Answer:
Step-by-step explanation:
can be thought of as 6 blocks with dimensions 4 x 4 x 5
V = 6(4)(4)(5) = 480 in³
Answer:
And if we find the individual probability we got:
And replacing we got:
Step-by-step explanation:
Previous concepts
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".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find this probability:
And we can use the complement rule and we got:
And if we find the individual probability we got:
And replacing we got:
You don't have to give me that many points. :)
OK so let's write this in equation form. First thing we think about is if the equation arithmetic (they add the same amount of money each week) or geometric (they add steadily increasing or decreasing amounts of money each week). Since Nancy and Fred add a fixed amount of $3 and $1 respectively, we're going to call them arithmetic sequences.
The equation for an arithmetic sequence is
an=a0+dn, where d is the amount of money added every week, n is the week number they're on and a0 is the amount of money they would've had a week before the first week. I'll explain this more in detail.
So Nancy increases by $3 every week: d=3. n is what we want to find. She starts out with $15. Imagine she had the same rule (increasing by $3) but started a week earlier. The term before 15 is 12. So a0 is 12. Her equation is an=12+3n. Let's do the same for Fred.
Fred increases by $1 and if he started a week earlier, he would've started with $14, so his equation is an=14+n. Now you want to find n so that Nancy's account (the first equation equals two times as much money as Fred has (the second equation.
So 12+3n=2(14+n).
Solving for n,
12+3n=28+2n
Combine like terms, so subtract 2n from both sides and then subtract 12 from both sides.
12+n=28
n=16
So on the 16th week, Nancy will have twice as much money as Fred. Hope this helped!
Answer:
The events being a heavy smoker and having emphysema are not independent.
Step-by-step explanation:
We are given the following in the question:
Number of women = 2000
Number of heavy smoker = 340
Number of women who has emphysema = 25
Number of women who has emphysema and are heavy smoker = 21
P(Smoker) =
P(emphysema) =
P(Smoker and emphysema) =
Two events A and B are said to be independent if
Checking conditions for independence:
Thus, the events being a heavy smoker and having emphysema are not independent.
All of a triangles angles added up make 180. when theres a 90, its a lot easier, all you have to do is take 180-90 which is 90 and divide 90 by 2 because there are two unknown angles which is 45 and angle A is slightly bigger than angle B (we'll say about 5 degrees bigger) so the answer would be 3) 50