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Tcecarenko [31]
3 years ago
8

Find the base length of a shipping box in the shape of a triangular prism the shipping box has a volume of 276 cubic feet a base

height of 6.9 ft and a height of 10 ft
Mathematics
1 answer:
Luba_88 [7]3 years ago
5 0
The volume is given by:
 V = A * H
 Where,
 A: area of the base
 H: prism height
 Clearing the area we have:
 A = V / H
 A = 276/10
 A = 27.6 feet ^ 2
 The area of the base is given by:
 A = (1/2) * (b) * (h)
 Where,
 b: base of the triangle
 h: height of the triangle
 Clearing b we have:
 b = (2 * A) / (h)
 Substituting values:
 b = (2 * 27.6) / (6.9)
 b = 8 feet
 Answer:
 
the base length is:
 
b = 8 feet
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A group of people went to a coffee shop.
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Answer:

Fraction of the people chose a tart = \frac{13}{45}

Step-by-step explanation:

Given - A group of people went to a coffee shop. Each person chose a

            drink  and a treat. number of people who chose coffee: number of  

            people who chose tea = 1:4. Of those who chose coffee,  number of  

            people who chose a muffin number of people who chose a tart =    

            2:7. Of  those who chose tea,  number of people who chose a muffin  

            : number of people who chose a tart = 5:1.

To find - What fraction of the people chose a tart?

Proof -

Let the Total number of People went to a coffee shop = 5x

Now,

As given, number of people who chose coffee: number of people who chose tea = 1:4

⇒Total number of people who chooses coffee = \frac{1}{5}.5x = x

  Total number of people who chooses tea  = \frac{4}{5}.5x = 4x

Now,

As given,

Of those who choose coffee,  number of people who chose a muffin number of people who chose a tart = 2:7

⇒Total number of people who choose muffin after coffee = \frac{2}{9}x

   Total number of people who choose tart after coffee = \frac{7}{9}x

Also,

Given that

Of those who chose tea,  number of people who chose a muffin : number of people who chose a tart = 5:1

⇒Total number of people who choose muffin after tea = \frac{5}{6}.4x = \frac{20}{6}x

   Total number of people who choose tart after tea = \frac{1}{6}.4x = \frac{4}{6}x

∴ we get

Total number of people who chooses tart = Total number of people who choose tart after coffee + Total number of people who choose tart after tea

⇒Total number of people who chooses tart = \frac{7}{9}x + \frac{4}{6}x

                                                                         = \frac{7}{9}x + \frac{2}{3}x

                                                                         = \frac{7x + 6x}{9}

                                                                         = \frac{13}{9}x

⇒Total number of people who chooses tart = \frac{13}{9}x

Now,

Fraction of the people chose a tart = \frac{People choose tart}{Total people}

                                                           = \frac{\frac{13}{9}x }{5x}

                                                           = \frac{13}{45}

⇒Fraction of the people chose a tart = \frac{13}{45}

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Hello!!

Total = 3/7 + 4/5 + 2/3

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