Answer:
120
Step-by-step explanation:
The absolute value is 120. Think about it on a number line, the absolute value is the amount of spaces that -120 is away from 0. Therefore, the amount of spaces -120 is from 0, is 120.
Answer:
And for this case we want to find this probability:

And we can use the probability mass function and we got:
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
Let X the random variable of interest, on this case we now that:
And for this case we want to find this probability:

And we can use the probability mass function and we got:
The sum of a geometric sequence is:
s(n)=a(1-r^n)/(1-r) in our case:
s(n)=3(1-4^n)/(1-4)
s(n)=-(1-4^n)
s(n)=(4^n)-1 and s=1023
(4^n)-1=1023
4^n=1024
n ln4=ln1024
n=(ln1024)/(ln4)
n=5
Answer:
12.8 units
Step-by-step explanation:
Adding a diagonal makes it into 2 of the same right-angled triangles.
In right angled triangles, you can use Pythagoras' therorem which says that a^2+b^2=c^2 where a and b are the shorter sides and c is the diagonal.
This means that 8^2+10^2=diagonal^2=64+100=164
The diagonal is then the square root of 164 which equals 12.806248...