108 - 18 1/4 = 89 3/4
Jaden has 89 3/4 measures left to learn.
The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
<h3>How to determine the characteristics of the roots of a quadratic equation by discriminant</h3>
Herein we have a <em>quadratic</em> equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
- d < 0 - <em>conjugated complex</em> roots.
- d = 0 - <em>equal real</em> roots (real and rational root).
- d > 0 - <em>different real</em> roots (real and irrational root).
If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
To learn more on quadratic equations: brainly.com/question/2263981
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9514 1404 393
Answer:
a) weights: 0.32688, 0.18402, 0.35593, 0.13317
b) geometric average return: 5.42%
Step-by-step explanation:
The total of amounts invested is ...
13500 +7600 +14700 +5500 = 41300
The respective weights for the weighted average are these values divided by the total. For example, 13500/41300 ≈ 0.32688. The remaining weight values are shown in the attached spreadsheet.
The weighted geometric average return is 1 less than the product of 1 more than the individual returns raised to the power of the weight*. That is, ...
weighted average return
= (1.097^0.327)(1.124^0.184)(0.945^0.356)(1.172^0.133) -1
= 1.0542 -1 = 5.42%
_____
* Technically, the weighted geometric average is root of the products of the values to the power of the weight. The root index is the sum of the weights. Here, the sum of weights is 1, so the root is simply the product itself.