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AlgebraQuestion and Answers: Page 327

Question Number 48559    Answers: 3   Comments: 0

Question Number 48553    Answers: 1   Comments: 2

In a hospital unit,there are 8 nurses and 5 physicians. 7 of them are female nurses and 3 of them are male physicians. what is the the probability of selecting a staff who is Nurse or Male? plzz help

$$\mathrm{In}\:\mathrm{a}\:\mathrm{hospital}\:\mathrm{unit},\mathrm{there}\:\mathrm{are}\:\mathrm{8}\:\mathrm{nurses} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{physicians}.\:\mathrm{7}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{female}\:\mathrm{nurses}\:\mathrm{and}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{male}\:\mathrm{physicians}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{selecting}\:\mathrm{a}\:\mathrm{staff}\:\mathrm{who}\:\mathrm{is}\:\mathrm{Nurse}\:\mathrm{or} \\ $$$$\mathrm{Male}? \\ $$$$\mathrm{plzz}\:\mathrm{help} \\ $$$$ \\ $$$$ \\ $$

Question Number 48509    Answers: 0   Comments: 0

For every natural numbers n Find the value of Σ_(0≤j≤i≤n) (((−1)^j )/((n − i)! j!))

$${For}\:\:{every}\:\:{natural}\:\:{numbers}\:\:{n}\:\: \\ $$$${Find}\:\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}\leqslant{j}\leqslant{i}\leqslant{n}} {\sum}\:\:\frac{\left(−\mathrm{1}\right)^{{j}} }{\left({n}\:−\:{i}\right)!\:{j}!} \\ $$

Question Number 48482    Answers: 0   Comments: 0

(at−h)^2 +((a/t)−k)^2 =R^( 2) where a, h, k, R are constants. Then find s^2 =(t_1 −t_2 )^2 (1+(1/(t_1 ^2 t_2 ^2 ))) where t_1 , t_2 are roots of eq. at top.

$$\left({at}−{h}\right)^{\mathrm{2}} +\left(\frac{{a}}{{t}}−{k}\right)^{\mathrm{2}} ={R}^{\:\mathrm{2}} \\ $$$${where}\:\:\:{a},\:{h},\:{k},\:{R}\:{are}\:{constants}. \\ $$$${Then}\:{find}\: \\ $$$$\:\:\:{s}^{\mathrm{2}} \:=\left({t}_{\mathrm{1}} −{t}_{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{t}_{\mathrm{1}} ^{\mathrm{2}} {t}_{\mathrm{2}} ^{\mathrm{2}} }\right)\: \\ $$$${where}\:{t}_{\mathrm{1}} ,\:{t}_{\mathrm{2}} \:{are}\:{roots}\:{of}\:{eq}.\:{at}\:{top}. \\ $$

Question Number 48447    Answers: 0   Comments: 4

Find the sum Σ_(k=0) ^(10) ^(20) C_k .

$${Find}\:{the}\:{sum}\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:^{\mathrm{20}} {C}_{{k}} \:. \\ $$

Question Number 48443    Answers: 1   Comments: 3

Coefficient of x^4 in (2−x+3x^2 )^6 =?

$${Coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:\left(\mathrm{2}−{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{6}} =? \\ $$

Question Number 48368    Answers: 1   Comments: 0

Question Number 48367    Answers: 2   Comments: 0

Question Number 48306    Answers: 1   Comments: 0

x^2 +4x+1=9

$$\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{1}=\mathrm{9} \\ $$

Question Number 48295    Answers: 1   Comments: 0

Question Number 48294    Answers: 2   Comments: 3

Question Number 48272    Answers: 0   Comments: 1

z^5 =32 find all root z

$$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$

Question Number 48225    Answers: 1   Comments: 0

prove that exp(((2+πi)/4))=(√(e/2))(1+i) cos (z_1 +z_2 )=cos z_1 cos z_2 −sin z_1 sin z_2

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$

Question Number 48224    Answers: 1   Comments: 0

e^z =1−(√3)i z=..

$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$

Question Number 48222    Answers: 0   Comments: 0

f(x)=Σ_(i=0) ^(n) a_i x^i =a_n x^n +a_(n−1) x^(n−1) +a_(n−2) x^(n−2) +…+a_2 x^2 +a_1 x+a_0 f^(−1) (x)=...

$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}} {\Sigma}}{a}_{{i}} {x}^{{i}} ={a}_{{n}} {x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} {x}^{{n}−\mathrm{2}} +\ldots+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 48204    Answers: 1   Comments: 0

2(x^4 −2x^2 +3)(y^4 −3y^2 +4)=7 Find (x,y) .

$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$

Question Number 48161    Answers: 1   Comments: 1

f(z)=((1−z)/(1+z)) u(x,y)=.. v(x,y)=..

$${f}\left({z}\right)=\frac{\mathrm{1}−{z}}{\mathrm{1}+{z}} \\ $$$${u}\left({x},{y}\right)=.. \\ $$$${v}\left({x},{y}\right)=.. \\ $$$$ \\ $$$$ \\ $$

Question Number 48075    Answers: 1   Comments: 1

solve (∣x^2 −1∣−(1/2))x+((√6)/(18))=0

$$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$

Question Number 48055    Answers: 2   Comments: 6

Solve the system: { ((x^3 +x^2 y−4xy^2 −4y^3 =0)),((x^2 −2xy−3y^2 −x−y=0)) :}

$${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$

Question Number 47993    Answers: 0   Comments: 5

Solve in R ((59+(√(x−2))))^(1/3) +((12−(√(x−11))))^(1/3) =6

$${Solve}\:{in}\:\mathbb{R} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{59}+\sqrt{{x}−\mathrm{2}}}+\sqrt[{\mathrm{3}}]{\mathrm{12}−\sqrt{{x}−\mathrm{11}}}=\mathrm{6} \\ $$

Question Number 47986    Answers: 3   Comments: 1

Question Number 47966    Answers: 1   Comments: 1

a(x^2 +y^2 )+b(x+y)= c & x^2 −y^2 = R^2 Solve for x or y .

$${a}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+{b}\left({x}+{y}\right)=\:{c} \\ $$$$\:\&\:\:\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:=\:{R}^{\mathrm{2}} \\ $$$${Solve}\:{for}\:{x}\:{or}\:{y}\:. \\ $$

Question Number 47916    Answers: 2   Comments: 1

Question Number 47807    Answers: 1   Comments: 0

sin xy^2 =y^2 +2x diferential express is

$$\mathrm{sin}\:{xy}^{\mathrm{2}} ={y}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$$ \\ $$$$\mathrm{diferential}\:{express}\:\mathrm{is} \\ $$

Question Number 47778    Answers: 1   Comments: 0

f(x)=2x^3 +x^2 −2x−1 f^(−1) (x)=...

$${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 47712    Answers: 0   Comments: 0

show that ^(^2 C_2 ) C_n = (1/((1−n)!(n−1)(n−2)(n−3)...3(2)(1)))

$${show}\:{that}\: \\ $$$$\:\:^{\:^{\mathrm{2}} \:{C}_{\mathrm{2}} \:} {C}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{1}−{n}\right)!\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{3}\right)...\mathrm{3}\left(\mathrm{2}\right)\left(\mathrm{1}\right)} \\ $$

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