Tutors Answer Your Questions about Linear-systems (FREE)
Question 1209934: a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice
Click here to see answer by ikleyn(52781)   |
Question 1209934: a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice
Click here to see answer by CPhill(1959)  |
Question 1169746: 4) The equations defining a model of two trading nations are given by
π π πΆ1 = 0.7π1 + 50 πΆ2 = 0.8π2 + 100 πΌ πΌ π1 = 0.3π1 π2 = 0.1π2
a. Express this system in matrix form and hence find the values of π1 and π2.
b.Calculate the balance of payments between these countries
Click here to see answer by CPhill(1959) |
Question 1173100: Mr.Agoncillo has a savings account in two banks. The combined amount of these savings is at least Php 150,000. One bank gives an interest of 4% while the other bank give 6%. In a year, Mr. Agoncillo receive at most Php. 12,000.
Write and graph a system of linear inequalities that shows all the posible solutions.
Click here to see answer by CPhill(1959) |
Question 1174275: A certain mobile company offers a monthly plan of Php 799 and an additional charge of Php 7.50 per minute when calling to other networks.How much is the monthly bill if the costumer made a 5 minute call to other networks?
A.What is the independent and dependent variable?
B.What is the slope,y-intercept and the linear inequalities?''.
C.What is the value of y?
Click here to see answer by CPhill(1959) |
Question 1176798: Determine which of A-D form a solution to the given system for any choice of the free parameter s1. List all letters that apply. If there is more than one answer, type them as a comma separated list.
-8x1 + 3x2 + 15x3 = -52
-3x1 + x2 + 6x3 = -20
HINT: All of the parameters of a solution must cancel completely when substituted into each equation.
a)(5+3s1,7-6s1,s1)
b)(8+3s1,4+3s1,s1)
c)(4+s1,s1,-(4-s1/3))
d)(-(6-3s1/16),s1,-(2-2s1/45))
Click here to see answer by CPhill(1959) |
Question 1209773: If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + a_1 = 17,
a_{18} + a_{19} + a_1 + a_2 = 18,
a_{19} + a_1 + a_2 + a_3 = 19,
what is the value of a_19?
Click here to see answer by ikleyn(52781) |
Question 1209773: If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + a_1 = 17,
a_{18} + a_{19} + a_1 + a_2 = 18,
a_{19} + a_1 + a_2 + a_3 = 19,
what is the value of a_19?
Click here to see answer by CPhill(1959) |
Question 1178476: According to the American Society of Heating, Refrigerating
and Air-Conditioning Engineers, Inc. (ASHRAE), a nonsmoking classroom
should have a ventilation rate of 15 ft3 per min for each person in the room.
(a) Write an equation that models the total ventilation V (in cubic feet per hour)
necessary for a classroom with x students.
(b) A common unit of ventilation is air change per hour (ach). One ach is equivalent
to exchanging all the air in a room every hour. If x students are in a classroom
having volume 15,000 ft3, determine how many air exchanges per hour (A) are
necessary to keep the room properly ventilated.
(c) Find the necessary number of ach (A) if the classroom has 40 students in it.
(d) In areas like bars and lounges that allow smoking, the ventilation rate should
be increased to 50 ft3 per min per person. Compared to classrooms, ventilation
should be increased by what factor in heavy smoking areas?
Click here to see answer by CPhill(1959) |
Question 1184642: A landscaping supply company produces decorative stones. A ton of coarse stones requires 2 hours ofcrushing, 5 hours of sifting, and 8 hours of drying. A ton of fine stones requires 6 hours of crushing, 3hours of sifting, and 2 hours of drying. The coarse stones sell for$400 per ton. The fine stones sell for$500per ton. In a work week, the plant is capable of 36 hours of crushing, 30 hours of sifting, and 40 hours ofdrying. Based on the demand forecast, the quantity of coarse stones produced should be at least twice thequantity of fine stones produced.
First
1. Formulate an optimization model to decide how much of each kind of stones to produce to maximizetotal revenue.
2. Solve your model using the Excel solver.
3. Using a two-dimensional plot, solve your model graphically.
Then, by modifying your two-dimensional plot, answer the following questions:
4. How much would it be worth to get another hour of crushing time?
5. How much would it be worth to get another hour of sifting time?
6. Could you find the range of the prices for the fine stones such that in the optimal solution, thequantity of coarse stones produced is exactly twice the quantity of fine stones produced.
Click here to see answer by CPhill(1959) |
Question 1186380: Ridership on a small regional airline has been declining, approximately at a linear rate. In 1981 the number of passengers was 245,000; in 1986 the number was 215,000. If n equals the number of passengers using the airline per year and t equals time measured in year (t=0 for 1981)
Determine the linear estimating function n=f(t)
Interpret the meaning of the slope
What is the number of riders expected to equal in the year 2000?
It is estimated that the airline will go out of business if ridership falls below 180,000. According to your function in part a, when will this happen?
Click here to see answer by CPhill(1959) |
Question 1199840: ABC Dairy Company wishes to make a new cheese from two of its current cheeses: Cheese X and Cheese Y. The mixture is to weight at least than 4 pounds and is to contain 6 ounces of the sharpness Ingredients S. Each pound of X costs $4 and contains 3 ounces of S, whereas each pound of Y costs $1 and contains one ounce of S. find the minimum cost of the mixture if the amount of Cheese Y cannot exceed the amount of Cheese X by more than one pound.
Click here to see answer by ElectricPavlov(122) |
Question 1201735: Let X be the design matrix of a linear regression problem with m rows (samples) and d columns (variables/features). Let yβR^m be the response vector corresponding the samples in X. Recall that for some vector space VβR^d the orthogonal complement of V is: V^β₯:={xβR^dβ£β¨x,vβ©=0βvβV}
1. Prove that: Ker(X)=Ker(X^β€X)
2. Prove that for a square matrix A:Im(A^β€)=Ker(A)^β₯
3. Let y=Xw be a non-homogeneous system of linear equations. Assume that X is square and not invertible. Show that the system has β solutions βyβ₯Ker(X^β€).
4. Consider the (normal) linear system X^β€Xw=X^β€y. Using what you have proved above prove that the normal equations can only have a unique solution (if X^β€X is invertible) or infinitely many solutions (otherwise).
Please help me to solve question 3 and 4.
Click here to see answer by asinus(45) |
Question 1209081: One ordered pair (a,b) satisfies the two equations ab^4 = 48 and a^2 b^3 = 24/b^5. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)
Click here to see answer by ikleyn(52781) |
Question 1209008: Sophie's favorite number is a two-digit number. If she reverses the digits, the result is $45$ less than her favorite number. The sum of the digits in her favorite number is $6$. What is Sophie's favorite number?
Click here to see answer by ikleyn(52781) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515
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