Answer:
B. 
Step-by-step explanation:
Total number of students surveyed = 420
Of which only 
prefer rap.
So, the number of people who like rap is the product of the fraction of people who prefer rap and the total number of students.
The number of students that prefer rap is 105
So the equation is .
Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra II</u>
- Log/Ln Property:
<u>Calculus</u>
Derivatives
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative of Ln: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Differentiate</u>
- Rewrite:
- Rewrite [Ln Properties]:
- Differentiate [Ln/Chain Rule/Basic Power Rule]:
- Simplify:
- Rewrite:
- Combine:
- Reciprocate:
- Distribute:
Answer:
y = 0.5 (x^2 -2x + 16) has a y-intercept of 8.
Step-by-step explanation:
The x-coordinate of every y-intercept is zero. To determine which of the four quadratics given here has a y-intercept of 8, we need only substitute 0 for x in each; if the result is 8, we've found the desired quadratic.
O y = 0.5(x + 2)(x + 4) becomes y = 0.5(2)(4) = 4 (reject this answer)
O y = 0.5 (x - 2)(x + 8) becomes y = 0.5(-2)(8) = -8 (reject)
O y = 0.5(x2 -2x - 16) becomes y = 0.5(-16) = -8 (reject)
<em>O y = 0.5 (x2 -2x + 16) becomes y = 0.5(16) = 8 This is correct; that '8' represents the y-intercept (0, 8).</em>
Answer:
-1
Step-by-step explanation:
x^2 – 8
-----------
x + 6
Let x = -2
(-2)^2 – 8
-----------
-2 + 6
Exponents first
4 – 8
-----------
-2 + 6
Then complete the numerator and denominator
-4
-----
4
Then divide
-1
