Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
Answer:
<u>$4800</u>
Step-by-step explanation:
The expected net income is the probability when rains multiplied by net income (profit) summed with the probability of not raining with that days net income multiplied.
First, Chance of rain = 12% = 12/100 = 0.12
Profit/Loss = Income - Cost
Income is 5000
Cost = 9000
So,
Loss = 5000 - 9000 = 4000
Or, Net Income (profit) = - 4000
Now, Change of not raining = 100 - 12 = 88% = 88/100 = 0.88
Profit = Income - Cost
Income = 15,000
Cost = 9000
Net Income (profit) = 15000 - 9000 = 6000
So, we can write the expected net income as:
<u>Expected NI </u>= (0.12)(-4000) + (0.88)(6000) = <u>$4800</u>
1/5 goes into 37 185 times:
37 / (1/5) = 37*(5/1)=185
Answer:a=1/5
B=2/15
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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