What kind of room has no doors?

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour

Alexus [3.1K]

Answer:

a) the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

c) the required probability is 0.2000

Step-by-step explanation:

Given the data in the question;

During a specific ten-hour period, one defective circuit board was found.

Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.

Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.

f(y) = $\left \{ {{\frac{1}{b-a} }\\\ }} \right _0$ ; ( a ≤ y ≤ b ) $_{elsewhere$

= $\left \{ {{\frac{1}{10-0} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

f(y) = $\left \{ {{\frac{1}{10} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

Now,

a) the probability that it was produced during the first hour of operation during that period;

P( Y < 1 ) = $\int\limits^1_0 {f(y)} \, dy$

we substitute

= $\int\limits^1_0 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^1_0$

= $\frac{1}{10} [ 1 - 0 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) The probability that it was produced during the last hour of operation during that period.

P( Y > 9 ) = $\int\limits^{10}_9 {f(y)} \, dy$

we substitute

= $\int\limits^{10}_9 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^{10}_9$

= $\frac{1}{10} [ 10 - 9 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

c)

no defective circuit boards were produced during the first five hours of operation.

probability that the defective board was manufactured during the sixth hour will be;

P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )

= P( 5 < Y < 6 ) / P( Y > 5 )

we substitute

$= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)$

$= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)$

= ( 6-5 ) / ( 10 - 5 )

= 0.2000

Therefore, the required probability is 0.2000

4 0

3 years ago

If the mine winch drum diameter is 6 m, calculate how far the cage will drop for each single rotation of the drum.use formular c

frozen [14]

The cage will drop 18.84m for each single rotation of the drum.

It is given that the diameter of the mine winch, d= 6 m.

We can calculate that how far the cage will drop for each single rotation of the drum by using the formula of the circumference.

Circumference, c = 2πr

where,

r = d/2 (radius of the mine winch)

r = 6/2

⇒ r = 3m

Circumference, c = 2πr

⇒ c = 2π×(3)

⇒ c = 6π

⇒ c = 18.84m

Hence, the cage will drop 18.84m for each single rotation of the drum.

For similar questions, visit:

brainly.com/question/23986334

#SPJ9

6 0

2 years ago

Greatest percent

cricket20 [7]

Answer:

Percent change from 15 to 18.

You need to divide the numbers, but which one goes on top?

You know the number increases from 15 to 18, so the percentage must be greater than 100%.

The only way to get a number greater than 100% is to put the larger number on top.

Therefore, the answer is 18/15 = 1.2

Multiply by 100 to get a %

1.2 * 100 = 120%

2. Calculate percentage change

from V1 = 5 to V2 = 8

ans= 60%

overall answer gain of 15 yards and 18 yards

8 0

3 years ago

Can someone explain how to do these. Also on number 2, how do u find the ratio ?

KIM [24]

9514 1404 393

Answer:

2. D

3. B

4. D

5. A

Step-by-step explanation:

2. Write the ratio using the given words, then fill in the corresponding numbers. Factor out the greatest common factor.*

soccer players : volleyball players = 84 : 36 = 12·7 : 12·3 = 7 : 3

__

3. The angle bisector has angle marks on either side of it. The only angle marks are at angle G, where GL is the bisector.

__

4. The median is drawn from a vertex to the midpoint of the opposite side. The only side with a midpoint marked is IG with midpoint J. The median is HJ.

__

5. An altitude is drawn from a vertex to the opposite side, where it meets at right angles. Two right angles are shown: at J and at K. The perpendicular line at J does not meet any vertex. The perpendicular line at K meets vertex I, so KI is the altitude.

_____

* For larger numbers, or ones whose factors you aren't familiar with, it can be useful to know Euclid's method for finding the greatest common factor (GCF). Divide the larger number by the smaller and keep the remainder. If the remainder is 0, the smaller is the GCF. If not, replace the larger number with the remainder and repeat.

Here, that looks like ...

84 / 36 = 2 r 12

36 / 12 = 3 r 0 . . . . . 12 is the GCF

4 0

3 years ago

Simplify 8(x + 6) - 5(x + 8). 3x + 8 13x - 8 3x + 42

charle [14.2K]

Answer:

x=14

Step-by-step explanation:

after you take 3x+42 you have to divid by 3 and get

x=14

8 0

3 years ago