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Question Number 6799 Answers: 0 Comments: 2

What is the probability that 3 customers waiting in bank will be served in sequence of their arrival.

$${What}\:{is}\:{the}\:{probability}\:{that}\:\mathrm{3}\:{customers}\:{waiting}\:{in}\:{bank}\:{will}\: \\ $$$${be}\:{served}\:{in}\:{sequence}\:{of}\:{their}\:{arrival}. \\ $$

Question Number 6792 Answers: 0 Comments: 2

When the price of egg was raised by #2 an egg, the number of eggs which can be bought for #120 is reduced by #5. What is the present price of the egg.

$${When}\:{the}\:{price}\:{of}\:{egg}\:\:{was}\:{raised}\:{by}\:#\mathrm{2}\:{an}\:{egg},\:\:{the}\:{number}\:{of}\:{eggs} \\ $$$${which}\:{can}\:{be}\:{bought}\:{for}\:#\mathrm{120}\:{is}\:{reduced}\:{by}\:#\mathrm{5}.\:{What}\:{is}\:{the} \\ $$$${present}\:{price}\:{of}\:{the}\:{egg}. \\ $$

Question Number 6791 Answers: 1 Comments: 2

Question Number 6790 Answers: 0 Comments: 0

∫_0 ^1 ∫_y ^1 x^(−3/2) cos((πy)/(2x)) dx dy=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\int_{{y}} ^{\mathrm{1}} \:{x}^{−\mathrm{3}/\mathrm{2}} {cos}\frac{\pi{y}}{\mathrm{2}{x}}\:{dx}\:{dy}=? \\ $$

Question Number 6788 Answers: 0 Comments: 2

Question Number 6786 Answers: 0 Comments: 2

Three Arabs A,B and C were traveling together. On the lunch time A and B produce m and n loaves of bread respectively for eating but C have no loaf of bread. All the three ate together. After completing lunch C gave A and B m+n darhams. How shoud they divide this sum?

$${Three}\:{Arabs}\:{A},{B}\:{and}\:{C}\:{were}\:{traveling} \\ $$$${together}.\:{On}\:{the}\:{lunch}\:{time}\:{A}\:{and}\:\:{B} \\ $$$${produce}\:{m}\:{and}\:\:{n}\:{loaves}\:{of}\:{bread}\:{respectively} \\ $$$${for}\:{eating}\:{but}\:{C}\:{have}\:{no}\:{loaf}\:{of}\:{bread}.\:{All} \\ $$$${the}\:{three}\:{ate}\:{together}.\:\:{After}\:{completing} \\ $$$${lunch}\:{C}\:\:{gave}\:{A}\:{and}\:{B}\:{m}+{n}\:{darhams}. \\ $$$${How}\:{shoud}\:{they}\:{divide}\:{this}\:{sum}? \\ $$$$ \\ $$

Question Number 6775 Answers: 1 Comments: 0

∫_0 ^∞ e^t^2 e^(−st) dt please help

$$\int_{\mathrm{0}} ^{\infty} {e}^{{t}^{\mathrm{2}} } {e}^{−{st}} \:\:{dt} \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 6772 Answers: 0 Comments: 3

What is the smallest even number greater than 3 that cannot be expressed as the sum of two prime numbers ?

$${What}\:{is}\:{the}\:{smallest}\:{even}\:{number}\:{greater}\:{than}\:\mathrm{3}\:{that}\:{cannot} \\ $$$${be}\:{expressed}\:{as}\:{the}\:{sum}\:{of}\:{two}\:{prime}\:{numbers}\:? \\ $$

Question Number 6767 Answers: 0 Comments: 0

A molten plastic flows out of a tube that is 8.0cm long at a rate of 13cm^3 /min, when the pressure differential between the two ends of the tube is 18cm mercury. find the viscousity of the plastic. The internal diameter of the tube is 1.30mm. the density of mercury is 13.6g/cm^3

$${A}\:{molten}\:\:{plastic}\:{flows}\:{out}\:{of}\:{a}\:{tube}\:{that}\:{is}\:\mathrm{8}.\mathrm{0}{cm}\:{long} \\ $$$${at}\:{a}\:{rate}\:{of}\:\mathrm{13}{cm}^{\mathrm{3}} /{min},\:{when}\:{the}\:{pressure}\:{differential} \\ $$$${between}\:{the}\:{two}\:{ends}\:{of}\:{the}\:{tube}\:{is}\:\mathrm{18}{cm}\:{mercury}. \\ $$$${find}\:{the}\:{viscousity}\:{of}\:{the}\:{plastic}.\: \\ $$$${The}\:{internal}\:{diameter}\:{of}\:{the}\:{tube}\:{is}\:\:\mathrm{1}.\mathrm{30}{mm}.\: \\ $$$${the}\:{density}\:{of}\:{mercury}\:{is}\:\mathrm{13}.\mathrm{6}{g}/{cm}^{\mathrm{3}} \\ $$

