Answer: a. The correlation coefficient of the data is positive.
Step-by-step explanation:
Estimated slope of sample regression line = 
Here , confidence interval : (-0.181, 1.529)
Estimated slope of sample regression line = 
![=\dfrac{1.348}{2}\\\\=0.674\ \ \ \ [\text{ positive}]](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1.348%7D%7B2%7D%5C%5C%5C%5C%3D0.674%5C%20%5C%20%5C%20%5C%20%5B%5Ctext%7B%20positive%7D%5D)
⇒Correlation coefficient(r) must be positive, So a. is true.
But, d. and e. are wrong(0.674 ≠ 0 or 1.348).
We cannot check residuals or its sum from confidence interval of slope of a regression line, so b is wrong.
We cannot say that scatterplot is linear as we cannot determine it from interval, so c. is wrong
So, the correct option : a. The correlation coefficient of the data is positive.
<u>Option C is correct </u><u>(y + z = 6) ⋅ −3</u>
What is a linear equation in math?
- A linear equation only has one or two variables.
- No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.
- When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.
As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
Learn more about linear equation
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<u>The complete question is -</u>
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
Answer:
<h2> (-1, 3)</h2>
Step-by-step explanation:
2x + y = 1 ⇒ y = 1 - 2x
3x - y = -6
3x - (1 - 2x) = -6
3x - 1 + 2x = -6
+1 +1
5x = -5
÷5 ÷5
x = -1
y = 1 - 2(-1) = 1 + 2 = 3
The graphs of the inequalities given as
y > -1/4x - 5 and y > x - 2 is shown below;
