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3 years ago

Find d/dx(e^3ln(x)). a. e^3lnx b.e^3ln(x)/x c.3e^3lnx d.3x^2

Mathematics

1 answer:

kow [346]3 years ago

3 0

Answer:

D. 3x²

General Formulas and Concepts:

Algebra II

If you raise e to the natural log, they cancel out and vice versa

Calculus

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$f(x)=e^{3lnx}$

Step 2: Rewrite

$f(x) = x^3$

Step 3: Take Derivative

Basic Power Rule: f'(x) = 3x³⁻¹
Simplify: f'(x) = 3x²

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A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.

Vilka [71]

The 90% , 99% confidence interval for the population mean is 32.145 < $\rm \mu$ < 35.855 and 31.093 < $\rm \mu$ < 36.907

<h3>What is Probability ?</h3>

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

$\rm CI = \mu + z \dfrac{s}{\sqrt n}$

$\rm \mu$ is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% $\rm \alpha / 2$ = 0.05

Z = 1.64

34 $\rm \pm$ 1.64 * 8 / √50

34 $\rm \pm$ 1.855

32.145 < $\rm \mu$ < 35.855

(b) The 99% confidence interval for the population mean

99% $\rm \alpha / 2$ = 0.005

Z=2.57

34 $\rm \pm$ 2.57 * 8 / √50

34 $\rm \pm$ 2.907

31.093 < $\rm \mu$ < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7 resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

To know more about Probability

brainly.com/question/11234923

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8 0

2 years ago

Write an equation of the translated function of the parent function f(x)=|x| with the following transformations:

MrRa [10]

Answer:

Option b

Step-by-step explanation:

To write the searched equation we must modify the function f (x) = | x | in the following way:

1. Do y = f(x + 4)

This operation horizontally shifts the function f(x) = | x | by a factor of 4 units to the left on the x axis.

y = | x +4 |

2. Do $y = f (\frac{1}{4}x)$

This operation horizontally expands the function f (x) = | x | in a factor of 4 units. $y = |\frac{1}{4}x + 1|$

3. Do $y = f(x)-4$

This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.

$y = |\frac{1}{4}x +1| -4$

4. After these transformations the function f(x) = | x | it looks like:

$f(x) = |\frac{1}{4}x +1| -4$

Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)

$f(-4) = |\frac{1}{4}(-4) +1| -4 = -4$

8 0

3 years ago

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t

Umnica [9.8K]

Step-by-step explanation:

the answer is in the image above

4 0

3 years ago

What is the missing value in the equation shown □ x1/10=0.034

grin007 [14]

Answer:

0.34

Step-by-step explanation:

Do the inverse operation so;

0.034 / 1/10 = 0.34

Now go back and subsitute,

0.34 * 1/10 = 0.034

4 0

3 years ago

Which type of equation can be used to model the data in the table below?

leva [86]

X| 2|4|6jsososodidididjfjfifififififofioff

7 0

3 years ago