The following time series shows the sales of a particular product over the past 12 months.

(a)

Construct a time series plot.

(b)

Use α = 0.3 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)

(c)

Use a smoothing constant of α = 0.5 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.)

Does a smoothing constant of 0.3 or 0.5 appear to provide more accurate forecasts based on MSE?

A smoothing constant of 0.5 is better than a smoothing constant of 0.3 since the MSE is greater for 0.5 than for 0.3.

A smoothing constant of 0.3 is better than a smoothing constant of 0.5 since the MSE is greater for 0.3 than for 0.5.

A smoothing constant of 0.3 is better than a smoothing constant of 0.5 since the MSE is less for 0.3 than for 0.5.

A smoothing constant of 0.5 is better than a smoothing constant of 0.3 since the MSE is less for 0.5 than for 0.3.

The lifetime of a particular brand of tire is modeled with a normal distribution with mean μ = 75,000 miles and standard deviation σ = 5,000 miles.

a) What is the probability that a randomly selected tire lasts less than 67,000 miles?

b) If a random sample of 35 tires is taken, what is the probability that the sample mean is greater than 70,000 miles?

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2643 miles, with a standard deviation of 368 miles. If he is correct, what is the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles? Round your answer to four decimal places.

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,700 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,775 bus miles and a sample standard deviation of 325 bus miles.

a. Is there evidence that the population mean bus miles is more than 3,700 bus miles? (Use a 0.10 level of significance.) State the null and alternative hypotheses.

b. Find the test statistic for this hypothesis test.

c. The critical value(s) for this test statistic is(are)

d. Determine the p-value and interpret its meaning.

answer all questions please!!!

The mean gas mileage for a hybrid car is

56

miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of

3.2

miles per gallon.​ (a) What proportion of hybrids gets over

62

miles per​ gallon? (b) What proportion of hybrids gets

52

miles per gallon or​ less?

left parenthesis c right parenthesis What(c) What

proportion of hybrids gets between

58

and

62

miles per​ gallon? (d) What is the probability that a randomly selected hybrid gets less than

45

miles per​ gallon?

LOADING...

Click the icon to view a table of areas under the normal curve.

​(a) The proportion of hybrids that gets over

62

miles per gallon is

nothing.

​(Round to four decimal places as​ needed.)

I have to write a c program for shipping calculator. anything that ships over 1000 miles, there is an extra 10.00 charge. I have tried everything. no matter what I put, it will not add the 10.00. please help here is my code

#include <stdio.h>
#include <stdlib.h>

int main()
{
double weight, miles, rate, total;

printf("Enter the weight of the package:");
scanf("%lf", &weight);

if (weight > 50.0) {
puts("we only ship packages of 50 pounds or less.");
return 0;

}
if ( miles > 1000 ){
total = rate + 10.00;
printf("rate is $%.2lf \n", rate);

}
printf("Enter the amount of miles it would take:");
scanf("%lf", &miles);

if (weight <= 10.0)
rate = 3.00;

else
rate = 5.00;

printf("Shipping charge is $%.2lf \n", (int)((miles + 499.0) / 500.0) * rate);
if (miles >= 1000){
("shipping charge + 10.00");
}
system("pause");
}

III. A common utility function used to illustrate economic examples is the Cobb-Douglas function where U(X, Y)= XαYβ, where α and β are decimal exponents that sum to 1.0 (for example, 0.3 and 0.7).

a. For this utility function, the MRS is given by MRS = MUX=MUY = αY/βX. Use this fact together with the utility-maximizing condition (and that α+ β =1) to show that this person will spend the fraction of his other income on good X and the fraction of income on good Y— that is, show PXX/I = α, PYY/I = β.

b. Use the results from part a to show that total spending on good X will not change as the price of X changes so long as income stays constant.

c. Use the results from part a to show that a change in the price of Y will not affect the quantity of X purchased.

d. Show that with this utility function, a doubling of income with no change in prices of goods will cause a precise doubling of purchases of both X and Y.

The Lennard-Jones potential energy, U(x), is a function of “x” the separation distance between a pair of atoms in a molecule. It is frequently called the van der Walls potential between atoms for dipole-dipole interactions. The potential is

U(x) = C12/ x¹² - C6/x⁶,                                                                    [1]

Where

C₁₂ = 1.51 x 10^-134 J∙m¹²

C₆ = 1.01 x 10^-77 J∙m⁶.

(a) Determine the shape of the potential energy curve vs. distance of separation (x) between the atoms using Equation [1] by plotting the equation to scale on graph paper for “x” ranging from 0.3 – 1.0 nm.

(b) Calculate the equilibrium distance “x_e” between the atoms at the minimum potential energy from Equation [1].

(c) Assuming the atoms are spherical balls with a spring between them, what is the spring constant (k) of the bond as atoms are pulled apart from their equilibrium position? Recall that F (force) = dU/dx, and F = kx.

Consider the system modeled by the differential equation

                              dy/dt - y = t    with initial condition y(0) = 1

the exact solution is given by y(t) = 2et − t − 1

Note, the differential equation dy/dt - y =t can be written as

                                              dy/dt = t + y

using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt

                              (y(t + Dt) – y(t))/ Dt = (t + y)

                               y(t + Dt) = (t + y)Dt + y(t)

                              New Value = change + current value

1. Using R implement Euler’s method directly to numerically solve the equation and construct a Table as below – list data to four digits past the decimal point. Submit your R session

               time     ∆t = 0.1           ∆t = 0.0001        Exact Value       %Relative                  %Relative

                                                                                                             Error ∆t = 0.1       Error ∆t = 0.0001                    

                  0

                 0.1

                 0.2

                 0.3

                 0.4

                 0.5

                 0.6

                 0.7

                 0.8

                 0.9

                 1.0