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Question Number 205422 Answers: 1 Comments: 0

If (a + 1)(b + 1)(c + 1) = 8 Then: a^2 + b^2 + c^2 ≥ 3

$$\mathrm{If} \\ $$$$\left(\mathrm{a}\:+\:\mathrm{1}\right)\left(\mathrm{b}\:+\:\mathrm{1}\right)\left(\mathrm{c}\:+\:\mathrm{1}\right)\:=\:\mathrm{8} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\geqslant\:\mathrm{3} \\ $$

Question Number 205420 Answers: 1 Comments: 0

If a^3 + b^3 + a^2 + b^2 = 4 Then: a^4 + b^4 ≥ 2

$$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:\geqslant\:\mathrm{2} \\ $$

Question Number 205409 Answers: 0 Comments: 0

let x, y, z be random numbers from 0 to 10 where x,y,z∈R what is the probability that a) all the following is satisfied ∣x−y∣≥2 ∣x−z∣≥2 ∣y−z∣≥2 b) the probability that one or two of them are not satisfied c) the probability that all of them are not satisfied

$$\mathrm{let}\:{x},\:{y},\:{z}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y},{z}\in\mathbb{R} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\left.{a}\right)\:\mathrm{all}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{satisfied} \\ $$$$\mid{x}−{y}\mid\geqslant\mathrm{2} \\ $$$$\mid{x}−{z}\mid\geqslant\mathrm{2} \\ $$$$\mid{y}−{z}\mid\geqslant\mathrm{2} \\ $$$$\left.{b}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\:\mathrm{one}\:\mathrm{or}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$\left.{c}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{all}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$ \\ $$

Question Number 205406 Answers: 3 Comments: 2

Question Number 205403 Answers: 1 Comments: 0

Question Number 205472 Answers: 1 Comments: 0

Question Number 205421 Answers: 0 Comments: 0

If a,b,c>0 and abc=1 Then: (a/b^(2024) ) + (b/c^(2024) ) + (c/a^(2024) ) ≥ a + b + c

$$\mathrm{If} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}=\mathrm{1} \\ $$$$\mathrm{Then}: \\ $$$$\frac{\mathrm{a}}{\mathrm{b}^{\mathrm{2024}} }\:+\:\frac{\mathrm{b}}{\mathrm{c}^{\mathrm{2024}} }\:+\:\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{2024}} }\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c} \\ $$

Question Number 205393 Answers: 0 Comments: 0

Question Number 205394 Answers: 1 Comments: 0

let x and y be random numbers from 0 to 10 where x,y∈R ∣x−y∣≥d what is the probability that their sum is less than 10 in the following cases a) d=0 b) d=1 c) d=2

$$\mathrm{let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y}\in\mathbb{R} \\ $$$$\mid{x}−{y}\mid\geqslant{d} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{10} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{cases} \\ $$$$\left.{a}\right)\:{d}=\mathrm{0} \\ $$$$\left.{b}\right)\:{d}=\mathrm{1} \\ $$$$\left.{c}\right)\:{d}=\mathrm{2} \\ $$

Question Number 205379 Answers: 2 Comments: 0

Question Number 205380 Answers: 3 Comments: 0

Question Number 205372 Answers: 0 Comments: 0

Question Number 205371 Answers: 1 Comments: 2

Question Number 205367 Answers: 1 Comments: 0

Question Number 205353 Answers: 2 Comments: 0

If ax^2 + bx + c = 0 had two roots p and q and p^2 + q^2 = p^3 + q^3 then show that b^3 − 2a^2 c + ab^2 = 3abc.

$$\mathrm{If}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{had}\:\mathrm{two}\:\mathrm{roots}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{and}\:{p}^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \:=\:{p}^{\mathrm{3}} \:+\:{q}^{\mathrm{3}} \:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{3}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {c}\:+\:{ab}^{\mathrm{2}} \:=\:\mathrm{3}{abc}. \\ $$

Question Number 205350 Answers: 1 Comments: 2

A man invested U24000.00 in U5.00 shares of a firm. After a period of time, it appreciated to U5.50 per share. How much dividend did he receive, if the dividend declared is 50k per share?

$${A}\:{man}\:{invested}\:{U}\mathrm{24000}.\mathrm{00}\:{in}\:{U}\mathrm{5}.\mathrm{00} \\ $$$${shares}\:{of}\:{a}\:{firm}.\:{After}\:{a}\:{period}\:{of} \\ $$$${time},\:{it}\:{appreciated}\:{to}\:{U}\mathrm{5}.\mathrm{50}\:{per}\:{share}. \\ $$$${How}\:{much}\:{dividend}\:{did}\:{he}\:{receive},\:{if} \\ $$$${the}\:{dividend}\:{declared}\:{is}\:\mathrm{50}{k}\:{per}\:{share}? \\ $$

Question Number 205360 Answers: 2 Comments: 0