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3 years ago

The average amount of trail mix in each bag

Mathematics

1 answer:

11111nata11111 [884]3 years ago

6 0

OK so from what I have there are 24 bags. 4 ¼ bags and from all the ½ bags they = 2 lb. So convert 2 lb into ¼ lb bag, you get 8. Next you have the ¾ bags which = 3 lb. Now you need to turn the ¾ into ¼ and find out how many times ¼ goes into 3. So the answer would then be 12. Next add them all together 4 + 8 + 12 = 25. So 24 is your answer.

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Determine the 18th term of the sequence 3,9,27,...

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Answer:

$x_{18}=387420489$

Step-by-step explanation:

So we have the sequence:

3, 9, 27...

First, note that this is a geometric sequence because each subsequent term <em>not </em>increasing linearly.

To find the 18th term, we can write an explicit formula.

The standard explicit formula for a geometric sequence is:

$x_n=a(r)^{n-1}$

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From the sequence, we can see that the initial term a is 3. The common ratio is 3 since each subsequent term is 3 times the previous term. So, substitute:

$x_n=3(3)^{n-1}$

To find the 18th term, substitute 18 for n. So:

$x_{18}=3(3)^{18-1}$

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$x_{18}=3(3)^{17}$

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3 years ago

Holly made 12 pair of earrings for each of her girlfriends. To wrap the pairs individually, she creates a simple cardboard gift

Mekhanik [1.2K]

Answer:

3280cm²

Step-by-step explanation:

We are told the gift box is folded into a Pyramid with a square base.

Hence, we are to find the Surface Area of a square pyramid

From the question, we are given:

Length of the base of the square = 10cm

Triangle

Side length = 10cm

Height = 8 2/3 cm

A square Pyramid has 5 faces: 4 triangles and 1 square.

Step 1

Find the Area of the square

Formula = Side length² this is because all the side of a square is equal.

Length of the base = 10cm

Area of the square = (10cm)²

= 100cm²

Step 2

Find the Area of the triangle. We are told the 4 triangles are equilateral, which means their side are equal.

Hence, for one triangle.

Area of a triangle = 1/2 × base × height

Base = side length = 10cm

Height = 8 2/3 = 8.6666666667cm

Area of a triangle = 1/2 × 10 × 8.6666666667

Area of a triangle = 43.333333333cm²

Since we have 4 triangles

We would have : 4 × 43.333333333cm²

= 173.33333333cm²

The Area of the 4 equilateral triangles =

173.33333333cm²

Step 3

The Surface area of the Square Pyramid

= Sum of the areas of all the faces.

= 100cm² + 173.33333333cm²

= 273.33333333cm²

Therefore, the minimum amount of cardboard needed to make one gift box = 273.33333333cm²

Step 4

The minimum amount of cardboard Holly needs to create 12 gift boxes to wrap each pair of earrings individually is calculated as: 12 × 273.33333333cm²

= 3280cm²

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