PLEASE HELP!!!

Find four numbers that are evenly divisible by both 2 and 9

Hatshy [7]

Answer:

18

36

72

144

Step-by-step explanation:

For numbers to be divisible by 2 they must end in an even number

For numbers to be divisible by 9 the sum of the digits must be divisible by 9

3 0

2 years ago

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose

Furkat [3]

Answer:

a) 0.164 = 16.4% probability that a disk has exactly one missing pulse

b) 0.017 = 1.7% probability that a disk has at least two missing pulses

c) 0.671 = 67.1% probability that neither contains a missing pulse

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

In which

x is the number of sucesses

$
e = 2.71828$ is the Euler number

$\mu$ is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Poisson mean:

$\mu = 0.2$

a. What is the probability that a disk has exactly one missing pulse?

One disk, so Poisson.

This is P(X = 1).

$P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164
$

0.164 = 16.4% probability that a disk has exactly one missing pulse

b. What is the probability that a disk has at least two missing pulses?

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

$P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819$

$P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164
$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017$

0.017 = 1.7% probability that a disk has at least two missing pulses

c. If two disks are independently selected, what is the probability that neither contains a missing pulse?

Two disks, so binomial with n = 2.

A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so $p = 0.181$

We want to find P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671$

0.671 = 67.1% probability that neither contains a missing pulse

8 0

3 years ago

Please Elijah and Aubrey have summer jobs Elijah deposits the same amount of money in his account every week the equation is y =

Anika [276]

Answer:

Part a) $y=125x+23$

Part b) The graph of the equation for Aubrey's balance is parallel to the graph of Elijah's balance

Part c) Parallel graphs mean that their slopes are the same and that they deposited the same amount of $125 per week into their account balance during the summer.

Step-by-step explanation:

The correct question is

Elijah and Aubrey have summer jobs. Elijah deposits the same

amount of money in his account every week. The equation y = 125x + 72 represents his bank balance any given week of the summer. Aubrey also deposits the same amount into her account every week. At the end of the third week she has $398. At the end of the sixth week she has $773.

a. Write an equation to represent Aubrey's bank balance any given week of the summer.

b. Would the graph of the equation for Aubrey's balance be parallel to the graph of Elijah's balance? Explain.

c. What do the parallel graphs mean in terms of the situation?

Part a)

Let

x ----> the number of weeks

y ----> represent bank's balance

we know that

Elijah

$y=125x+72$ -----> equation A

Aubrey

we have the points

(3,398) and (6,773)

Find the slope m

$m=(773-398)/(6-3)$

$m=375/3$

$m=125$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=125$

$point\ (3,398)$

substitute

$y-398=125(x-3)$ ----> equation in point slope form

Convert to slope intercept form

$y=mx+b$

$y-398=125x-375$

$y=125x-375+398$

$y=125x+23$ ----> Aubrey's bank balance

Part b)

Compare the equations

$y=125x+72$ ----> Elija's bank balance

$y=125x+23$ ----> Aubrey's bank balance

Remember that

If two lines are parallel, then their slopes are equal

In this problem the slopes are equal

$m=125\frac{\$}{week}$

therefore

The graph of the equation for Aubrey's balance is parallel to the graph of Elijah's balance

Part c) Parallel graphs mean that their slopes are the same and that they deposited the same amount of $125 per week into their account balance during the summer.

5 0

3 years ago

Your company has 1486 employees in the maintenance department and 1985 employees in the operations department. About how many em

kupik [55]

3471(1486+1985) rounded to the nearest thousand will be 3000......................
hope its correct

6 0

3 years ago

Which equation represents this situation?

aalyn [17]

Answer:

dirk =13.25 hours

charlie =11 75 hours

Step-by-step explanation:

c+d=25------(1)

d-1.5=c-----(2)

from (1),

c+d=25

c=25-d-----(3)

substitude (3) into (2)

d-1.5=c

d-1.5=25-d

2d=26.5

d=13.25

if d=13.25 hours

c+d=25

c+13.25=25

c=25-13.25

c=11.75

7 0

3 years ago