Answer. First option: t > 6.25
Solution:
Height (in feet): h=-16t^2+729
For which interval of time is h less than 104 feet above the ground?
h < 104
Replacing h for -16t^2+729
-16t^2+729 < 104
Solving for h: Subtracting 729 both sides of the inequality:
-16t^2+729-729 < 104-729
-16t^2 < -625
Multiplying the inequality by -1:
(-1)(-16t^2 < -625)
16t^2 > 625
Dividing both sides of the inequality by 16:
16t^2/16 > 625/16
t^2 > 39.0625
Replacing t^2 by [ Absolute value (t) ]^2:
[ Absolute value (t) ]^2 > 39.0625
Square root both sides of the inequality:
sqrt { [ Absolute value (t) ]^2 } > sqrt (39.0625)
Absolute value (t) > 6.25
t < -6.25 or t > 6.25, but t can not be negative, then the solution is:
t > 6.25
Let x be the old price
X= 1200$
The price decreased 20% after 1 year to become price y :
Y= 0.8x
= 0.8 (1200)
= 960$
In the year after y also decreased 20% to be price y’:
Y’= 0.8y
= 0.8 (960)
= 768 $
The price y’ then decreased 20% to become price y’’:
Y’’ = 0.8 y’
= 0.8 (768)
= 614.4 $
Then the price will be 614.4 $ after 3 years
Answer:
Mean for a binomial distribution = 374
Standard deviation for a binomial distribution = 12.97
Step-by-step explanation:
We are given a binomial distribution with 680 trials and a probability of success of 0.55.
The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 680 trials
r = number of success
p = probability of success which in our question is 0.55
So, it means X <em>~ </em>
<em><u>Now, we have to find the mean and standard deviation of the given binomial distribution.</u></em>
- Mean of Binomial Distribution is given by;
E(X) = n
p
So, E(X) = 680
0.55 = 374
- Standard deviation of Binomial Distribution is given by;
S.D.(X) =
=
=
= 12.97
Therefore, Mean and standard deviation for binomial distribution is 374 and 12.97 respectively.
X=3, y=4
x=-2, y=9
Set x equal to anything, then isolate y to get the other number.