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Solve the inequalities. Give your answer in interval notation, and indicate the answer geometrically on the real-number line. a. t + 6 ≤ 2 + 3t
b. 3(2 – 3x) > 4(1 – 4x)
In the following problems, perform the operations and simplify as much as possible.
a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x 2 – 4x + 4)
b. (x2 + 6x + 9)/x/(x + 3)
c. 1/(3x – 1) + x/(x2 – 9)
Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.
a. Show that f is one-to-one and onto.
b. Show that g is one-to-one and onto.
c. Determine the composition function g o f
d. Determine the inverse functions f -1 and g -1 .
e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1 .
- If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.
- Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?
Calculate the concentration of OH- in a 0.15 M solution of NH3. Kb = 1.8 × 10-5
How many grams of C2,H2,O2,CO2 and H2O are present after the reaction complete
Find Larange’s interpolating polynomial passing through set of points
(0,2) (2,-2),(3,-1),Use it to find
at x = 2
Tom wants his balloon back to normal size so he decides to put it on a heating vent. If
the balloon initially has a volume of 0.6 L and a temperature of 293 K, what will be the volume of
the balloon when it heats up to a temperature of 176°C?
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Find the value of current if the loop has 60 μΩ and 20 V
Blocks A and B are moving toward each other. A has a mass of 6.1 kg and a velocity of 1.5m/s, while B has a mass of 1.7kg and a velocity of −9.8m/s. They suffer a completely inelastic collision. During the collision, how much kinetic energy is lost?
