Answer:
2/3
Step-by-step explanation:
2/12+4/9
Find a common denominator
16/72+ 32/72
48/72
Simplify
=2/3
Hope this helps
Answer:
C. It would be shifted up.
Step-by-step explanation:
We base it off the y-intercept. Since -7 is <em>less</em><em> </em><em>than</em><em> </em>1, and our new function has a positive y-intercept, it would indeed be shifted up.
I am joyous to assist you anytime.
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
<u>Calculus</u>
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule: ![\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
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)
Quotient Rule: ![\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
-xy - 2y = -4
Rate of change of the tangent line at point (-1, 4)
<u>Step 2: Differentiate Pt. 1</u>
<em>Find 1st Derivative</em>
- Implicit Differentiation [Product Rule/Basic Power Rule]:

- [Algebra] Isolate <em>y'</em> terms:

- [Algebra] Factor <em>y'</em>:

- [Algebra] Isolate <em>y'</em>:

- [Algebra] Rewrite:

<u>Step 3: Find </u><em><u>y</u></em>
- Define equation:

- Factor <em>y</em>:

- Isolate <em>y</em>:

- Simplify:

<u>Step 4: Rewrite 1st Derivative</u>
- [Algebra] Substitute in <em>y</em>:

- [Algebra] Simplify:

<u>Step 5: Differentiate Pt. 2</u>
<em>Find 2nd Derivative</em>
- Differentiate [Quotient Rule/Basic Power Rule]:
![y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}](https://tex.z-dn.net/?f=y%27%27%20%3D%20%5Cfrac%7B0%28x%2B2%29%5E2%20-%208%20%5Ccdot%202%28x%20%2B%202%29%20%5Ccdot%201%7D%7B%5B%28x%20%2B%202%29%5E2%5D%5E2%7D)
- [Derivative] Simplify:

<u>Step 6: Find Slope at Given Point</u>
- [Algebra] Substitute in <em>x</em>:

- [Algebra] Evaluate:

Answer and explanation:
Null hypothesis: p is not 54%
Alternative hypothesis : p is equal 54%
First find standard deviation
Standard deviation is:
σ = √[ P ( 1 - P ) / n ] = √[ 0.54×0.46/220 ] =0.033
The z score is calculated p-P/σ = (0.54-0.50)/0.033 = 1.2121
Therefore we can conclude that proportions are not same and fail to reject the null hypothesis
Answer:
Jelly Bean price per pound = $3.25, Trail Mix price per pound = $1.25
Step-by-step explanation:
Let jb = price per pound of jelly beans
Let tm = price per pound of trail mix
equation 1 -> 6*jb + 2*tm = 22
equation 2 -> 3*jb + 5*tm = 16
simplify equation 1
6*jb + 2tm = 22
2*tm = 22 - 6*jb
divide by 2
tm = 11 - 3*jb
plug this into equation 2
3*jb + 5*tm = 16
3*jb + 5*(11-3*jb) = 16
3*jb + 55 - 15*jb = 16
-12*jb + 55 = 16
-12*jb = 16 - 55
-12*jb = -39
jb = -39/-12
jb = 3.25
then, plug the cost per pound of jelly beans back into the simplified equation 1
tm = 11 - 3*jb
tm = 11 - 3*3.25
tm = 1.25