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LenaWriter [7]
3 years ago
15

2 number cubes are rolled. (a) List the sample space. (b)What is the probability, as a simplified fraction, that the sum of the

numbers is 4 or that the sum of the numbers is greater than 9? Show your work.
Mathematics
1 answer:
melomori [17]3 years ago
7 0

Solution:

When two number cubes  are rolled,

Sample space= Total Possible outcome {11,22,33,44,55,66,12,21,13,31,14,41,15,51,16,61,23,32,24,42,25,52,26,62,34,43,35,53,36,63,45,54,46,64,56,65}=36

Probability of an event = \frac{\text{Total favorable outcome}}{\text{Total possible outcome}}

Sum of 4 is obtained when ={13,31,22}=3

Probability of getting 4 when 2 number cubes are rolled= \frac{3}{36}=\frac{1}{12}

Sum of the numbers is greater than 9= 10, 11,12={55,64,46,56,65,66}=6

Probability of getting(Sum of the numbers is greater than 9)=\frac{6}{36}=\frac{1}{6}



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Answer:

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes

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The given parameters are;

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We have;

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The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³

When the volume is two-thirds the maximum volume, we have;

2/3 × 696556.67 ft³ = 464371.11 ft³

The value of the radius, r₂ at that point is found as follows;

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r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³

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r₂ = ∛(348278.33 ft³) ≈ 70.36 ft

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The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.

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