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Dafna11 [192]
3 years ago
10

Julia is making pasta necklaces and wreaths. She uses n noodles in a necklace and 3/5 that number of noodles in wreaths. Which e

xpression shows the number of noodles Julia uses if she makes 9 necklaces and 20 wreaths?
Mathematics
1 answer:
Fofino [41]3 years ago
6 0

Answer:

the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths

  = (9 \times n ) + (20 \times (3/5)n) = 9n + 12n = 21n

Step-by-step explanation:

i) there are n noodles in a necklace

ii) there are 9 necklaces

iii) therefore the number of noodles used to make the nine necklaces = 9 \times n = 9n

iv) there are 3/5 noodles in a wreath

v) there are 20 wreaths

vi) therefore the number of noodles used to make the nine necklaces

     = 20 \times (3/5)n = 12n

vii) the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths

  = (9 \times n ) + (20 \times (3/5)n) = 9n + 12n = 21n

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What are the answer
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Answer:

1)556.11 cm²

2)164.05 cm²

3)117.70 cm²

Step-by-step explanation:

1) We have a cylinder and a cone on top of it.

Formula for total surface area of cylinder is;

T.S.A = 2πrh + 2πr²

However, the top is not available for calculation here. Thus, we will use;

TSA = 2πrh + πr²

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The top is a cone but it's bottom is not included and so we will use lateral surface area of cone = πrL

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L = √(5² + 4²)

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Thus;

LSA = π × 5 × √41 = 100.58 cm²

Overall surface area = 455.53 + 100.58. Overall surface area = 556.11 cm²

2) for the box down;

TSA = 2lw + 2lh + 2hw

Since the top face is not used, then

TSA = lw + 2lh + 2hw

TSA = (5 × 5) + 2(5 × 5) + 2(5 × 5)

TSA = 125 cm²

For the prism on top, since the bottom is not included, we will use lateral surface are;. LSA = ½Pl

Where P is perimeter of base and L is slant height.

P = 5 × 4 = 20 cm

Radius is 5/2 = 2.5 and so using pythagoras theorem;

L = √(2.5² + 3²)

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Thus;

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Overall surface area = 39.05 + 125 = 164.05 cm²

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Since the top face is not used, then

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Surface area ;

T.S.A = 2πrh + 2πr²

Since half cylinder;

TSA = πrh + πr²

TSA = π((2 × 4) + 2²))

TSA = 37.7 cm²

Overall total surface area = 80 + 37.7 ( 117.70 cm²

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