Question Number 6778 Answers: 0 Comments: 1

If two forces P and Q acting at 0 are represented by line OA and OB with φ being the angle between the two forces . find their resultant in R in terms of P

$${If}\:{two}\:{forces}\:{P}\:{and}\:{Q}\:{acting}\:{at}\:\mathrm{0}\:{are}\:{represented}\:{by}\:{line}\:{OA} \\ $$$${and}\:{OB}\:{with}\:\phi\:{being}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{forces}\:. \\ $$$${find}\:{their}\:{resultant}\:{in}\:{R}\:{in}\:{terms}\:{of}\:{P} \\ $$

Question Number 6762 Answers: 1 Comments: 2

Question Number 6758 Answers: 0 Comments: 4

A circle of radius r has a point O as its centre. Points A and B are points on the circumference. For △OAB, OA^(−) =OB^(−) =r, AB^(−) =d, ∠AOB=θ. What is (r/d)?

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:{r}\:\mathrm{has}\:\mathrm{a}\:\mathrm{point}\:{O}\:\mathrm{as}\:\mathrm{its} \\ $$$$\mathrm{centre}.\:\mathrm{Points}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{circumference}. \\ $$$$ \\ $$$$\mathrm{For}\:\bigtriangleup{OAB},\:\overline {{OA}}=\overline {{OB}}={r},\:\overline {{AB}}={d},\:\angle{AOB}=\theta. \\ $$$$\mathrm{What}\:\mathrm{is}\:\frac{{r}}{{d}}? \\ $$

Question Number 6750 Answers: 3 Comments: 0

Question Number 6748 Answers: 1 Comments: 0

Question Number 6746 Answers: 1 Comments: 0

Evaluate I = ∫_1 ^2 ∫_2 ^4 (x + 2y) dx dy

$${Evaluate}\: \\ $$$$ \\ $$$${I}\:=\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\int_{\mathrm{2}} ^{\mathrm{4}} \:\:\:\left({x}\:+\:\mathrm{2}{y}\right)\:\:{dx}\:{dy}\: \\ $$

Question Number 6743 Answers: 1 Comments: 0

P and Q are partners in a venture, P contributed #20,000 for nine month, and Q contributed #50,000 for one year. find each person share of profit of #6,300

$${P}\:{and}\:{Q}\:{are}\:{partners}\:{in}\:{a}\:{venture},\:\:{P}\:\:{contributed}\:#\mathrm{20},\mathrm{000}\:{for} \\ $$$${nine}\:{month},\:{and}\:{Q}\:{contributed}\:#\mathrm{50},\mathrm{000}\:{for}\:{one}\:{year}.\:{find}\:{each} \\ $$$${person}\:{share}\:{of}\:\:{profit}\:{of}\:#\mathrm{6},\mathrm{300} \\ $$$$ \\ $$

Question Number 6739 Answers: 1 Comments: 0

Find the 102rd term of f(x) = e^(2x^3 ) at x = 0

$${Find}\:{the}\:\mathrm{102}{rd}\:{term}\:{of}\:\:\:{f}\left({x}\right)\:=\:{e}^{\mathrm{2}{x}^{\mathrm{3}} } \:\:\:{at}\:\:{x}\:=\:\mathrm{0} \\ $$

Question Number 6737 Answers: 0 Comments: 1

If z(x) is a complex function, is the following true: ∫zdx=∫ℜ(z)dx+i∫ℑ(z)dx

$$\mathrm{If}\:{z}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{function}, \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{true}: \\ $$$$\int{zdx}=\int\Re\left({z}\right){dx}+{i}\int\Im\left({z}\right){dx} \\ $$

Question Number 6736 Answers: 0 Comments: 0

Question Number 6733 Answers: 1 Comments: 0

Question Number 6726 Answers: 1 Comments: 0

Find the value of x x^2 = 16^x please help with workings.

$${Find}\:{the}\:{value}\:{of}\:{x} \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:=\:\mathrm{16}^{{x}} \\ $$$$ \\ $$$${please}\:{help}\:{with}\:{workings}. \\ $$

