I think this is how you do it, each triangle is 3, and the square is .5625 so 3 x 4 is 12+ .5625 so 12.5625, i hope i helped
Answer:
a. X is the number of adults in America that need to be surveyed until finding the first one that will watch the Super Bowl.
b. X can take any integer that is greater than or equal to 1. 
.
c. 
.
d. 
.
e. 
.
f. 
.
Step-by-step explanation:
<h3>a.</h3>
In this setting, finding an adult in America that will watch the Super Bowl is a success. The question assumes that the chance of success is constant for each trial. The question is interested in the number of trials before the first success. Let X be the number of adults in America that needs to be surveyed until finding the first one who will watch the Super Bowl.
<h3>b.</h3>
It takes at least one trial to find the first success. However, there's rare opportunity that it might take infinitely many trials. Thus, X may take any integer value that is greater than or equal to one. In other words, X can be any positive integer: .
<h3>c.</h3>
There are two discrete distributions that may model X:
- The geometric distribution. A geometric random variable measures the number of trials before the first success. This distribution takes only one parameter: the chance of success on each trial.
- The negative binomial distribution. A negative binomial random variable measures the number of trials before the r-th success. This distribution takes two parameters: the number of successes
and the chance of success on each trial 
.
(note that 
) is equivalent to 
. However, in this question the distribution of 
takes two parameters, which implies that shall follow the negative binomial distribution rather than the geometric distribution. The probability of success on each trial is 
.
.
<h3>d.</h3>
The expected value of a negative binomial random variable is equal to the number of required successes over the chance of success on each trial. In other words,
.
<h3>e.</h3>
.
Some calculators do not come with support for the negative binomial distribution. There's a walkaround for that as long as the calculator supports the binomial distribution. The r-th success occurs on the n-th trial translates to (r-1) successes on the first (n-1) trials, plus another success on the n-th trial. Find the chance of (r-1) successes in the first (n-1) trials and multiply that with the chance of success on the n-th trial.
<h3>f.</h3>
.
The planes will pass each other in 1.14 hours.
Why?
To solve the problem, we must remember that since both planes are heading toward each other, the speed to the calculations will be their combined speeds.
The speed will be:
Now, calculating the time, we have:
Hence, the planes will pass each other in 1.14 hours.
Have a nice day!
In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.
To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB.
1. Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3
A (-2,-1) and B(-6, -7)The distance between A and B would be:
x= x2-x1 = -6 - (-2)= -4
y= y2-y1 = -7 - (-1)= -6
Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.
Point C(-3.6, -3.4) divides AB in the ratio 2:3
x3= x1 + AB ratio* AB distance
x3= -2 + (2/2+3)*(-4)= -3.6
y3= y1 + AB ratio* AB distance
y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4
2. Point C(0, 1) divides AB in the ratio 4:7
A(4,-3) and B(-7,8)
The distance between A and B would be:
x= x2-x1 = -7 - (4)= -11
y= y2-y1 = 8 - (-3)= 11
Since both x and y distance is 11, let's try answer with total ratio 11
Point C(0, 1) divides AB in the ratio 4:7
x3= x1 + AB ratio* AB distance
x3= 4 + (4/4+7)*(-11)= 4- 4=0
y3= y1 + AB ratio* AB distance
y3= -3 + (4/4+7)*(11)= -3 +4= 1
3. Answer: Point C(8, 9) divides AB in the ratio 5:3
A(3,4) and B(11,12)The distance between A and B would be:
x= x2-x1 = 11 - (3)= 8
y= y2-y1 = 12 - (4)= 8
Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.
Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus
Point C(-2, 5) divides AB in the ratio 2:6 -----> total ratio 8, x minus
Point C(8, 9) divides AB in the ratio 5:3 -----> total ratio 8, both x and y plus
x3= x1 + AB ratio* AB distance
x3= 3 + (5/5+3)*(8)= 3+ 5=8
y3= y1 + AB ratio* AB distance
y3= 4 + (5/5+3)*(8)= 4 +5= 9
4. Point C(-2, 5) divides AB in the ratio 2:6
A(-5,2)and B(7, 14)
The distance between A and B would be:
x= x2-x1 = 7 - (-5)= 12
y= y2-y1 = 14 - (2)= 12
Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.
Point C(4, 1.6) divides AB in the ratio 3:2 -----> x more than y
Point C(-2, 5) divides AB in the ratio 2:6 -------> y plus, y more than xx3= x1 + AB ratio* AB distance
x3= -5 + (2/2+6)*(12)= -5+ 3=-2
y3= y1 + AB ratio* AB distance
y3= 2 + (2/2+6)*(12)= 2 +3= 5
