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LUCKY_DIMON [66]
2 years ago
13

Out of 190 CDs tested, 26 are defective. Estimate the number of defective CDs in a batch of 1000.

Mathematics
1 answer:
liberstina [14]2 years ago
3 0

Divide the number of defective by the number checked:

26/190 = 0.1368

Multiply that by 1000:

0.1368 x 1000 = 136.8

Round up to 137

Out of 1000 cd’s 137 would be defective

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Solve for r. 35r-21<-35r+19
Mnenie [13.5K]

Good morning ☕️

Answer:

r < \frac{4}{7}

Step-by-step explanation:

35r-21 < -35r+19

⇌ 35r + 35r < 19 + 21

⇌ 70r < 40

⇌ r < 40/70

⇌ r < 4/7

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5 0
3 years ago
A striped ball has 6 purple and 5 yellow stripes which are all the same size. The radius of the spherical ball is 13 in. The sur
tiny-mole [99]

Answer:

https://bridgeprepriverview.com/ourpages/auto/2020/2/4/54307042/Student%20textbook.pdf

their is the link for the answers.

Step-by-step explanation:

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3 years ago
Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers
lora16 [44]

Answer:

Part A)

\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}

Where <em>P</em> is the number of eggs laid, <em>x</em> is the number of workers, and <em>y</em> is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of <em>x</em>. We can raise both sides to 10/7. Hence:

\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}

Simplify:

\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y

Divide both sides by<em> </em>the <em>x</em> term to acquire:

\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}

Take the derivative of both sides with respect to <em>x: </em>

\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]

Apply power rule. Note that P is simply a constant. Hence:

\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})

Simplify. Hence, our derivative is:

\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}

Part B)

We want to evaluate the derivative when <em>x</em> is 30 and when <em>y</em> is $10,000.

First, we will need to find <em>P</em>. Our original equations tells us that:

P=x^{0.3}y^{0.7}

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>is:

P=(30)^{0.3}(10000)^{0.7}

Therefore, for our derivative, we will have:

\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)

Use a calculator. So:

\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0
3 years ago
an outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is mor
Ira Lisetskai [31]

Supposing a normal distribution, we find that:

The diameter of the smallest tree that is an outlier is of 16.36 inches.

--------------------------------

We suppose that tree diameters are normally distributed with <u>mean 8.8 inches and standard deviation 2.8 inches.</u>

<u />

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}

  • 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, which is the percentile of X.<u> </u>

<u />

In this problem:

  • Mean of 8.8 inches, thus \mu = 8.8.
  • Standard deviation of 2.8 inches, thus \sigma = 2.8.

<u />

The interquartile range(IQR) is the difference between the 75th and the 25th percentile.

<u />

25th percentile:

  • X when Z has a p-value of 0.25, so X when Z = -0.675.

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

-0.675 = \frac{X - 8.8}{2.8}

X - 8.8 = -0.675(2.8)

X = 6.91

75th percentile:

  • X when Z has a p-value of 0.75, so X when Z = 0.675.

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

0.675 = \frac{X - 8.8}{2.8}

X - 8.8 = 0.675(2.8)

X = 10.69

The IQR is:

IQR = 10.69 - 6.91 = 3.78

What is the diameter, in inches, of the smallest tree that is an outlier?

  • The diameter is <u>1.5IQR above the 75th percentile</u>, thus:

10.69 + 1.5(3.78) = 16.36

The diameter of the smallest tree that is an outlier is of 16.36 inches.

<u />

A similar problem is given at brainly.com/question/15683591

3 0
2 years ago
Place the steps for finding f(x) in the correct order.
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The answer is C
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Someone told me
8 0
2 years ago
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