Question and Answers Forum

A machine manufactures washers, and 20% of the production is substandard. A random sample o f 10 washers is selected. Find the mean and standard deviation of the number of substandard washers in the sample.

$$\mathrm{A}\:\mathrm{machine}\:\mathrm{manufactures}\:\mathrm{washers},\:\mathrm{and}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{production}\:\mathrm{is} \\ $$$$\mathrm{substandard}.\:\mathrm{A}\:\mathrm{random}\:\mathrm{sample}\:\mathrm{o}\:\mathrm{f}\:\mathrm{10}\:\mathrm{washers}\:\mathrm{is}\:\mathrm{selected}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{substandard}\:\mathrm{washers}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sample}. \\ $$

Question Number 105661 Answers: 2 Comments: 1

lim_(x→π/2) tan^2 x (√((x−(π/2))−cos ^2 x)) ?

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{tan}\:^{\mathrm{2}} {x}\:\sqrt{\left({x}−\frac{\pi}{\mathrm{2}}\right)−\mathrm{cos}\:\:^{\mathrm{2}} {x}}\:? \\ $$

Question Number 105659 Answers: 2 Comments: 0

(d^2 y/dx^2 ) + (dy/dx)−2y=2x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}−\mathrm{2}{y}=\mathrm{2}{x}\: \\ $$

Question Number 105650 Answers: 2 Comments: 0

cos^(−1) (2x)+ cos^(−1) (x)=(π/6) find x

$$\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)+\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)=\frac{\pi}{\mathrm{6}} \\ $$$${find}\:{x} \\ $$

Question Number 105646 Answers: 1 Comments: 0

Solve the differential equation; y′′−2ay′+(1+a^2 )y=te^(at) +sint

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$

Question Number 105638 Answers: 2 Comments: 0

(d^2 y/dx^2 ) + 9y = cos 4x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{9}{y}\:=\:\mathrm{cos}\:\mathrm{4}{x} \\ $$

Question Number 105634 Answers: 0 Comments: 0

Question Number 105632 Answers: 1 Comments: 0

Given I_n =∫_0 ^1 (((1−x)^n )/(n!))e^x dx , n∈N a\Show that ∀x∈[0,1], (1−x)^n e^x ≤e and deduce that the Sequence (I_n )_n converges to zero. b\Establish a recurrence relation between I_n and I_(n+1) c\ Deduce that e=lim_(n→∞) Σ_(k=0) ^n ((1/(k!)))

$$\mathrm{Given}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} }{\mathrm{n}!}\mathrm{e}^{\mathrm{x}} \mathrm{dx}\:,\:\mathrm{n}\in\mathbb{N} \\ $$$$\mathrm{a}\backslash\mathrm{Show}\:\mathrm{that}\:\forall\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right],\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} \mathrm{e}^{\mathrm{x}} \leqslant\mathrm{e}\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{Sequence}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{to}\:\mathrm{zero}. \\ $$$$\mathrm{b}\backslash\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{I}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{I}_{\mathrm{n}+\mathrm{1}} \\ $$$$\mathrm{c}\backslash\:\mathrm{Deduce}\:\mathrm{that}\:\mathrm{e}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{k}!}\right) \\ $$

Question Number 105630 Answers: 0 Comments: 2

Question Number 105625 Answers: 1 Comments: 0

prove that ((m),(m) ) ((( n)),((n−k)) )+ ((( m)),((m−1)) ) ((( n)),((n−k+1)) ) + ((( m)),((m−2)) ) ((( n)),((n−k+2)) )+......+ ((( m)),((m−k)) ) ((n),(n) ) = (((m+n)),(( k)) )

$${prove}\:{that} \\ $$$$\begin{pmatrix}{{m}}\\{{m}}\end{pmatrix}\begin{pmatrix}{\:\:\:{n}}\\{{n}−{k}}\end{pmatrix}+\begin{pmatrix}{\:\:\:\:{m}}\\{{m}−\mathrm{1}}\end{pmatrix}\begin{pmatrix}{\:\:\:\:\:\:\:{n}}\\{{n}−{k}+\mathrm{1}}\end{pmatrix} \\ $$$$+\begin{pmatrix}{\:\:\:{m}}\\{{m}−\mathrm{2}}\end{pmatrix}\begin{pmatrix}{\:\:\:\:\:\:\:\:{n}}\\{{n}−{k}+\mathrm{2}}\end{pmatrix}+......+\begin{pmatrix}{\:\:\:\:{m}}\\{{m}−{k}}\end{pmatrix}\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix} \\ $$$$=\begin{pmatrix}{{m}+{n}}\\{\:\:\:\:\:{k}}\end{pmatrix} \\ $$

Question Number 105619 Answers: 2 Comments: 0

find General solution cot x+cot 2x+cot3x= 0

$${find}\:\mathcal{G}{eneral}\:{solution}\:\mathrm{cot}\:{x}+\mathrm{cot}\:\mathrm{2}{x}+\mathrm{cot3}{x}=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 105616 Answers: 2 Comments: 0