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• ​How many ordered pairs #(x,y)# satisfy the system of equations #x​=2y+5# and #y​=(2x−3)(x+9)#?
  
• Why does the atomic mass of an atom equal the weight of 1 mol of that atom in grams?
  
• When do I use the molar mass of diatomic oxygen instead of atomic oxygen in stoichiometry problems?
  
• 30% of the 20 people in the Math Club have blonde hair. If 3 people are selected at random from the club, what is the probability that none have blonde hair?
  
• #abs(2x-1)=4x +5# has how many numbers in its solution set?
  
• How do I find the solutions to #1 <= abs(x-2) <= 4# algebraically?
  
• Two dice are thrown. Event #A# is "the sum of two dice is #7#" and Event #B# is "at least one die is #6#". Are #A# and #B# independent?
  
• If the mean, actual observed values, and standard deviation are multiplied by #2#, does the z-score stay the same?
  
• If #f(x^2) = 1/x# then what is #f(1/x)#?
  
• With what speed does the rock hit the bottom?
  
• Why does #lim_(x->+-oo) f(x) = lim_(x->0) f(1/x)#?
  
• Solve #(-12)/(-x+12)>=4# algebraically?
  
• Find all the values of #x# such that #abs(7-abs(4-x))>11#?
  
• Why is #y=1/x# a continuous function?
  
• What is the root of #x^3 - x - 1 = 0# in exact form?
  
• Find #lim_(x->oo) (6x+1)/abs(-2x+6)# algebraically?
  
• Can you use a colon to replace "because"?
  
• Do I use semicolons or commas in this sentence?
  
• Solve for #x#: #absx = abs(x-2) - abs(x+4)#?
  
• If #3^(x+2) = 2^(2x-1)# and #x = log A / log B#, what is the product #AB#?
  
• What is the major factor that accounts for most of the difference in these two values of pressure (ideal gas law vs. van der Waals equation)?
  
• What is the total number of orbitals possible at the #n = 4# energy level?
  
• Solve for #x# in #|2x-4| >= -5#? Why doesn't the usual method work in this case?
  
• Why isn't the notation for the second derivative #dy^2/dx#?
  
• Which has the lowest ionization energy: #S, S^(2-), S^(2+)#?
  
• Subject-verb agreement question? One of the only...
  
• Why is the #O^(2-) (g)# ion unstable? Doesn't its electron configuration match that of Neon?
  
• Explain why the Chain Rule formula #dy/dx = (dy)/(du) * (du)/(dx)# is not simply the well-known rule for multiplying fractions?
  
• If #x=sint# and #y=cost#, then #(d^2y)/dx^2# = ?
  
• #sp^3# hybridization - can somebody explain what my book is trying to say?
  
• There are 8 tiles in a box, each numbered with a different digit from 1 to 8. What is the probability of selecting 3 odd tiles and 1 even tile when four tiles are drawn one at a time with replacement?
  
• Can someone tell me where my error is in finding the derivative of #y=x^(lnx)#?
  
• Find the value of #(dr)/dt# at #t=0# if #r=(theta^2 +7)^(1/3)# and #theta^2t + theta =1#?
  
• In a salt solution, which species (cation/anion) is responsible for the absorbance spectrum?
  
• Question on standard deviation/variance?
  
• Differentiate #f(x) = lnabs(x/(1+x^2))#?
  
• Why do you say #y=x^2# decreases on the interval #(-oo, 0]#? Why is #0# included?
  
• Why is the normal boiling point of a liquid the point at which the vapor pressure is equal to atmospheric pressure, #"760 torr"#?
  
• Find the points of inflection: #y=x^(1/3)(x-4)#?
  
• At which intervals is #y=x^2e^(1/x^2)# increasing?
  
• A student attempted to dissolve a liquid ionic solute in a nonpolar solvent. The resulting mixture showed three distinct layers...?
  
• Calculate the molarity of a solution containing KCl and water whose osmotic pressure at 38.0°C is 125 torr. Assume complete dissociation of the salt?
  
• Question dealing with pseudo-first order reaction?
  
• In what direction should you swim across a river if you want to minimize the time spent in the water?
  
• A conical tank has a circular base with radius 5 ft and height 12 ft. If water is flowing out of the tank at a rate of 3 ft^3/min, how fast is the height of the water changing when the height is 7 ft?
  
• [Equilibrium] Does my book contradict itself?
  
• Gaseous #HI# is synthesized from #H_2 (g)# and #I_2 (g)# at a temperature where #K_c = 1.00 xx 10^2#. Suppose that #HI# at #5.000 xx 10^(-1) atm#, #H_2# at #1.000 xx 10^(-2) atm#, and #I_2# at #5.000 xx 10^(-3) atm# are mixed in a #5#-#L# flask?
  
• Which step would be the rate-determining step?
  
• Prove #tan^-1 (cot (theta)) /2 = pi/4 + theta/2#?
  
• Prove #-cot theta = tan (theta + pi/2)#?
  
• What is the relationship between the roots and coefficients of a polynomial?
  
• Let #a#, #b#, and #c# be real numbers with #a <= b <= c#. What are all the ordered triples #(a,b,c)# such that the product of any two of the numbers is #3# more than the sum of that pair?
  
• Factor #(3xx4^x)+ (6xx2^xy) - (45y^2)#?
  
• The chord of circle #x^2 + y^2 = 25# connecting #A(0,5)# and #B(4,3)# is the base of an equilateral triangle with the third vertex #C# in the first quadrant. What is the smallest possible #x#-coordinate of #C#?
  
• What is the pH of #1.0 xx 10^(-10)# #"M HCl"#?
  
• Evaluate #intcos^5x dx# using u-substitution or tabular integration?
  
• How would diluting HA from 0.15 M to 0.005 M affect the pH of the solution? #K_a = 1.0 xx 10^-8#.
  
• A 1.0 L solution of #AgNO_3# and #Pb(NO_3)_2# has a silver ion concentration of 0.020 M and a lead ion concentration of 0.0010 M. A 0.0010 mol sample of #K_2SO_4# (s) is added to the solution. Which precipitate will form?
  
• A student mixes a 10.0 mL sample of 1.0 M NaOH with a 10.0 mL sample of 1.0 M HCl in a polystyrene container. The temperature of the solutions before mixing is was #20.0^@ C#; the final temperature is #26.0^@ C#. What is the value of #DeltaH_(rxn)#?
  
• Based on the ionization energies of element X given in the table, which of the following is most likely the empirical formula of an oxide of element X?
  
• #CH_3OH (g) -> CO (g) + 2H_2 (g)# and #Delta H = 91 "kJ"/"mol"#. What can be inferred about #DeltaS# for the reaction at 600K?
  
• P(E) = 0.5 and P(F) = 0.6. Which of the following is true of P(E and F)?