Select the graph that would represent the best presentation of the solution set. |y+2| > 6

Mathematics

1 answer:

umka2103 [35]3 years ago

4 0

Answer:

Step-by-step explanation:

make 2 equations:

-equation 1: y+2>6

equation 2: -y-2>6

Then solve for each, and you will end up with -8>y>4

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Suppose 80% of people enjoy swimming. Suppose 70% of people enjoy running.

Ede4ka [16]

Answer:

95%

Step-by-step explanation:

In this case we can apply a formula that tells us that:

# (AUB) = #A + #B - #AnB

Where A would be the ones who enjoy swimming and B would be the ones who enjoy running. AnB is the intersection of both sets, that is, those who enjoy doing both things, these values we have, if we replace them we have left:

#(AUB) = 80% + 70% - 55%

#(AUB) = 95%

Which means that 95% of people enjoy either swimming or running

6 0

3 years ago

Find the derivative.

krek1111 [17]

Answer:

$\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Expanding/Factoring

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{\sqrt{x}}{e^x}$

Step 2: Differentiate

Derivative Rule [Quotient Rule]: $\displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}$
Basic Power Rule: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}$
Exponential Differentiation: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}$
Simplify: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}$
Rewrite: $\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}$
Factor: $\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$