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3 years ago

Please help with my homework

Mathematics

2 answers:

nlexa [21]3 years ago

8 0

The user @Hrishii is correct about the value of angle B.

Once you know all three angles, you can use the law of sines to find the missing sides.

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Let's use the law of sines to find side b

b/sin(B) = a/sin(A)

b/sin(22) = 1/sin(18)

b = sin(22)*1/sin(18)

b = 1.21225240111352

b = 1.21 rounding to two decimal places

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Repeat for side c

c/sin(C) = a/sin(A)

c/sin(140) = 1/sin(18)

c = sin(140)*1/sin(18)

c = 2.08010440004024

c = 2.08 rounding to two decimal places

==============================================

The fully solved triangle is

A = 18 degrees

<h3>B = 22 degrees</h3>

C = 140 degrees

a = 1

decimal values are approximate

Lina20 [59]3 years ago

3 0

Step-by-step explanation:

$\angle \: A + \angle \: B + \angle \: C = 180 \degree \\ \therefore \: 18 \degree + \angle \: B + 140 \degree = 180 \degree \\ \therefore \: \angle \: B + 158 \degree = 180 \degree \\ \therefore \: \angle \: B = 180 \degree - 158 \degree \\ \huge \red{ \boxed{\therefore \: \angle \: B = 22 \degree}}$

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Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have sol

aalyn [17]

Answer:

(a) 0.09

(b) 0.06

(d) 0.9118

(e) 0.03

Step-by-step explanation:

Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.

The proportion of boards having solder defects is, P (A) = 0.06.

The proportion of boards having surface-finish defects is, P (B) = 0.03.

It is provided that the events A and B are independent, i.e.

$P(A\cap B)=P(A)\times P(B)$

(a)

Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:

= P (A or B) + P (A and B)

$=P(A)+P(B)-P(A\cap B)+P(A\cap B)\\=P(A)+P(B)\\=0.06+0.03\\=0.09$

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.

(b)

The probability that a solder defect is found is 0.06.

(c)

The probability that both defect are found is:

$P(A\cap B)=P(A)\times P(B)\\=0.06\times0.03\\=0.0018$

Thus, the probability that both defect are found is 0.0018.

(d)

The probability that none of the defect is found is:

$P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118$

Thus, the probability that none of the defect is found is 0.9118.

(e)

The probability that the defect found is a surface finish is 0.03.

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