MATHEMATICS COLLEGE

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3

Answers

Answer 1

Answer:

$(d(lnx))/(dx)=(1)/(x)$

Answer:

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Step-by-step explanation:

We are given that a function

$y=e^(x^2)ln(4x^3)$

We have to differentiate w.r.t x

$(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2$

By using formula

$(d(lnx))/(dx)=(1)/(x)$

$(d(e^x))/(dx)=e^x$

$(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))$

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Hence, the derivative of function

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

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If f(x) = 2x – 5 and g(x) = x +4, then f(g(2)) =

Answers

Answer:

Step-by-step explanation:

f(g(2))

f(x+4) and you would replace x with two, so you would get

f(2+4) = f(6)

You would then plug in 6 for the x in the f(x) equation:

2(6) - 5 = 12-5 = 7

What is the solution to -4 (2x +6)=-24

Answers

Answer:

x=0

Step-by-step explanation:

Distribute -4

-8x - 24 = -24

Add 24 to both sides

-8x = 0

x=0

Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4(2x+6)=−24

(−4)(2x)+(−4)(6)=−24(Distribute)

−8x+−24=−24

−8x−24=−24

Step 2: Add 24 to both sides.

−8x−24+24=−24+24

−8x=0

Step 3: Divide both sides by -8.

−8x

−8

x=0

Answer:

x=0

Salma sold 600 liters of soda at a baseball game. How much is this in milliliters?Be sure to include the correct unit in your answer.
mL
mg
kL
kg

Answers

Final answer:

600 liters of soda is equal to 600,000 milliliters.

Explanation:

To convert liters to milliliters, we multiply by 1000 since there are 1000 milliliters in one liter. So, 600 liters of soda is equal to 600,000 milliliters.

Learn more about Converting units here:

brainly.com/question/31429209

Suppose 41%41% of American singers are Grammy award winners. If a random sample of size 860860 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%5%?

Answers

Answer:

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{(p(1-p))/(n)}$

In this question:

$n = 860, p = 0.41$

$\mu = 0.41, s = \sqrt{(0.41*0.59)/(860)} = 0.0168$

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%?

This is the pvalue of Z when X = 0.41 + 0.05 = 0.46 subtracted by the pvalue of Z when X = 0.41 - 0.05 = 0.36. So

X = 0.46

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (0.46 - 0.41)/(0.0168)$

$Z = 2.98$

$Z = 2.98$ has a pvalue of 0.9986

X = 0.36

$Z = (X - \mu)/(s)$

$Z = (0.36 - 0.41)/(0.0168)$

$Z = -2.98$

$Z = -2.98$ has a pvalue of 0.0014

0.9986 - 0.0014 = 0.9972

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

Recent statistics show that 62% of people wash their hands after using the restroom.If you shake hands with three random people, what is the probability that all of them washed their hands after previously using the restroom?

Answers

Answer:

p = 0.62

Step-by-step explanation:

Probability that all three has washed their hands after previously using the restroom = 0.2383 approx. The probability that all of the 3 washed their hands after previously using the restroom is 0.2383. Explanation: It is given that, 62% of people wash their hands after using the restroom that is p = 0.62.

X/3+11=16
What is the value of x

Answers

Answer:

x = 15

Move 11 to the other side, with "16" after the equal sign.

We need to subtract: 16-11 = 5

x/3 = 5

x = 5 x 3

x = 15

To double check...

15/3 + 11 = 16

5 + 11 = 16

PS: In algebra we actually use "*" but for the sake of it I will use "x"

Have a nice day!

Answer:

Step-by-step explanation:

First you take all of the non-variables on to the other side of the equal sign. It then turns out to be SUPER easy. x/3 = 16 - 11

x/3 = 5

x = 5*3

x = 15

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