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3 years ago

14

Situation D: Suppose that, in a one-minute period during an electrical storm, the number of lightning strikes on a radar antenna

follows a Poisson distribution with a mean of 2.40. Question D1: Find the probability that the antenna will be struck exactly once during this time period.

1 answer:

Crank3 years ago

3 0

Answer:

21.77% probability that the antenna will be struck exactly once during this time period.

Step-by-step explanation:

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.

In this question:

$\mu = 2.40$

Find the probability that the antenna will be struck exactly once during this time period.

This is P(X = 1).

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

$P(X = 1) = \frac{e^{-2.40}*2.40^{1}}{(1)!} = 0.2177$

21.77% probability that the antenna will be struck exactly once during this time period.

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Avery deposited $400 in an account that earned 2.47% interest compounded annually. She did not make additional deposits or withd

aev [14]

Answer:

Amount ($451.9), Interest ($51.9)

Step-by-step explanation:

We need to use the formula of A = P(1 + $\frac{r}{n}$ )^n*t

A = Total Amount

P = Principle/Deposited money

R = Annual Interest Rate

N = Number of times compounder per year

T = time in years

We have P = $400, r = 2.47%, n = 1 and t = 5 years.

Now lets plug it all in!

$A = 400 (1 + \frac{0.0247}{1})^{1*5}$

$A = 400 * 1.0247^5$

$A = 400 * 1.129753$

A = 451.9

Now we need to find the interest...

We will use A = P + I since A is 451.9 and P = 400

451.9 = 400 + I

I = 451.9 - 400

I = 51.9

6 0

2 years ago

PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

5 0

3 years ago

Let f(x) = 4x – 1, h(x) = -x-1.<br><br> Find (f o h)(6)<br><br> (foh)(6) =

Ludmilka [50]

Answer:

(foh)(6) = -29

Step-by-step explanation:

(f o h)(6) is f(h(x)) when x = 6.

We have that:

f(x) = 4x - 1

h(x) = -x-1

f(h(x)) = 4(-x-1) - 1 = -4x - 4 - 1 = -4x - 5

(foh)(6) = -4(6) - 5 = -29

(foh)(6) = -29

6 0

3 years ago

On a chilly day in New York, the temperature changed at -4 degrees per hour. How many hours did it take for the temperature to c

Aleks04 [339]

Answer:

9 hours

Step-by-step explanation:

36 degrees total /4 degrees per hour = 9 hours

6 0

3 years ago

Read 2 more answers

After 5 tests Dara's average score was 88 what score must she average on the next two tests to have a seven-test average of 90?

Tomtit [17]

After 5 tests, her average was 88. To have a seven-test average of 90, the total must be:

$90 \times 7 = 630$

Her average after 5 tests was 88. Her total score on the 5 tests is:

$88 \times 5 = 440$

Subtract:

$630-440 = 190$

Find the average by dividing by 2:

$190 \div 2 = 95$

Her average must be 95

3 0

3 years ago