Answer: The solution is (2, 2)
Step-by-step explanation:
We have the system of equations:
y = 2*x - 2
x + y = 4
The first step is to write both equations as linear equations in the slope-intercept form.
y = 2*x - 2
y = -x + 4
Now we have two lines, and we can just graph them, the easiest way is the replace the value of x and obtain two points that belong to the line, and then draw a line that passes through both lines.
For example with the first one, we can firt replace x by 0 to get:
y = 2*0 - 2
y = -2
Then the point (0, -2) belongs to this line.
Now we can replace x by 1 to get:
y = 2*1 - 2 = 0
y = 0
The point (1, 0) belongs to this line.
Then we can draw these two points in the graph, and just draw a line that passes through these two points.
Once you have your two lines drawn, the solution of the system will be the point in which the lines intersect.
Below, you can see the two lines graphed (the green is the first one and the red is the second one)
And we can see that they intersect in the point (2, 2)
Then the solution of the system is (2, 2)
Answer:
Step-by-step explanation:
In order to add or subtract numbers in scientific notation, the powers of ten must have the same exponent. In this caes the diameter of an average human body cell is a power of -4 and the diameter of a plant cell is a power of -3. In order to add them, we can move the decimal over for the body cell diameter:
Add the two values:
Answer:
a) 75
b) 4.33
c) 0.75
d) probability that no one in a simple random sample of 100 young adults owns a landline
e) probability that everyone in a simple random sample of 100 young adults owns a landline.
f) Binomial, with
g) probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
Step-by-step explanation:
For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
This means that
(a) On average, how many young adults do not own a landline in a random sample of 100?
Sample of 100, so
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
(c) What is the proportion of young adults who do not own a landline?
The estimation, of 75% = 0.75.
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
This is P(X = 100), that is, all do not own. So
probability that no one in a simple random sample of 100 young adults owns a landline.
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
This is P(X = 0), that is, all own. So
probability that everyone in a simple random sample of 100 young adults owns a landline.
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
Binomial, with
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
This is P(X = 50). So
probability that exactly half the young adults in a simple random sample of 100 do not own a landline.