Using the Pythagorean theorem:
Hypotenuse = sqrt( 20^2 + 15^2)
Hypotenuse = sqrt( 400 + 225)
Hypotenuse = sqrt(625)
Hypotenuse = 25
Answer: 25 inches
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2.
H - head
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T) = 0.8
urn
3 red and 5 blue
when heads is obtained
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12
when tails is obtained
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3
using bayes rule the answer can be found out,
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
= 0.12 / (0.12 + 0.3)
= 0.12 / 0.42
= 0.286
the final answer is 0.286
Answer:
It is a growth.
Step-by-step explanation:
If the number in parenthesis (exponential base) is greater than 1, then it is a growth. If it is between 1 and 0, then it is a decay.
An absolute value cannot equal a negative number. So c, if it was a negative number, would have no solution.
Answer:
A) 48/13 ft/sec
B) 22/13 ft/sec
Step-by-step explanation: Given that:
A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.
A) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?
Using similar triangles, we can say:
12/L = 55/(L - x)
Cross multiply to get:
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Taking the derivative with respect to time we get:
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
Since dx/dt = 2 so
dl/dt = (12/6.5)(2)
= 24/6.5
= 48/13 ft/sec
B) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole ?
Subtract the rate the shadow is going from the rate the man is going. Therefore
48/13 - 2 = 22/13 ft/sec.
