Chocolate chip and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four
1 answer:
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Answer:
90% of the variation in the dependent variable is explained by the independent variable.
Step-by-step explanation:
We are given the following in the question:
coefficient of determination = 0.9
We have to find the percentage of variation in the dependent variable explained by the variation in the independent variable.
Coefficient of Determination:
- The coefficient of determination is a measure that explains and predicts the dependent variable.
- It explains the variation in the dependent variable caused by the independent variable.
- The coefficient of determination, also known as the R squared value and is obtained by squaring the coefficient of correlation.
Thus, 90% of the variation in the dependent variable is explained by the independent variable.
The exact value is found by making use of order of operations. The
functions can be resolved using the characteristics of quadratic functions.
Correct responses:
- x = -4, y = 12
- When P = 1, V = 6
ii. The function has a minimum point
iii. The value of <em>x</em> at the minimum point, is <u>1.25</u>
iv. The equation of the axis of symmetry is <u>x = 1.25</u>
<h3>Methods by which the above responses are found</h3>First part:
The given expression, , can be simplified using the algorithm for arithmetic operations as follows;
Second part:
y = 8 - x
2·x² + x·y = -16
Therefore;
2·x² + x·(8 - x) = -16
2·x² + 8·x - x² + 16 = 0
x² + 8·x + 16 = 0
(x + 4)·(x + 4) = 0
- <u>x = -4</u>
y = 8 - (-4) = 12
- <u>y = 12</u>
Third part:
(i) P varies inversely as the square of <em>V</em>
Therefore;
V = 3, when P = 4
Therefore;
K = 3² × 4 = 36
When P = 1, we have;
- When P = 1, V =<u> 6</u>
Fourth Part:
Required:
Solving for <em>x</em> in the equation; 2·x² + 5·x - 3 = 0
Solution:
The equation can be simplified by rewriting the equation as follows;
2·x² + 5·x - 3 = 2·x² + 6·x - x - 3 = 0
2·x·(x + 3) - (x + 3) = 0
(x + 3)·(2·x - 1) = 0
Fifth part:
The given function is; f(x) = 2·x² - 5·x + 8
i. Required; To write the function in the form a·(x + b)² + c
The vertex form of a quadratic equation is f(x) = a·(x - h)² + k, which is similar to the required form
Where;
(h, k) = The coordinate of the vertex
Therefore, the coordinates of the vertex of the quadratic equation is (b, c)
The x-coordinate of the vertex of a quadratic equation f(x) = a·x² + b·x + c, is given as follows;
Therefore, for the given equation, we have;
Therefore, at the vertex, we have;
a = The leading coefficient = 2
b = -h
c = k
Which gives;
Therefore;
ii. The coefficient of the quadratic function is <em>2</em> which is positive, therefore;
- <u>The function has a minimum point</u>.
iii. The value of <em>x</em> for which the minimum value occurs is -b = h which is therefore;
- The x-coordinate of the vertex = h = -b =<u> 1.25 </u>
iv. The axis of symmetry is the vertical line that passes through the vertex.
Therefore;
- The axis of symmetry is the line <u>x = 1.25</u>.
Learn more about quadratic functions here: