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Akimi4 [234]
3 years ago
7

A rectangle that is twice as long as it is wide forms the base of a rectangular pyramid that is 60cm high. If the volume of the

pyramid is 4000 cm cubed, what are the dimensions of the rectangle?
Full show working out ty;)
Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0

Answer:

10 * 20 cm.

Step-by-step explanation:

Let the width of the base = x, then it's length is 2x cm  and the area = 2x^2 cm^2.

Volume = 1/3 * height * area of the base

4000 = 1/3 * 60 * 2x^2

2x^2 = 4000 / (1/3 * 60)

2x^2 = 4000 / 20 = 200

x^2 = 200/2 = 100 cm.

x = 10 cm.

So the dimension of the rectangle =  10 * 20 cm.

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Answer:

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From the question we are told that

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Generally  the degree of freedom for this data set is mathematically represented as

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Given that the level of confidence is  90%  the significance level is mathematically evaluated as

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Now   \frac{\alpha }{2}  =  \frac{0.10}{2}  = 0.05

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           t_{df, \frac{ \alpha}{2}   } = t_{63,  0.05   } =  1.669

   The margin for error is mathematically represented as

          MOE  =  t_{df ,  \frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

substituting values  

          MOE  = 1.699  *   \frac{4 }{\sqrt{64} }

         MOE  = 0.85

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           \= x - MOE  <  L  <  \= x  + E

substituting values  

         20  - 0. 85 <  L  <   20  + 0.85

         19.15<  L  <   20.85

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