" Explain how you used the bar model in Exercise 2 to solve the problem "

Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the firs

strojnjashka [21]

Answer:

Answer has explained below.

Step-by-step explanation:

Consider the function is:

F(x) = 25x3 – 6x2 +7x -88

Differentiate with respect to x, we get

F’(x) = 25. 3x2 – 6.2x + 7

= 75x2 – 12x +7

At x = 2, we have

F (2) = 25(2)3 – 6(2)2 + 7(2)-88

=102

And f’(2) = 75(2)2 – 12 (2) +7

=283

Now, calculate forward divided difference as:

xi + 1 = xi + h

=2 + 0.25

=2.25

F (xi + 1) = f (2.25) = 25 (2.25)3 – 6(2.25)2 +7(2.25) -88

=182.21

f’(2) = f(2.25) – f(2) / 0.25 = 182.21 – 102 / 0.25

= 320.84

Єt = 283 – 320.8 / 283 = -13.36%

Now calculate backward divided difference:

Xi-1 = xi –h = 2 – 0.25 = 1.75

F(xi-1)= f(1.8) = 25 . (1.8)3 -6 (1.8)2 + 7 (1.8) – 88

= 50.96

F’(2) = f(2) – f(1.8) / 0.25 = 102 – 50.96 / 0.25 = 204.16

Єt = 283 – 204.16 / 283 = 27.86%

Finally, centered divided difference is obtain by inserting f(xi+1) and f (xi-1):

F’(2) = f(2.25) – f(1.8) /2 x 0.25 = 320.84 -50.96 / 0.5 = 539.68

Єt = 283 – 539.68 / 283 = -90.7%

6 0

2 years ago

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable

topjm [15]

Answer:

(A) 0.15625

(B) 0.1875

(C) Can't be computed

Step-by-step explanation:

We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let X = Amount of time taken by student to complete a statistics quiz

So, X ~ U(32 , 64)

The PDF of uniform distribution is given by;

f(X) = $\frac{1}{b-a}$ , a < X < b where a = 32 and b = 64

The CDF of Uniform distribution is P(X <= x) = $\frac{x-a}{b-a}$

(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)

P(X > 59) = 1 - P(X <= 59) = 1 - $\frac{x-a}{b-a}$ = 1 - $\frac{59-32}{64-32}$ = $1-\frac{27}{32}$ = 0.15625

(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)

P(X <= 43) = $\frac{43-32}{64-32}$ = $\frac{11}{32}$ = 0.34375

P(X < 37) = $\frac{37-32}{64-32}$ = $\frac{5}{32}$ = 0.15625

P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) Probability that student complete the quiz in exactly 44.74 minutes

= P(X = 44.74)

The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.

3 0

2 years ago

A researcher is studying a group of field mice. the distribution of the weight of field mice is approximately normal with mean 2

Svetllana [295]

Answer:

b

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 107 homicides. After

leonid [27]

Answer:

P(0) = 0.6825

P(1) = 0.2607

Step-by-step explanation:

From the given information, the number of homicide is 107 and the total number of homicides per city –year is 280.

Let us denote the number of homicides per city-year as X.

The mean value, X is calculated as:

\begin{array}{c}\\{\rm{Mean}} = \frac{{107}}{{280}}\\\\ = 0.382\\\end{array}

Mean= 107/280 = 0.382

The mean number of homicides per city- year \left( {\lambda = \mu } \right)(λ=μ) is 0.382.

a. The probability that zero homicides is obtained is as below:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}

P(X=0) = e −0.382 (0.382)⁰/1

= (0.6825)(1) /1

P(X=0) = 0.6825

Thus, the probability that zero homicides P(0) is 0.6825.

b. The probability that one homicides is obtained is as below:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}

P(X=1) = e −0.382 (0.382)¹/1

= (0.6825)(0.382)/1

P(X=1) = 0.2607

Thus, the probability that zero homicides P(0) is 0.2607.

5 0

2 years ago

fifteen darts have landed on the dart board shown. each dart scores 3,5, or 7 points. in how many different ways can the fifteen

lukranit [14]

Answer:

The answer is "8".

Step-by-step explanation:

Let the number are a, b, c then value is as follows:

a= 3

b= 5

c= 7

The addition of equation ⇒ a+b+c =15....................(i)

multiply by the value ⇒ 3a + 5b + 7c = 75 ...............(ii)

let b= 15-a-c which subtract from equation (ii)

equation:

⇒ 3a + 5b + 7c = 75

⇒ 3a + 5(15-a-c) + 7c = 75

⇒ 3a +75-5a-5c+7c = 75

⇒ 3a -5a-5c+7c = 75-75

⇒ -2a + 2c = 0

⇒ 2(c-a) = 0

⇒ (c-a) = 0

⇒ c=a

if we put value in between 0 to 7 from it satisfies the two equations, with c=a and b = 15 - a - c. So, the correct answer is 8.

3 0

2 years ago