Suppose we want to use Twitter activity to predict box office receipts on the opening weekend for movies. Assuming a linear relationship, the Excel output for this regression model is given below.

Excel output:

(a) State the regression equation for this problem.

(b) Interpret the meaning of b₀ and b₁ in this problem.

(c) Predict the box office receipts on the opening weekend for a movie that has a Twitter activity of 110,000.

(d) At the 0.05 level of significance, is there evidence of a linear relationship between the Twitter activity and the box office receipts on the opening weekend for a movie?

(e) Construct a 95% confidence interval estimate of the population slope β₁. Interpret the confidence interval estimate.

(f) How useful do you think this regression model is for predicting the box office receipts on the opening weekend for a movie?

A particular mattress company has three factories (1,2,3), each of which produces three types of mattresses: (1) spring, (2) foam, and (3) hybrid. In the matrix

? = [ 80 50 25

45 110 60]

??? represents the number of mattresses of type ? produced at factory ? in one day. Find the production levels if production increases by 15%.

Here are mass spectrometric signals for methane in H2:

CH2 (Vol %) 0 0.062 0.122 0.245 0.486 0.971 1.921

Signal (mV) 9.1 47.5 95.6 193.8 387.5 812.5 1671.9

a) Subtract blank value from all other values. Then use the method of least squares to find the slope and intercept and their uncertainties.

b)Replicate measurements of an unknown gave 152.1, 154.9, 153.9, and 155.1 mV and a blank gave 8.2, 9.4, 10.6, and 7.8 mV. Subtract average blank from average unknown to find average corrected signal for the unknown.

c) Find concentration of the unknown and uncertainty.

3) consider computing e^x-1/x

a) Explain when and why a loss of significance can happen.

b) show how you can remedy the problem. Hint: use a Taylor series.

Put a metric ρ on all the words in a dictionary by defining the distance between two distinct words to be 2^−n if the words agree for the first n letters and are different at the (n+1)st letter. A space is distinct from a letter. E.g., ρ(car,cart)=2^−3 and ρ(car,call)=2^−2.

a) Verify that this is a metric.
b) Suppose that words w1, w2 and w3 are listed in alphabetical order.
Find a formula for ρ(w1,w3) in terms of ρ(w1,w2) and ρ(w2,w3).

using / for integral

Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the trapezoidal region with vertices (1,0), (2,0), (0,2), and (0,1)

A manufacturer of animal feed makes two grades of food. Each bag of high grade feed contains 10kg of wheat brand and 5kg of maize, while each bag of low-grade feed contains 12kg of wheat brand and 3kg of maize. There are 1920kg of wheat brand and 780kg of maize currently available. The manufacture can make a profit of ¢12,000 on each bag of high grade and ¢10000 on each bag of the low-grade feed. Determine the number of bags of each grade to produce to maximize profit.

For a binary FSK system, s1(t)=A cos (ω0+Ω)t and s2(t)=A cos (ω0-Ω)t are defined.

a) Prove that the above signals are orthogonal if ΩT=nπ, where T is the bit interval and n is a positive integer.

b) Determine probability of error for the system

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}.

(b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}.

(c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}.

*(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive.

(a) For what value of k is this an hyperbola and for what value of k is this an ellipse?

(b) Plot one of each.

Justify your answer.

Without using a calculator, find the cube root of 2, correct to 1 decimal place.

Show that a monotone sequence converges if and only if it is bounded.

a)

Select all solutions of (d^2/dx^2)y(x)+64y(x)=0.

b)

Select all solutions of (d^2/dx^2)y(x)+36y(x)=0.

3. The Bay City Parks and Recreation Department has received a federal grant of $600,000 to expand its public recreation facilities. City council representatives have demanded four different types of facilities—gymnasiums, athletic fields, tennis courts, and swimming pools. In fact, the demand by various communities in the city has been for 7 gyms, 10 athletic fields, 8 tennis courts, and 12 swimming pools. Each facility costs a certain amount, requires a certain number of acres, and is expected to be used a certain amount, as follows:

The Parks and Recreation Department has located 50 acres of land for construction (although more land could be located, if necessary). The department has established the following goals, listed in order of their priority:

(1) The department wants to spend the total grant because any amount not spent must be returned to the government.

(2) The department wants the facilities to be used by a total of at least 20,000 people each week.

(3) The department wants to avoid having to secure more than the 50 acres of land already located.