The table shows conversions of common units of capacity. Units of Capacity Customary System Units Metric System Units 1 gallon 3
2 answers:
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Answer:
The missing probability is, P (X = 7) = 0.24.
Step-by-step explanation:
The complete question is:
A psychology experiment on memory was conducted which required participants to recall anywhere from 1 to 10 pieces of information. Based on many results, the (partial) probability distribution below was determined for the discrete random variable (X = number of pieces of information remembered (during a fixed time period)).
What is the missing probability P(X=7)? Your answer should include the second decimal place.
X = # information | probability:
1 | 0.0
2 | 0.02
3 | 0.04
4 | 0.07
5 | 0.15
6 | 0.18
7 | ?
8 | 0.14
9 | 0.11
10 | 0.05
Solution:
The sum of the probabilities of all events of an experiment is always 1.
Use the above theorem to compute the missing probability.
Thus, the missing probability is, P (X = 7) = 0.24.
Answer:
The volume in terms of π is 144 ft³
The volume rounded to the nearest tenth is 452.4 ft³
Step-by-step explanation:
The formula of the volume of a cone is V = π r² h , where r is its radius and h is its height
The formula of the area of a circle is A = π r²
∵ The area of the base of the cone is 36π ft²
- Equate the formula of the area of the circle by 36π to find r
∵ πr² = 36π
- Divide both sides by π
∴ r² = 36
- Take √ to both sides
∴ r = 6 ft
∵ The height of the cone is equal to twice the radius
∵ The radius of the cone is 6 ft
- Multiply 6 by 2 to find the height
∴ h = 2(6) = 12 ft
∴ The height of the cone is 12 ft
Substitute the values of h and r in the formula of the volume of the cone to find it
∵ V = π(6)²(12)
∴ V = 144 π ft³
∴ V = 452.3893421 ft³
- Round it to the nearest tenth
∴ V = 452.4 ft³