Question and Answers Forum

A box contains 5 balls, 2 balls were drawn at random, both of which turned out tobe white. what is the probability that all the balls in the box are white ?

$${A}\:{box}\:{contains}\:\mathrm{5}\:{balls},\:\mathrm{2}\:{balls}\:{were} \\ $$$${drawn}\:{at}\:{random},\:{both}\:{of}\:{which} \\ $$$${turned}\:{out}\:{tobe}\:{white}.\:{what}\:{is}\:{the} \\ $$$${probability}\:{that}\:{all}\:{the}\:{balls}\:{in}\:{the}\:{box} \\ $$$${are}\:{white}\:? \\ $$

Question Number 105851 Answers: 1 Comments: 0

Each of the students in the class was in the theater exactly two times during the winter holidays,while performances A,B and C were seen by 25,12 and 23 students,respectively .How many students are there in the class?How many of them saw performances A and B,B and C,C and A?

$$\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}\:\mathrm{was} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{theater}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{times}\:\mathrm{during}\: \\ $$$$\:\mathrm{the}\:\mathrm{winter}\:\mathrm{holidays},\mathrm{while} \\ $$$$\mathrm{performances}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{were}\:\mathrm{seen}\:\mathrm{by} \\ $$$$\mathrm{25},\mathrm{12}\:\mathrm{and}\:\mathrm{23}\:\mathrm{students},\mathrm{respectively} \\ $$$$.\mathrm{How}\:\mathrm{many}\:\mathrm{students}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{class}?\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{them}\:\mathrm{saw}\:\mathrm{performances} \\ $$$$\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\mathrm{B}\:\mathrm{and}\:\mathrm{C},\mathrm{C}\:\mathrm{and}\:\mathrm{A}? \\ $$

Question Number 105850 Answers: 0 Comments: 0

A bit modification of Mr. W′s question How many numbers are there with atleast one zero between 1 to 12345 ? For instance consider 10020 as 1 number ? Can the answer ofQ105791 be derived from the answer of this question ?

$$\mathrm{A}\:\mathrm{bit}\:\mathrm{modification}\:\mathrm{of}\:\mathrm{Mr}.\:\mathrm{W}'\mathrm{s}\:\mathrm{question} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{there}\:\mathrm{with}\:\mathrm{atleast}\:\mathrm{one} \\ $$$$\mathrm{zero}\:\mathrm{between}\:\mathrm{1}\:\mathrm{to}\:\mathrm{12345}\:?\:\mathrm{For}\:\mathrm{instance}\:\mathrm{consider} \\ $$$$\mathrm{10020}\:\mathrm{as}\:\mathrm{1}\:\mathrm{number}\:?\:\mathrm{Can}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{ofQ105791}\: \\ $$$$\mathrm{be}\:\mathrm{derived}\:\mathrm{from}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\mathrm{this}\:\mathrm{question}\:? \\ $$

Question Number 105843 Answers: 3 Comments: 0

(3x)^(1+log _3 (3x)) > 81x^2 find the solution set

$$\left(\mathrm{3}{x}\right)^{\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}{x}\right)} \:>\:\mathrm{81}{x}^{\mathrm{2}} \\ $$$${find}\:{the}\:{solution}\:{set}\: \\ $$

Question Number 105842 Answers: 0 Comments: 0

A wheel revolving at 6rev/s has an angular acceleration of 4rad/s^2 . find the number of turns the wheel must take to reach 26rev/s and the time required.

$$\mathrm{A}\:\mathrm{wheel}\:\mathrm{revolving}\:\mathrm{at}\:\mathrm{6rev}/\mathrm{s}\:\mathrm{has}\:\mathrm{an}\:\mathrm{angular}\: \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{4rad}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{turns}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{must}\:\mathrm{take}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{26rev}/\mathrm{s} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{time}\:\mathrm{required}. \\ $$

Question Number 105840 Answers: 0 Comments: 0

A Car wheel 30cm in radius is turning at a rate of 8rev/s when the car begins to slow uniformly to rest in a time 14s. find the number of revolutions made by the wheel and the distance the car goes in the 14s.

$${A}\:{Car}\:{wheel}\:\mathrm{30}{cm}\:{in}\:{radius}\:{is}\:{turning}\:{at}\:{a} \\ $$$${rate}\:{of}\:\mathrm{8}{rev}/{s}\:{when}\:{the}\:{car}\:{begins}\:{to}\:{slow}\:\: \\ $$$${uniformly}\:{to}\:{rest}\:{in}\:{a}\:{time}\:\mathrm{14}{s}.\:{find}\:{the}\: \\ $$$${number}\:{of}\:{revolutions}\:{made}\:{by}\:{the}\:{wheel} \\ $$$${and}\:{the}\:{distance}\:{the}\:{car}\:{goes}\:{in}\:{the}\:\mathrm{14}{s}. \\ $$

Question Number 105868 Answers: 1 Comments: 1

lim_(x→0) cos((((√x)−1)/x))=????? please i need your help

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}cos}}\left(\frac{\sqrt{\boldsymbol{{x}}}−\mathrm{1}}{\boldsymbol{{x}}}\right)=????? \\ $$$${pl}\boldsymbol{{ease}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$

Question Number 105839 Answers: 0 Comments: 0

A wheel 25cm in a radius turning at 120rpm uniformly increases its frequency to 660rpm in 9s. Find (a) the constant angular acceleration in rad/s^2 and (b) tangential acceleration of a point on its rim.