Question Number 6725 Answers: 0 Comments: 1

a+b=c a+a=ac c−a=b b+b=bc a^2 +b=c^3 a+D=b^2 b+D=a^2 a′b′+D=c′D ab+D=c_D ab+c=abc a′b′c′+D=D_(abc) abc+D=abc_D a^2 +b^± =Dab^(±2) (√(a^b +b^+_− ))=D^± (((a/b)+D))^(1/∂) =cot^(−1) a′b′

$${a}+{b}={c} \\ $$$${a}+{a}={ac} \\ $$$${c}−{a}={b} \\ $$$${b}+{b}={bc} \\ $$$${a}^{\mathrm{2}} +{b}={c}^{\mathrm{3}} \\ $$$${a}+{D}={b}^{\mathrm{2}} \\ $$$${b}+{D}={a}^{\mathrm{2}} \\ $$$${a}'{b}'+{D}={c}'{D} \\ $$$${ab}+{D}={c}_{{D}} \\ $$$${ab}+{c}={abc} \\ $$$${a}'{b}'{c}'+{D}={D}_{{abc}} \\ $$$${abc}+{D}={abc}_{{D}} \\ $$$${a}^{\mathrm{2}} +{b}^{\pm} ={Dab}^{\pm\mathrm{2}} \\ $$$$\sqrt{{a}^{{b}} +{b}^{+_{−} } }={D}^{\pm} \\ $$$$\sqrt[{\partial}]{\frac{{a}}{{b}}+{D}}=\mathrm{cot}^{−\mathrm{1}} {a}'{b}' \\ $$

Question Number 6723 Answers: 0 Comments: 1

An MTN mask is erected at a point P in ilaro town. At a point B due west, The angle of elevation of its top is β and at point C due south, the angle of elevation is α. With the aid of an appropriate diagam. show that the angle of elevation of the top from a point due south of B and due west of C is cot^(−1) [cot^2 (β) + cot^2 (α)]^(1/2)

$${An}\:{MTN}\:{mask}\:{is}\:{erected}\:{at}\:{a}\:{point}\:{P}\:\:{in}\:{ilaro}\:{town}.\:{At}\:{a}\:{point} \\ $$$${B}\:{due}\:{west},\:{The}\:{angle}\:{of}\:{elevation}\:{of}\:{its}\:{top}\:{is}\:\beta\:{and}\:{at}\:{point}\: \\ $$$${C}\:{due}\:{south},\:{the}\:{angle}\:{of}\:{elevation}\:{is}\:\alpha.\:{With}\:{the}\:{aid}\:{of}\:{an}\: \\ $$$${appropriate}\:{diagam}.\:{show}\:{that}\:{the}\:{angle}\:{of}\:{elevation}\:{of}\:{the}\:{top} \\ $$$${from}\:{a}\:{point}\:{due}\:{south}\:{of}\:{B}\:{and}\:{due}\:{west}\:{of}\:{C}\:{is}\: \\ $$$$ \\ $$$${cot}^{−\mathrm{1}} \left[{cot}^{\mathrm{2}} \left(\beta\right)\:+\:{cot}^{\mathrm{2}} \left(\alpha\right)\right]^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$

Question Number 6722 Answers: 0 Comments: 0

If 8789=89 7690=79 5478=69 then 5230=?

$${If}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{8789}=\mathrm{89} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{7690}=\mathrm{79} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{5478}=\mathrm{69} \\ $$$${then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{5230}=? \\ $$

Question Number 6716 Answers: 1 Comments: 0

Prove that the locus of a point which moves its distance from the point (−b, 0) is p times its distance from the point (b, 0) is (p^2 − 1)(x^2 + y^2 + b^2 ) − 2b(p^2 + 1)x = 0 Show that this locus is a circle and find its radius.

$${Prove}\:{that}\:{the}\:{locus}\:{of}\:{a}\:{point}\:{which}\:{moves}\:{its}\:{distance}\:{from}\: \\ $$$${the}\:{point}\:\left(−{b},\:\mathrm{0}\right)\:{is}\:{p}\:{times}\:{its}\:{distance}\:{from}\:{the}\:{point}\:\left({b},\:\mathrm{0}\right)\:{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right)\:−\:\mathrm{2}{b}\left({p}^{\mathrm{2}} \:+\:\mathrm{1}\right){x}\:=\:\mathrm{0} \\ $$$${Show}\:{that}\:{this}\:{locus}\:{is}\:{a}\:{circle}\:{and}\:{find}\:{its}\:{radius}. \\ $$

Question Number 6715 Answers: 1 Comments: 0

Solve the following equation for 0 < Θ < 360^o cosx + cos3x + cos5x + cos7x = 0

$${Solve}\:{the}\:{following}\:{equation}\:{for}\:\mathrm{0}\:<\:\Theta\:<\:\mathrm{360}^{{o}} \\ $$$${cosx}\:+\:{cos}\mathrm{3}{x}\:+\:{cos}\mathrm{5}{x}\:+\:{cos}\mathrm{7}{x}\:=\:\mathrm{0} \\ $$

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