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3 years ago

9

What is the answer to this equation

\frac{x}{4}=5 " alt=" \frac{x}{4}=5 " align="absmiddle" class="latex-formula">

1 answer:

Marizza181 [45]3 years ago

8 0

Multiply both sides by 4 to isolate the x term.

x = 5 × 4

x = 20

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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:

<u>Algebra I</u>

Terms/Coefficients

Expanding/Factoring

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<em>Identify</em>

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

<u>Step 2: Differentiate</u>

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

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

2 years ago

Suppose that scores on the mathematics part of a test for eighth-grade students follow a Normal distribution with standard devia

riadik2000 [5.3K]

Answer:

We need an SRS of scores of at least 153.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large an SRS of scores must you choose?

This is at least n, in which n is found when $M = 20, \sigma = 150$ . So

$M = z*\frac{\sigma}{\sqrt{n}}$

$20 = 1.645*\frac{150}{\sqrt{n}}$

$20\sqrt{n} = 1.645*150$

$\sqrt{n} = \frac{1.645*150}{20}$

$\sqrt{n} = 12.3375$

$(\sqrt{n})^{2} = (12.3375)^{2}$

$n = 152.2$

Rounding to the next whole number, 153

We need an SRS of scores of at least 153.

8 0

3 years ago

What is the LCM of 6, 10, and 15?<br> 50

Thepotemich [5.8K]

Answer:

okay

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

How do you graph the equation y=|x|?

Rufina [12.5K]

graph looks like the letter v

2 around x means no matter what value x is y will be positive

plot points would be

(-2,2) (-1,1) (0,0) (1,1) (2,2)

8 0

3 years ago

Divide $150 into the ratio 2:5:3

pentagon [3]

Answer:

$30, $75, $45

Step-by-step explanation:

We can set up an equation, where x is an unknown value:

2x+5x+3x=150

10x = 150

x=15

Now that we know what x is, we can plug x in to solve for 2x, 5x, and 3x:

2x=2*15=30

5x=5*15=75

3x=3*15=45

Therefore, the answer is $30, $75, $45

5 0

2 years ago