$${A}\:{wheel}\:\mathrm{25}{cm}\:{in}\:{a}\:{radius}\:{turning}\:{at}\:\mathrm{120}{rpm} \\ $$$${un}\mathrm{i}{formly}\:{increases}\:{its}\:{frequency}\:{to}\:\mathrm{660}{rpm} \\ $$$${in}\:\mathrm{9}{s}.\:{Find}\:\left({a}\right)\:{the}\:{constant}\:{angular}\: \\ $$$${acceleration}\:{in}\:{rad}/{s}^{\mathrm{2}} \:{and}\:\left({b}\right)\:{tangential} \\ $$$${acceleration}\:{of}\:{a}\:{point}\:{on}\:{its}\:{rim}. \\ $$

Question Number 105838 Answers: 0 Comments: 0

A mass of 1.5kg out in space moves in a circle of radius 25cm at a constant 2rev/s. Calculate (a) the tangential speed (b) acceleration and (c) the required centripetal force for the motion.

$${A}\:{mass}\:{of}\:\mathrm{1}.\mathrm{5}{kg}\:{out}\:{in}\:{space}\:{moves}\:{in}\: \\ $$$${a}\:{circle}\:{of}\:{radius}\:\mathrm{25}{cm}\:{at}\:{a}\:{constant}\:\mathrm{2}{rev}/{s}. \\ $$$${Calculate}\:\left({a}\right)\:{the}\:{tangential}\:{speed}\: \\ $$$$\left({b}\right)\:{acceleration}\:{and}\:\left({c}\right)\:{the}\:{required}\: \\ $$$${centripetal}\:{force}\:{for}\:{the}\:{motion}. \\ $$

Question Number 105822 Answers: 2 Comments: 0

Given f(x+(1/(2x))) = x^2 +(1/(4x^2 ))+3x+(3/(2x)) find f(2)

$$\mathcal{G}{iven}\:{f}\left({x}+\frac{\mathrm{1}}{\mathrm{2}{x}}\right)\:=\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}} }+\mathrm{3}{x}+\frac{\mathrm{3}}{\mathrm{2}{x}} \\ $$$${find}\:{f}\left(\mathrm{2}\right)\: \\ $$

Question Number 105815 Answers: 1 Comments: 0

Question Number 105812 Answers: 1 Comments: 0

In a by-election 20% of the electorate voted for Mr X. If 5 voters are chosen at random from this electorate, what is the probability that 20% of the sample voted for Mr X ? (a) 1 (b) (1/5) (c) (1/(625)) (d) ((256)/(625))

$$\mathrm{In}\:\mathrm{a}\:\mathrm{by}-\mathrm{election}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electorate}\:\mathrm{voted}\:\mathrm{for}\:\mathrm{Mr}\:\mathrm{X}. \\ $$$$\mathrm{If}\:\mathrm{5}\:\mathrm{voters}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{this}\:\mathrm{electorate},\:\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{voted}\:\mathrm{for}\:\mathrm{Mr}\:\mathrm{X}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1}\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{1}}{\mathrm{625}}\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{256}}{\mathrm{625}} \\ $$

Question Number 105807 Answers: 0 Comments: 0

Question Number 105806 Answers: 0 Comments: 0

Question Number 105805 Answers: 0 Comments: 0

Question Number 105803 Answers: 3 Comments: 1

The sum of two numbers are 20 and their LCM is 24. What are the two numbers?

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{20}\:\mathrm{and} \\ $$$$\mathrm{their}\:\mathrm{LCM}\:\mathrm{is}\:\mathrm{24}. \\ $$$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{numbers}? \\ $$

Question Number 105810 Answers: 0 Comments: 0

Question Number 105799 Answers: 1 Comments: 0

Question Number 105791 Answers: 1 Comments: 1

From 1 to 12345, how many numbers contain the digit 0? Find the number of zeros in all these numbers. Example: 10020 has three zeros.

$${From}\:\mathrm{1}\:{to}\:\mathrm{12345},\:{how}\:{many}\:{numbers} \\ $$$${contain}\:{the}\:{digit}\:\mathrm{0}?\:{Find}\:{the}\:{number} \\ $$$${of}\:{zeros}\:{in}\:{all}\:{these}\:{numbers}. \\ $$$${Example}:\:\mathrm{10020}\:{has}\:{three}\:{zeros}. \\ $$

Question Number 105781 Answers: 1 Comments: 1

Please, I need help. Exercise We have : J_n = ∫_0 ^( (π/4)) tan^n (x) dx 1) Establish a recurrence relation between J_(n+2) and J_n . 2) Calculate J_0 and J_1 , then deduce the expression of J_n as a function of n. The deduction of the last question, please.

$$\mathrm{Please},\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}. \\ $$$$\mathrm{Exercise} \\ $$$$\mathrm{We}\:\mathrm{have}\:: \\ $$$$\mathrm{J}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$$\mathrm{between}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}+\mathrm{2}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} . \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Calculate}\:\boldsymbol{\mathrm{J}}_{\mathrm{0}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\mathrm{1}} ,\:\mathrm{then} \\ $$$$\mathrm{deduce}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{of}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} \:\mathrm{as}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}. \\ $$$$\mathrm{The}\:\mathrm{deduction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last} \\ $$$$\mathrm{question},\:\mathrm{please}. \\ $$

Pg 1120 Pg 1121 Pg 1122 Pg 1123 Pg 1124 Pg 1125 Pg 1126 Pg 1127 Pg 1128 Pg 1129

Contact: info@tinkutara.com