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3 years ago

Find the value of x and y. Put a box around your answer

Mathematics

1 answer:

serg [7]3 years ago

6 0

Step 1

Find the value of y

we know that

(2y-30)=y ------> by corresponding angles

solve for y

2y-y=30

y=30°

Step 2

Find the value of x

we know that

x+y=180 ------> by supplementary angles

x+30=180

x=180-30

x=150°

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Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam

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Answer:

$P(A) = \frac{30}{100}$

$P(B) = \frac{77}{100}$

$P(A\ n\ B) = \frac{22}{100}$

$P(A\ u\ B) = \frac{85}{100}$

Step-by-step explanation:

Given

See attachment for proper format of table

$n = 100$ --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

In this row:

$Yes = 22$ and $No = 8$

So, we have:

$n(A) = Yes + No$

$n(A) = 22 + 8$

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P(A) is then calculated as:

$P(A) = \frac{n(A)}{Sample}$

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Solving (b): P(B)

Here, we only consider data in the Yes column.

In this column:

$(1) = 22$ $(2) = 25$ and $(3) = 30$

So, we have:

$n(B) = (1) + (2) + (3)$

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P(B) is then calculated as:

$P(B) = \frac{n(B)}{Sample}$

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Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

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And it is represented with; n(A n B)

So, we have:

$n(A\ n\ B) = 22$

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$P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}$

$P(A\ n\ B) = \frac{22}{100}$

Solving (d): P(A u B)

This is calculated as:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$

This gives:

$P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}$

Take LCM

$P(A\ u\ B) = \frac{30+77-22}{100}$

$P(A\ u\ B) = \frac{85}{100}$

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