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:
(2,-1)
Step-by-step explanation:
(-2+6)/2 (2+4)/2
Answer:
25.5 days
Step-by-step explanation:
Mean number of days (μ) = 22 days
Standard deviation (σ) = 6 days
Z-score for the 72nd percentile (according to tabulated values) = 0.583
The z-score for any number of days, X, is determined by:
The value of X that is greater than 72% of the trial times is:
Therefore, 72% of all of these types of trials are completed within 25.5 days.
Answer:
Daniel (now) is 3 years old, (2 years ago) is 1 year old.
Kevin (now) is 6 years old, (2 years ago) is 4 years old.
Step-by-step explanation:
Now:
-Kevin: k = d + 3
-Daniel: d
2 years ago:
-Kevin: k - 2 = 4(d - 2)
-Daniel: d - 2
We have the equation:
(k - 2) + 2 = k
4(d - 2) + 2 = d + 3
4d - 8 + 2 = d + 3
3d - 6 = 3
3d = 9
d = 3
k = d + 3 = 3 + 3 = 6
