Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function:

    S = 20 L^0.3C ^0.7

In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100.

Prove that every bipartite graph G with size m satisfies α prime(G) ≥ m/∆(G).

Tulia Company manufactures agricultural implements. At the beginning of the third quarter of 2018, the company had planned to produce 400 units of output during the quarter; this level of demand was considered “normal” for the period and reflected the average demand in the third quarter for the previous three years. However, a marketing decision by Tulia’s management to cut prices by 5 percent during the quarter led to an uptick in demand, with the result that the company increased production to 450 units for the quarter. The company tracks four factory inputs: direct materials, direct labor, variable factory overhead, and fixed factory overhead. Both variable and fixed factory overhead are applied using predetermined rates based on direct labor hours. For each of the following cost components, an examination of the records revealed the following amounts:

Direct materials: Standard cost per unit of direct materials: $3.50 per pound.

Direct materials price variance: $350 U.

Total pounds of standard direct materials allowed for the actual output achieved: 2,700 pounds. Direct materials quantity variance: $70 U. Actual quantity of direct material purchased: 3,500 pounds.

1. Compute the following amounts (make sure you indicate the direction of any variance computed):

a. Standard cost of direct material allowed per unit of output: $_______________ .

b. Actual cost per pound of direct materials purchased: $_______________.

c. Actual quantity of materials used in production: _______________ pounds.

Let A be an n × n real symmetric matrix with its row and column sums both equal to 0. Let λ₁, . . . , λ_n be the eigenvalues of A, with λ_n = 0, and with corresponding eigenvectors v₁,...,v_n (these exist because A is real symmetric). Note that v_n = (1, . . . , 1). Let A[i] be the result of deleting the ith row and column.

Prove that detA[i] = (λ₁···λ_n-1)/n. Thus, the number of spanning trees of G is the product of the nonzero eigenvalues of L, divided by n.

Which of the following statistics associated with the Golden Gate Bridge in San Francisco, California, are exact numbers and which have some inherent uncertainty?

Part 1: The roadway is six lanes wide. Choose one:

A. Exact number

B. number with limited precision.

Part 2: The width of the bridge is 27.4 m. Choose one:

A. exact number

B. number with limited precision

Part 3: The bridge has a mass of 3.808x10⁸ kg. Choose one:

A. exact number

B. number with limited precision

Part 4: The length of the bridge is 2740 m. Choose one:

A. exact number

B. number with limited precision

Part 5: The toll for a car traveling south increased to $6.00 on September 1, 2008. Choose One:

A. exact number

B. number with limited precision

1. Is the following set of connectives functionally complete? Justify your answer.{∧,∨,→,↔}

MATLAB. Design your own low-cut shelving filter which can cut the low frequency of given music signal. Include magnitude and phase plot of your filter.

We have a poker deck of 52 cards. Abby randomly shuffles the card, and divides it into 13 piles of 4 cards each. Use Hall marriage theorem to show that it is possible to pick a card from each pile, so that you get all 13 numbers from A to K.

How many cyclic codes of length 4 are there over F5? Find a generator matrix and a parity check matrix for each 2-dimensional code.

1. Mike took clothes to the cleaners three times last month. First, he brought 4 shirts and 1 pair of slacks and paid 11.95. Then he brought 5 shirts, 2 pairs of slacks, and 1 sports coat and paid 25.92. Finally, he brought 4 shirts and 2 sport coats and paid 23.94. How much was he charged for each shirt, each pair of slacks, and each sports coat?

2. At a pottery​ factory, fuel consumption for heating the kilns varies with the size of the order being fired. In the ​past, the company recorded the figures in the table.

A. Find an equation of the form y=ax^2+bx+c whose graph contains the three points corresponding to the data in the table.

B. How many platters should be fired at one time in order to minimize the fuel cost per platter? What is the minimum fuel cost per platter?

Use the secant Method to find a root for the function:

f(x) = x^3 + 2x^2 + 10x -20, with x_0 = 2, and x_1 = 1.

Please Use Matlab to do this problem:

The cross-sectional area measurements (??2) from 7 cells are as follows:

? = [153.3 91.2 99.3 115.0 101.7 135.8 102.4 ]

Assuming the cross-sectional areas of the cells are normally distributed, construct a two-sided 95% confidence interval for the mean cross-sectional area of the entire batch.
Then, generate one figure:

• Plot all 7 data points on x-axis, mark them with red circles;

• Plot the mean value, which is going to be the center of your interval, mark it with

  blue x;

• Plot the upper and lower limit of the interval, mark them with black squares;

• Have your x-axis range from 70 to 180;

• Have your y-axis range from -1 to +1. (So, your x-axis will be in the middle of

  your figure)

• You can play with the line width and font to make your figure more reader friendly.

I apologize but this is one question that has multible parts .

There are currently (as of July 2018) 411 parts per million of CO2 in our atmosphere. In July 2000 the concentration of CO2 was 365 ppm. a) calculate the average exponential growth rate in this period b) at this growth rate what will the concentration of CO2 in the year 2100. A reasonable approximation of the amount of surface temperature (in degrees C) increase as related to CO2concentration is given by: ΔT = 0.8 * ΔF where for CO2 ΔF = 5.35 * LN(Cnow/Cbefore); Cbefore = 280 ppm Note that LN stands for the natural logarithm; for instance ln(10) = 2.32 (just type ln 10 in to Google) ΔF (what we call climate forcing) represents the change in flux due to changing CO2 levels and that determines ΔT c) Using the result obtained in Part b, what is the predicted temperature change in the year 2100 and is this prediction above or still below the Paris accord agreement of no more than 2C before 2100 above the pre-industrialized temperature? Over the last few years, CO2 growth is occurring at a larger rate than long term average. The following list gives you the necessary values to compute the relevant growth rates for the question below. Jan 1970 325 ppm Jan 1990 353 ppm Jan 2005 378 ppm Jan 2019 411 ppm d) Using the same calibration as above, calculate the exponential growth rate and predicted 2100 temperature from that growth rate for the periods 1970-1990 1990-2005 2005-2019 please explain step by step how you came to this answer. I would like to beable to do this myself in the future. thank you

In the equation SEND + MORE = MONEY each letter represents a different digit (0-9). The addition is done in the usual way from right to left, first adding D and E to obtain Y (possibly with a carry-over), then adding N and R, and so on. Solve this problem using linear programming with integer and binary variables. (No credit is given for a solution without the appropriate spreadsheet model in Excel.)

What is the technique of variation of parameters doing? What does it assume about the solution? How does it compare with undetermined coefficients? (What do they calculate? Do they give you the same thing? How are they different?)