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stepladder [879]
3 years ago
5

Find the derivative. 4) y=(4x+3)^5

Mathematics
1 answer:
Feliz [49]3 years ago
7 0

Answer:

y'=20(4x+3)^{4}

Step-by-step explanation:

We can find the derivative using the <u>chain rule.</u>  

To get the derivative of an expression with an exponent you multiply the expression by the exponent and raise it to the power of the exponent minus one.

Then multiply it by the derivative of the expression inside the parentheses.  

The derivative of 4x+3 is 4, so multiply the rest by 4.  

Therefore the derivative is:

y'=5(4x+3)^{4} *4\\y'=20(4x+3)^{4}

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Find the inverse of h(x)=(2x-4)/3
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Answer:

The inverse of the h(x) is h^{-1}(x)=\frac{3x}{2}+2           Step-by-step explanation:

Given : Expression h(x)=\frac{2x-4}{3}

To find : The inverse of the expression ?

Solution :

Expression h(x)=\frac{2x-4}{3}

Let, h(x)=y then  y=\frac{2x-4}{3}

For inverse we replace the value of x and y and find the value of y in terms of x.

Replace the value of x and y,

x=\frac{2y-4}{3}

Solve for y by cross multiply,

3x=2y-4

Adding 4 both side,

3x+4=2y

Dividing by 2 both side,

\frac{3x+4}{2}=y

Therefore, The inverse of the h(x) is h^{-1}(x)=\frac{3x}{2}+2

5 0
3 years ago
Read 2 more answers
According to the Bureau of Labor Statistics, the average weekly pay for a U.S. production worker was $441.84 in 1998 (The World
Oksanka [162]

Using the normal distribution, it is found that a production worker has to make $542.64 a week to be in the top 30% of wage earners.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It 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, which is the percentile of X.

In this problem:

  • The mean is of \mu = 441.84.
  • The standard deviation is of \sigma = 120.
  • The lower bound of the top 30% is the 70th percentile, which is X when Z has a p-value of 0.7, so <u>X when Z = 0.84.</u>

Z = \frac{X - \mu}{\sigma}

0.84 = \frac{X - 441.84}{120}

X - 441.84 = 0.84(120)

X = 542.64

A production worker has to make $542.64 a week to be in the top 30% of wage earners.

You can learn more about the normal distribution at brainly.com/question/24663213

3 0
2 years ago
Sarah wants to buy a new pair of sandals. The sandals are $45 and she has a coupon for 30% off. What is the price of her sandles
baherus [9]

Answer:

$31.5

Step-by-step explanation:

-$45

-30 percent off of $45

30 times 45 divided by 100

1350/100

13.5

45-13.5

$31.5

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Step-by-step explanation:

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hope it helps

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3.00 + 0.50m = 9.50

2. true 
5. true


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