There are two possible ways for X=1: first light is green and second is red OR first light is red and second is green. The probabilities for these two options are to be summed: 0.6*0.4 + 0.4*0.6 to give the probability of exactly one light being green, namely 0.48.
Answer:
39/60 is a rational number halfway b/w the given numbers.
Step-by-step explanation:
Add both of these numbers and then divide the result by 2.
(1/3+3/10)/2
=((30+9)/30)/2
=(39/30)*1/2
=39/60
Answer:
4m
Step-by-step explanation:
m+m+m+m
There is an implied 1 in front of each term
1m+1m+1m+1m
Factor out the m
(1+1+1+1)m
4m
Answer:
Simple springs obey Hooke's Law. Hooke's Law states that the force on a spring is proportional to it's displacement from it's resting length:
F = -k*x
Where F is the force, x is how far the string is stretched or compressed, and k is a proportionality constant called the spring constant. The negative sign is because the spring resists stretching.
In this case, we can solve for k using the first case:
(100N) = -k * (5cm)
k = ???
And plug that answer in to find x in the second case:
(360N) = -k * x
This is a "Hooke's Law" problem: the restoring force required to compress or stretch a spring is proportional to the distance the spring is deformed. You can figure solve it by setting up a proportion equation and then using the algebraic tool of cross multiplication to solve for the unkown "stretch".
1) set up the proportion equation
100 = 360
5 x
2) cross multiply to get a linear equation
100x = 5*360
3) solve for x
100x = 1800
x = 18
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Answer:
Step-by-step explanation:
Since the incubation times are approximately normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = incubation times of fertilized eggs in days
µ = mean incubation time
σ = standard deviation
From the information given,
µ = 19 days
σ = 1 day
a) For the 20th percentile for incubation times, it means that 20% of the incubation times are below or even equal to 19 days(on the left side). We would determine the z score corresponding to 20%(20/100 = 0.2)
Looking at the normal distribution table, the z score corresponding to the probability value is - 0.84
Therefore,
- 0.84 = (x - 19)/1
x = - 0.84 + 19 = 18.16
b) for the incubation times that make up the middle 97% of fertilized eggs, the probability is 97% that the incubation times lie below and above 19 days. Thus, we would determine 2 z values. From the normal distribution table, the two z values corresponding to 0.97 are
1.89 and - 1.89
For z = 1.89,
1.89 = (x - 19)/1
x = 1.89 + 19 = 20.89 days
For z = - 1.89,
- 1.89 = (x - 19)/1
x = - 1.89 + 19 = 17.11 days
the incubation times that make up the middle 97% of fertilized eggs are
17.11 days and 20.89 days
