided question, we can say that by unitary method for next 6 miles will charge  = 3*6 + 2*3 = $22

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

A delivery truck driver charges a fixed base price of = $6 for 2 miles

He charges an additional = $2 for every mile

so, for next 6 miles will charge  = 3*6 + 2*3 = $22

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The measure of side EF is 15.

The polygon that has three sides and three vertices is called a triangle.

When it comes to Euclidean geometry, two triangles are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be produced from the other more precisely by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.

Since the two triangles are equivalent, their corresponding sides are proportional. So we can write,

BC/EF = CD/FG

Given that, DC =8, BC=5, and FG =24. By substituting these values, we get

5/EF = 8/24

EF = (5*24)/8 = 15

Hence, the value of side EF is 15.

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The needed inequality is (6 X)   > (12 Y) .6 hens x 200 eggs per year = 1,200 eggs per year, or 23+ eggs per week.

According to the given data:

The number of eggs laid by first hen per week = 6 eggs

So, the number of eggs laid by first hen in X weeks

= (Eggs Laid per week) x  (X)   = 6 X

So, the first hen lays a total of (6 X) eggs in X weeks.

Similarly,

The number of eggs laid by second hen per week =  9 eggs

So, the number of eggs laid by second hen in Y weeks

= (Eggs Laid per week) x  (Y)   = 9 Y

So, the second hen lays a total of (9 Y) eggs in Y weeks.

As given:

The total number of eggs laid by the first hen >  The total number of eggs laid by the second hen.

⇒ (6 X)   > (9 Y)  

Hence, the needed inequality is (6 X)   > (9 Y) .

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We can rewrite g(x) = 6(2)ˣ⁺³ and y = 100(5)ˣ⁻² in the form y = a(b)ˣ as g(x) = 48(2)ˣ and y = 4(5)ˣ respectively

An exponential function is a mathematical function in which the input, or the variable, is raised to a power.

The most common form of an exponential function is f(x) = eˣ, where e is the base of the natural logarithm and x is the exponent.

In order rewrite g(x) = 6(2)ˣ⁺³ and y = 100(5)ˣ⁻² in the form y = a(b)ˣ, you need to apply your knowledge of indices.

g(x) = 6(2)ˣ⁺³ can be rewritten as:

g(x) = 6(2)ˣ⁺³

g(x) = 6(2)ˣ × 2³

g(x) = 6(2)ˣ × 8

g(x) = 48(2)ˣ

Also,  y = 100(5)ˣ⁻² can be rewritten as:

y = 100(5)ˣ⁻²

y = 100(5)ˣ × 5⁻²

y = 100(5)ˣ × (1/5²)

y = 100(5)ˣ × 1/25

y = 4(5)ˣ

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The exact value of the trigonometric cosine function cos 30° is √3/2.

In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. Using the unit circle, we can find the exact values of the trigonometric functions for angles in degrees or radians. One of the most important concepts in trigonometry is the unit circle.

A special triangle is a 30-60-90 triangle, where one angle is 30 degrees, another angle is 60 degrees, and the last angle is 90 degrees. The ratio of the adjacent side to the hypotenuse in this triangle is √3/2. Therefore, the exact value of cos 30° is √3/2. This means that the cosine of 30 degrees is the ratio of the adjacent side (x) to the hypotenuse (1) in the unit circle where x = √3/2.

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Answer:

Long division is a method of solving division problems by breaking them down into smaller steps. Here's how you can use long division to solve 110.5 / 13:

Write the problem as shown:

110.5 | 13

Divide the first digit of the dividend (110) by the divisor (13). This gives 8 with a remainder of 6. Write 8 above the dividend and the remainder (6) next to the dividend.

110.5 | 13

|- 8) 110

6

Bring down the next digit of the dividend (the digit after the decimal point) to get the new dividend. In this case, the new dividend is 0.5.

110.5 | 13

|- 8) 110

6.5

Divide the new dividend (6.5) by the divisor (13). This gives 0 with a remainder of 6.5

110.5 | 13

|- 8) 110

6.5

|- 0

6.5

You can see that 110.5 divided by 13 is 8 with a remainder of 6.5, so the quotient is 8 and the remainder is 6.5 .

110.5 / 13 = 8 remainder 6.5

Alternatively, you can express the remainder as a fraction, 110.5 / 13 = 8 + 6.5 / 13 = 8 + 0.5 = 8.5

The domain of the log function will match the range of the exponential function since g(x) = logb(x) is the inverse function of f(x), and vice versa. The range of g(x) = logb(x) is therefore (∞, ∞), while the domain is (0, ∞).

