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A carrier based on its anual records notes that its trucks cover 50000 km with a normal distribution with a detour of 12000 km. How many miles can be traveled at least 80% of trucks ?

$${A}\:{carrier}\:{based}\:{on}\:{its}\:{anual}\:{records}\:{notes}\:{that}\:{its}\:{trucks}\:{cover}\:\mathrm{50000} \\ $$$${km}\:{with}\:{a}\:{normal}\:{distribution}\:{with}\:{a}\:{detour}\:{of}\:\mathrm{12000}\:{km}. \\ $$$${How}\:{many}\:{miles}\:{can}\:{be}\:{traveled}\:{at}\:{least}\:\mathrm{80\%}\:{of}\:{trucks}\:? \\ $$

Question Number 17220 Answers: 1 Comments: 0

Show that ∫_a ^( b) f(kx)dx=(1/k)∫_(ka) ^( kb) f(x)dx

$$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{a}} ^{\:\mathrm{b}} {f}\left(\mathrm{kx}\right)\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{k}}\int_{\mathrm{ka}} ^{\:\mathrm{kb}} {f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 17219 Answers: 1 Comments: 1

∫_0 ^( 2a) xy dx=? where x^2 −y^2 =a^2 and y≥0

$$\int_{\mathrm{0}} ^{\:\mathrm{2a}} \mathrm{xy}\:\mathrm{dx}=?\:\:\mathrm{where}\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$

Question Number 17209 Answers: 1 Comments: 0

Spin only magnetic moment of _(25) Mn^(x+) is (√(15))B.M. Then the value of x is? i did following 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5 so to get 3 unpaired electron we need to 2 electron so x=2. book says x=4. Why?

$$\mathrm{Spin}\:\mathrm{only}\:\mathrm{magnetic}\:\mathrm{moment} \\ $$$$\mathrm{of}\:_{\mathrm{25}} \mathrm{Mn}^{\mathrm{x}+} \:\mathrm{is}\:\sqrt{\mathrm{15}}\mathrm{B}.\mathrm{M}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{is}? \\ $$$$\mathrm{i}\:\mathrm{did}\:\mathrm{following} \\ $$$$\mathrm{1s}^{\mathrm{2}} \mathrm{2s}^{\mathrm{2}} \mathrm{2p}^{\mathrm{6}} \mathrm{3s}^{\mathrm{2}} \mathrm{3p}^{\mathrm{6}} \mathrm{4s}^{\mathrm{2}} \mathrm{3d}^{\mathrm{5}} \\ $$$$\mathrm{so}\:\mathrm{to}\:\mathrm{get}\:\mathrm{3}\:\mathrm{unpaired}\:\mathrm{electron} \\ $$$$\mathrm{we}\:\mathrm{need}\:\mathrm{to}\:\mathrm{2}\:\mathrm{electron}\:\mathrm{so}\:\mathrm{x}=\mathrm{2}. \\ $$$$\mathrm{book}\:\mathrm{says}\:\mathrm{x}=\mathrm{4}.\:\mathrm{Why}? \\ $$

Question Number 17210 Answers: 1 Comments: 0

prove that ∫_0 ^( Π) f(sin x)dx=2×∫_0 ^( (Π/2)) f(sin x)dx

$$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\Pi} {f}\left(\mathrm{sin}\:\mathrm{x}\right)\mathrm{dx}=\mathrm{2}×\int_{\mathrm{0}} ^{\:\frac{\Pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\:\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 17206 Answers: 1 Comments: 0

What will be the vallu of ∫_(−a) ^( a) x^2 y dx ? Where x^2 +y^2 =a^2 and y≥0

$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{vallu}\:\mathrm{of}\:\int_{−\mathrm{a}} ^{\:\mathrm{a}} \mathrm{x}^{\mathrm{2}} \mathrm{y}\:\mathrm{dx}\:\:? \\ $$$$\mathrm{Where}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$

Question Number 17205 Answers: 1 Comments: 0

lim_(n→∞) Σ_(r=1) ^(n−1) (1/n)(√((n+r)/(n−r)))

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}}\sqrt{\frac{\mathrm{n}+\mathrm{r}}{\mathrm{n}−\mathrm{r}}} \\ $$

Question Number 17204 Answers: 2 Comments: 0

∫_0 ^( (Π/2)) sinθ cosθ(a^2 sin^2 θ+b^2 cos^2 θ)^(1/2) dθ