At the end of a snow storm, Amelia saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. After the storm, the snow started melting at a rate of 1.5 inches per hour and it is known that 4 hours after the storm ended, the depth of snow was down to 12 inches. Write an equation for S, in terms of t, representing the depth of snow on Amelia's lawn, in inches, t hours after the snow stopped falling.

Answer:

a

  [tex] P(X = 0) =  0.6065 [/tex]

b

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

c

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Step-by-step explanation:

From the question we are told that

  The rate  is [tex]\lambda =  \frac{1}{2}\   hr^{-1}[/tex]    =  0.5 / hr

  Generally  Poisson distribution formula is mathematically represented as

       [tex]P(X = x) =  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

Generally the probability that no error occurred during a day is mathematically represented as  

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

   [tex][tex]P(X = 0) =  \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}[/tex]

=>  [tex] P(X = 0) =  0.6065 [/tex]

Generally the probability that  a critical error occurs since the start of a day is mathematically represented as

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

      [tex]P(x \ge 25 ) =  1 - P(x <  25 )[/tex]

Here

     [tex]P(x <  25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}[/tex]

=>   [tex]P(x <  25 ) =  \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + 6.0*10^{-32}[/tex]

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

Considering question c

Here  t =  2  

Gnerally given that the  system just started up and an error occurred  the probability the next reset will occur within 2 hours

[tex]P(x \le 5 ) =  \sum_{n=0}^{5}  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{(0.5 *  2) ^ 0 e^{- 0.5  * 2 }}{0!} + \cdots  +   \frac{(0.5 *  2) ^ 5  e^{- 0.5  * 2 }}{5!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{1* 2.7183 }{1 } + \cdots  +   \frac{1  *2.7183 }{120}[/tex]

=>  [tex]P(x \le 5 ) =   2.7183 + \cdots  +   0.0226525[/tex]

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Answer:

There is something wrong with the question because you cannot earn more interest during a year than the principal if you earn only 9% or 11%. You would have to earn more than 100%, so I will do this calculation based on $17,170 (not $171,700) earned in interest per year.

let S = amount received from short term note, and L = amount received from long term note

0.11S + 0.09L = 17170

S + L = 170000

S = 170000 - L

0.11 (170000 - L) + 0.09L = 17170

18700 - 0.11L + 0.09L = 17170

1530 - 0.02L = 0

1530 = 0.02L

L = 1530 / 0.02 = $76,500

S = 170000 - 76500 = $93,500

Answer:

-(-4)(-6)*3/5(10+15)

when there is a (-) in front of an expression in parentheses, change the sing of each term in the expression.

4*(-6)*3/5*(10+15)

Add the numbers (10+15)

4(-6)*3/5*25

multiplying an odd number of negative terms makes the product negative

-4*6*3/5*25

reduce the number with the greatest common factor 5

-4*6*3*5

calculate the product

solution

-360

Answer:

x = 9°

y = 119°

Step-by-step explanation:

Given,

y° = 61°+58° { the exterior angle formed by producing the side of triangle is equal to two non-adjacent angle}

or, y° = 119°

therefore, y° = 119°

Now,

52°+y°+x° = 180°{the sum of angle if triangle is 180°}

or, 52°+119°+x°= 180°

or, 171°+x° = 180°

or, x° = 180°-171°

or, x° = 9°

therefore, x° = 9°

Answer:

that what

Step-by-step explanation:

Answer:

not sure what you need but I would be happy to help

Answer:

i am pretty sure it would be 8

Step-by-step explanation:

when it rounds to 2 but also rounds to 100, 8 would be the best bet.

Answer: 16.4cm

Step-by-step explanation: 4cm=20km

82/20 is 4.1. 20 multiplied by 4.1 and you get 16.4cm

Answer:

A.) TRUE

B.) TRUE

C.) FALSE

D.) FALSE

E.) FALSE

Step-by-step explanation:

Given that :

SMARTPHONE A:

RAM : 256 MB

ROM : 32 GB

CAMERA RESOLUTION : 8 MP

SMARTPHONE B:

RAM : 288 MB

ROM : 64 GB

CAMERA RESOLUTION : 4 MP

SMARTPHONE C:

RAM : 128 MB

ROM : 32 GB

CAMERA RESOLUTION : 5 MP

Determine the truth value of each of these propositions.

A) Smartphone B has the most RAM of these three smart- phones.

TRUE ; 288 > (256 and 128)

B) Smartphone C has more R O M o r a higher resolution camera than Smartphone B.

C ROM > B ROM = FALSE

C CAMERA RESOLUTION > B camera resolution = TRUE

FALSE or TRUE = TRUE

C.) Smartphone B has more RAM, more R OM, and a higher resolution camera than Smartphone A.

RAM = TRUE ; ROM = TRUE ; CAMERA RESOLUTION = FALSE

TRUE and TRUE and FALSE = FALSE

d) If Smartphone B has more RAM and more R O M than Smartphone C, then it also has a higher resolution camera.

