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3 years ago

In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.

Mathematics

1 answer:

kykrilka [37]3 years ago

8 0

Answer:

$c=13.1\ units$

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

A+B+C=180°

we have

A=57°

B=37°

substitute

57°+37°+C=180°

94°+C=180°

C=180°-94°=86°

step 2

Find the measure of side c

Applying the law of sines

$\frac{a}{sin(A)}=\frac{c}{sin(C)}$

substitute

$\frac{11}{sin(57\°)}=\frac{c}{sin(86\°)}$

$c=\frac{11}{sin(57\°)}sin(86\°)$

$c=13.1\ units$

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Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

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So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

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Denote the probability od acceptance of a shipment by $p_2$ .

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Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

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$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

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