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a) A designer has a circular tablecloth with radius 0.5 m. He wants to sew a fringe around the cloth. The fringe is sold by the tenth of a meter.


(i) What length of fringe is needed?



(ii) One meter of fringe costs $4.70. How much will the fringe cost?



b) A semicircular mat has a diameter of 18 m. What is the area of the mat?

Answer is 3h after simplification.

Function is a mathematical expression that represent the relationship between an independent variable and dependent variable. The set of values of independent variable is termed as input of function and the set of value of dependent variable is called output.

given, a function. f(x) = 3x -8

if we want to write x + h instead of x

then the function will be f(x + h) = 3(x + h) - 8

f (x + h) - f(x) = 3(x+ h) - 8- (3x -8)

f( x + h) - f(x) = 3(x +h) - 8 - 3x+ 8

f(x + h) - f(x) = 3(x + h) - 3x

f(x + h) - f(x) = 3x + 3h - 3x

f(x +h) - f(x) = 3h

hence, the above is the result.

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Answer:

a = 45

b = 105

c = 30

Answer:

52m

Step-by-step explanation:

Seperate each place into its own section

Multiply each section

Add the product you get from each section

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

[tex]h^2= a^2+b^2.[/tex]

and the perimeter is [tex]P=h+a+b[/tex].

Since P=24 and a=6  we have these equations:

[tex]h^2=36+b^2\\24=h+6+b[/tex]

From the last equation we have [tex]h=18-b[/tex]. Replace h in the first equation we get that

[tex](18-b)^2=36+b^2[/tex]

[tex]18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8[/tex]

and h=18-8=10

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Answer:

b is 256 c is 48

Step-by-step explanation:

Answer:

D. g(-13) = 20

Step-by-step explanation:

Given information:

Option A, g(-4) = -11 cannot be true for g since the y-value of -11 is not in the given range.

Option B, g(7) = -1 cannot be true for g since the x-value of 7 is not in the given domain.

Option C, g(0) = 2 cannot be true for g since we have been given g(0) = -2.

Option D, g(-13) = 20 is true for g since the x-value of -13 is in the given domain, and the y-value of 20 is in the given range.

The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:

[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]

The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:

[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]

The volume of the given solid is given by:

[tex]$\frac{504\pi}{7}$[/tex]

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Answer:

$ 30,000

Step-by-step explanation:

c = 300 ³√n²

= 300× ³√1000²

= 300× 100

= 30,000

Answer: $30000

Step-by-step explanation:

[tex]300\sqrt[3]{n^2}[/tex]

[tex]300\sqrt[3]{1000^2}[/tex]

[tex]300\sqrt[3]{1000000}[/tex]

300 × 100 = 30000

Answer: To write an equation

y= 7x+38

Answer:

A group of tourists orders a special meal at a restaurant. The cost of each person's meal is $38. Each person will pay a $7 tip. What is the total restaurant bill for the group?

Answer:

sin

Step-by-step explanation:

its opposite over hypotenuse

Answer:

it should be sin

hope this work

Answer:

201.00

Step-by-step explanation:

X is 55 after rearranging the equation given

Answer:

x- coordinate of P is - 6

Step-by-step explanation:

The coordinates of any point in the form of an ordered pair (x, y )

Point P has coordinates P (- 6, 2 )

Answer:

Step-by-step explanation:

Every point has two coordinates

the first is x-coordinate (we read it from X-axis)

the second is y-coordinate (we read it from Y-axis)

coordinates of poin P: (-6, 2)

so, the x-coordunate of point P is -6

Answer:

14 students

Step-by-step explanation:

15 do not play any.

50-15=35

21 students play basketball.

35-21=14

14 students play only soccer

Answer:

Step-by-step explanation:

The difference quotient in general looks like

[tex]\frac{f(x+h)-f(x)}{h}[/tex]   Sometimes the symbol "delta x"  [tex]\Delta x[/tex]   is used instead of h.

For the exponential function, the difference quotient is

[tex]\frac{e^{x+h}-e^x}{h}[/tex]

Answer:

For those who dont want to read, its A.

Step-by-step explanation:

Edge 2021

Step-by-step explanation:

Area = 2LH + 2LW + 2WH

= 2(LH + LW + WH)

=2(30*90+30*60+60*90)

=2(2700+1800+5400)

=2(9900)

=19800cmsquare

Therefore to paint the solid box it will cost

0.03 * 19800

= £594

Answer:

h = 8

Step-by-step explanation:

5.50h=44

Divided both sides by 5.50

h = 8

Let's check

5.50(8) = 44

44 = 44

So, h = 8 is the correct answer!

The number of groups of like terms is 3

An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.

These algebraic expressions are also composed of mathematical operations, such as;

A term can be described a single variable, number or numbers and variables that are multiplied together.

From the information given, we have the terms;

3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰

The similar terms are;

3x¹³,  3x¹⁰,  3¹³

Hence, the number is 3

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On solving the provided question, we can say that An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Arithmetic sequences are groups of integers that are arranged in a certain order and share a common difference between each term. The tolerance, for instance, is six in the mathematical progression 3, 9, 15, 21, and 27. Arithmetic progression can also be referred to as such. a series that is produced by adding the same value repeatedly. for instance, 1, 4, 7, 10, 13, 16, 19, 22, and 25. Sequences that have an arithmetic difference between two successive phrases are known as arithmetic sequences. A progression in math with a tolerance of 2 is 2,4,6,8,10.

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. 2,4,6,8,10….is an arithmetic sequence with the common difference 2.

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Answer:

9.

Step-by-step explanation:

The square root of 10 is approximately 3.16 so it would be closer to 9.

Answer:

80

Step-by-step explanation:

Answer:

13/24x - 3

Step-by-step explanation:

Hope this helps!

The simplified form of expression 1/6x+3/4(1/2x−4) is 7/24x-3.

An expression is combination of variables, numbers and operators.

The given expression is  1/6x+3/4(1/2x−4)

One by six times of x plus three by four times of one by to of x minus four.

Apply distributive property to remove the parenthesis

1/6x+3/4(1/2)x-3/4(4)

1/6x+3/8x-3

The LCM of 6 and 8 is 24.

4x+3x-72/24

Add the like terms in the above expression.

7x/24-72/24

7x/24-3

Hence, the simplified form of 1/6x+3/4(1/2x−4) is 7/24x-3.

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The sequence is going to be {2,−5,2,−5,…}. Since we can see that options A and B are one and the same, the correct answer is options A and B.

A sequence is a successive arrangement of two or more things that are constructed on the basis of a given formula.

Here, the first term is = 2

Each previous term has been multiplied by = -1

And then, it has been subtracted by = 3

So, following the formula given, we conclude that the second value will be = 2×(-1)-3 = -5

Similarly, the formula is going to be applied to the second term now which is -5, and then the third term is going to be = -5×(-1)-3 = 2

In this fashion, we can make the sequence. Options A and B is the correct answer.

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So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.

The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.

Profit Percentage P% = {(selling price – cost price) / cost price} x 100.

The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50

Profit as a percent = (Profit / Original cost) * 100

Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

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