CAMERA RESOLUTION ON SMARTPHONE B IS LESS, HENCE, STATEMENT = FALSE

e) Smartphone A has more RAM than Smartphone B i f and only if Smartphone B has more RAM than Smart- phone A.

1st statement = FALSE

2nd condition = TRUE

FALSE and TRUE

= FALSE

Answer:

54 + 42 = 6(9 + 7)

Step-by-step explanation:

Using distributive property on the right side of the equality, you multiply 6 and nine and 6 and 7 to get rid of the parenthesis.

Answer:

its the last one

Step-by-step explanation:

Answer:

2 2/3 or 8/3

Step-by-step explanation:

Formula for each side = 2/3 x 2/3

2/3 x 2/3 = 4/9

6 sides

4/9 x 6 or 4/9 + 4/9 + 4/9 + 4/9 + 4/9 + 4/9

=2 2/3 or 8/3

Answer:

2 2/3

Is the answer

Answer:

hi to what. good bye???????

Answer:

look im putting this here bc i have to answer 50 questionsfor a quest sdo dont report me ;-;

Step-by-step explanation:

Answer:

8 quarts

Step-by-step explanation:

no explanation needed this should be correct.

Answer:

-5/6,-1/4,-0.11,0.567

Step-by-step explanation:

Answer:

z=2

Step-by-step explanation:

Just solve

1 + z = 3 (minus 1 on both sides)

z = 2

Plug in

3=(2+1)

3 = 3

Answer:

97.65

Step-by-step explanation:

97.65

Step-by-step explanation

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of at most 2 red cards is 0.5.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Using the given information the number of cards is 24 out of which 12 are red. Therefore, the probability of getting a red card is 0.5.

A) All red cards.

P(X=5) = ⁵C₅ (0.5⁵) (0.5⁰)

            = 0.03125

B.) at least two red cards.

P(X≥2) = 1 - ⁵C₀ (0.5⁰) (0.5⁵) - ⁵C₁ (0.5¹) (0.5⁴)

= 0.8125

C.)  At most 2 red cards.

P(X≤2) = ⁵C₀ (0.5⁰) (0.5⁵) + ⁵C₁ (0.5¹) (0.5⁴) + ⁵C₂ (0.5²) (0.5³)

           = 0.5

Learn more about Binomial Distribution:

https://brainly.com/question/14565246

#SPJ2

Answer:

(6,11)

I can confirm that this question is right.

12/2      22/2

(6   ,        11)

Answer:

The population will reach 980,000 in 26 years approximately.

Step-by-step explanation:

Initial Population of city = 490000

Rate of increase in population = 2.75%

We are supposed to find Approximately when  will the population reach 980,000

Formula : [tex]N(t)=N_0(1+r)^t[/tex]

N(t)= population after t years

[tex]N_0=[/tex] Initial population

t - time

r = rate of interest in decimals

So,[tex]980000=490000(1+\frac{2.75}{100})^t[/tex]

t=25.55

So, the population will reach 980,000 in 26 years approximately.

Answer:

4 students got three answers incorrectly.

The number of students got 3 answers incorrect is 4.

A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.

Now from the given histogram following informations are extracted-

Number of students got 1 answer incorrect = 2

Number of students got 2 answer incorrect = 3

Number of students got 3 answer incorrect = 4

Number of students got 4 answer incorrect = 1  

Number of students got 5 answer incorrect = 2

Thus from above we can conclude that,

Number of students got 3 answer incorrect = 4

Thus, the number of students got 3 answers incorrect is 4.

To learn more about histogram :

brainly.com/question/1593386

#SPJ2

Answer:

-15, -9, -3, 3

Step-by-step explanation:

First One:

y =3(-4)-3 is -15

Second:

y= 3(-2)-3 is -9

Third:

y= 3(0)-3 is -3

Last One:

y= 3(2)-3 is 3

Answer:hbjnhbgfvrdfghjhgfdfghjhgfghjkl

Answer:

Cash it at the issuing bank (this is the bank name that is pre-printed on the check)

Cash a check at a retailer that cashes checks (discount department store, grocery stores, etc.)

Cash the check at a check-cashing store.

Deposit at an ATM onto a pre-paid card account or checkless debit card account.

Step-by-step explanation:

Answer:

Amscot?

Step-by-step explanation:

Answer:

20°

Step-by-step explanation:

Step 1:

x + 40° = 3x       Vertical ∠'s

Step 2:

40° = 2x      Subtract x on both sides

Step 3:

x = 40° ÷ 2     Divide

Answer:

x = 20°

Hope This Helps :)

Answer:

Option C: an outline of a pine tree

Step-by-step explanation:

Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.

A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.

Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".

Thus, it is a bimorphic shape.

Answer:

C. an outline of a pine tree

Step-by-step explanation:

I just took the test!

Answer:

10%

Step-by-step explanation:

(a) What percentage of meals had less than 10 grams of fat?

(b) Round your answer to the nearest tenth of a percent.

To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.

(A) Total number of meals = 550

Number of meals having less than 10 grams of fat = 77

Percentage of meals having less than 10 grams of fat = 77/550 × 100

= 0.14 × 100 = 14%

(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').

The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%