Given the equation y=2x+3, write a second equation that would create an independent consistent linear system
1 answer:
Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).
This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:
They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).
In our case, we are asked to write an equation in order to create an independent consistent linear system.
Note: Consistent means that the system has a solution.
First, we graph the given equation:
There are many different equations that will form an independent consistent linear system with this equation.
We are going to choose the following line equation:
Because when we graph this equation next to the previous line:
We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.
Answer:
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Answer:
The probability that at most 50 say that they drink coffee during exam week is 0.166.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of college students who prefer to drink more coffee during the exams week.
The probability of the random variable <em>X</em> is <em>p</em> = 0.67.
A random sample of <em>n</em> = 80 college students are selected.
The response of every students is independent of the others.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 80 and <em>p</em> = 0.67.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
The mean of the distribution of <em>X</em> is:
The standard deviation of the distribution of <em>X</em> is:
A Normal distribution is a continuous distribution. So, the probability at a point cannot be computed for the Normal distribution. To compute the probability at a point we need to apply the continuity correction.
Compute the probability that at most 50 say that they drink coffee during exam week as follows:
Apply continuity correction:
*Use a <em>z</em>-table for the probability.
Thus, the probability that at most 50 say that they drink coffee during exam week is 0.166.
If you need to, you can write and solve an equation for the factor you seek.
... 6×10^10 = factor × 2×10^-3
Divide by 2×10^-3 to find the value of the factor:
... (6×10^10)/(2×10^-3) = factor
... factor = (6/2)×10^(10-(-3))
... factor = 3×10^13
The first number is 3×10^13 times the second number.
_____
An exponent signifies repeated multiplication.
... 10×10×10 = 10³
Just as you cancel common factors when you do division, you can subtract exponents.
The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.