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3 years ago

From a sample of 120 batteries, 3 are faulty. Work out the percentage of faulty batteries.

Mathematics

1 answer:

IrinaVladis [17]3 years ago

7 0

Answer:

2.5%

Step-by-step explanation:

% = (faulty batteries / total batteries) x 100

= (3/120) x 100

= 0.025 x 100

= 2.5

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$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
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When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
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and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

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3 years ago

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Answer:

Step-by-step explanation:

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The Centers for Disease Control and Prevention (CDC) report that gastroenteritis, or stomach flu, is the most frequently reporte

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b. <u>No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.</u>

Step-by-step explanation:

from the question, the number of successes is equal to 30

and it is more than the number of failures

for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.

if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.

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