Answer:
The second option
Step-by-step explanation:
The given system of equation is
x+2y=3
-x+y+z=2
y-2z=-3
The augment matrix is obtained by combining the coefficient matrix with the constant matrix to obtain;
Note that the absence of z, in the first equation means its coefficient is zero. The same thing applies to x in the last equation.
The correct choice is the second option.
Answer:
The median and mode of the students grade is 70.
Most of the students scored between 40 and 100.
Step-by-step explanation:
From the provided information it can be seen that the mean of the distribution is, <em>μ</em> = 70 and the standard deviation is, <em>σ</em> = 15.
For a Normal distributed data the mean, median and mode are the same.
So, the median and mode of the students grade is 70.
The standard deviation of the data represents the spread of the observation, i.e. how dispersed the values are along the curve.
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.
Assuming that maximum marks of the exam is 100, it can be said that most of the students scored between 40 and 100.
Part A: Option e:
Option f:
Part B: Option c:
Option d:
Part C: Option a:
Option b:
Explanation:
Part A: The equation is
Simplifying, we have,
Taking the term 5 common out, we have,
Thus, the above two expressions are equivalent to the equation .
Hence, Option e and Option f are the correct answers.
Part B: The equation is
Taking the term 15 common out, we have,
Also, the equation can be rewritten as,
Thus, the above two expressions are equivalent to the equation
Hence, Option c and Option d are the correct answers.
Part C: The equation is
Multiplying, we have,
The above expression can be rewritten as,
Thus, the above two expressions are equivalent to the equation
Hence, Option a and Option b are the correct answers.