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3 years ago

8

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from

each container, what is the probability that only one of the items is defective?

1 answer:

e-lub [12.9K]3 years ago

4 0

Answer:

The required probability is $\frac{19}{40}$

Step-by-step explanation:

The probability of obtaining a defective item from container 1 is $P(E_1)=\frac{3}{8}$

The probability of obtaining a good item from container 1 is $P(E_1)=\frac{5}{8}$

The probability of obtaining a defective item from container 2 is $P(E_1)=\frac{2}{5}$

The probability of obtaining a good item from container 2 is $P(E_1)=\frac{3}{5}$

The cases of the event are

1)Defective item is drawn from container 1 and good item is drawn from container 2

2)Defective item is drawn from container 2 and good item is drawn from container 1

Thus the required probability is the sum of above 2 cases

$P(Event)=\frac{3}{8}\times \frac{3}{5}+\frac{5}{8}\times \frac{2}{5}=\frac{19}{40}$

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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45$

To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

5 0

3 years ago

Between 02 30 and 05 30,the same day,the volume of water in a reservoir increased from 6000 L to 18 000 L.What was the average r

irinina [24]

Answer:

4,000 L/h

Step-by-step explanation:

First we'll find the amount of the change.

18,000 - 6,000 = 12,000 L

The time of the volume change was 3 hours: 0230 - 0530

Since we're looking for liters per hour, we will divide the liters (12,000) by the hours (3)

12,000/3 = 4,000 L/h

3 0

2 years ago

Help!! is it $486?

xxTIMURxx [149]

The answer on APEX would be $2430

8 0

3 years ago

Read 2 more answers

Please help, need answer fast!

AleksandrR [38]

The answer is
B. 13ab

5ab+9ab-ab
=(5ab+9ab)-ab
14ab-ab
=13ab

Hope it helped : )

3 0

3 years ago

Can someone help me do this

SCORPION-xisa [38]

Answer:

6

Step-by-step explanation:

Find the missing angle:

180⁰ - 82⁰ = 98⁰

Find the sum of the angles given without the missing angle:

180⁰ - 98⁰ = 82⁰

The sum of both the angles is 82⁰

Write an equation:

5x + 8 + 6x + 8 = 82⁰

Collect the like terms together

11x + 16⁰ = 82⁰

Subtract 16⁰ from both sides

11x = 66⁰

Divide by 11 on both sides

x = 6⁰

8 0

2 years ago