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

The domain of a function is the set of all input values (sometimes referred to as independent variables) for which the function is defined and produces an acceptable result (also called dependent variable). Most often, the domain is represented by a collection of numbers or a range of numbers.

The term "range" refers to the entire set of potential output values (dependent variable) that a function can produce for any set of valid input values inside its domain. Usually, a group of numbers or a range of numbers is used to represent the range.

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The highest common factor of 12, 18 and 24 is 6. This is because all three numbers can be divided by 6 without any remainder. Therefore, 6 is the greatest number that can divide all three numbers evenly.

The highest common factor (HCF) of 12, 18 and 24 is 6. This means that 6 is the largest number that can divide each of these numbers evenly without any remainder.

To find the highest common factor of any set of numbers, it is helpful to start by expressing each number as the product of its prime factors. For example, 12 can be expressed as 2 × 2 × 3, 18 can be expressed as 2 × 3 × 3, and 24 can be expressed as 2 × 2 × 2 × 3.

The HCF is the product of all prime factors shared by all of the given numbers. In this case, the common prime factors are 2 and 3, so the HCF is 2 × 3, or 6. This means that 6 is the greatest number that can divide all three numbers evenly.

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Answer:

For number 2 you need to multiply 3 and 4, dont add

remember when you multiply you add exponents

so your answer would be 12a^7

Step-by-step explanation:

The total savings on the men's clothing is not 60% to 65%

To determine if the total savings is 60% to 65%, we need to calculate the original price of the shirts given the final cost and the percentage of savings.

We start by calculating the original price of the shirts before the extra 50% off clearance:

Original = $11.06 / (1 - 0.60) = $27.65 i.e. 60% saved

$16.88 / (1 - 0.65) = $48.23 i.e. 65% saved

Now we need to find the price of the shirts before the extra 50% off clearance

$27.65 / (1-0.5) = $55.30

$48.23 / (1-0.5) = $96.46

The calculated prices of the shirts before the extra 50% off clearance are not between $29.50 to $45.00

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To create function h, function f was translated 2 units to the Left, translated 4 units down, and reflected at x = -2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given, The function fx= x³ has been transformed, resulting in function h.

h(x)=-(x+2)³-4

Since f(x) = x^3 is transformed to h(x) = -(x+2)³ -4, by

1. Adding 2 to x in x³ to give f'(x) = f(x + 2) = (x + 2)³.

2. We now translate f(x + 2) down by subtracting 4 from f(x + 2) to give

f''(x) = f'(x) - 4 = f(x +2) - 4 = (x + 2)³ - 4.

3. We now reflect f'(x) at x = -2 by multiplying (x + 2)³ by -1 to get

h(x) = -(x + 2)³ - 4.

Therefore, Function f was translated 2 units to the left, 4 units down, then reflected at x = -2 to generate function h.

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The figure for better understanding the situation Blue one is h and the red one is f:

[tex]$P(t)=\frac{19.71}{1+61.22 e^{-0.03513 t}}$[/tex]  can be used to simulate the population of New York state. where t is the number of years since 1800 and P is the population in millions.

A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. Between sample size and population, the population will always be larger in number. The entire group of individuals under study is referred to as the population.

250 persons, the size of the high school under study, make up the population in the case. The population mean can be computed by dividing the sum of all values in the given data/population by the total number of values in the given data/population. We can refer to the total of a set of numbers as a sum. A symbol that represents the population mean is  μ.

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The total volume of ice that the tray can make at one time is 201 cubic centimeters.

Volume is defined as the space covered by any solid body in the three-dimensional plane. For semicircle the parameter is radius and for cylinder, the parameters are height and radius.

Given that,

Each sphere of ice has a radius of 2 cm

One tray makes 6 spheres

The total volume of each sphere is 33.51 cm³

The tray can hold 6 of these at a time

The volume will be calculated as:-

Volume = 33.5 x  6

Volume = 201 cubic centimeters

Hence, 201 cm³ is the total volume of ice that the tray can make at one time.

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The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the functions is given below.

Equation  1: f(x) = 2x³ + 24x + 2

Equation 2: f(x) = 4ˣ

The graph of the functions is given below.

From the graph, the intersection of the graph is at (-0.044, 0.9407).

The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

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