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Compotition of two finctions: Adrenced\newlineFor the real-yalued functions f(x)=3x+30 f(x)=\sqrt{3 x+30} and g(x)=x−5 g(x)=x-5 , find the composition f∘g f \circ g and specfy its domain using interyel notation\newline(f∘z)(x)=□ (f \circ z)(x)=\square \newlineDomain of f∘g: f \circ g: \newline\begin{tabular}{|ccc}\newline\hline \frac{}{} & 口P ^{P} & □ \sqrt{\square} \\\newline미미 & (0,,□) (0,, \square) & {[0,□] [0, \square] } \\\newline미 & (0,□] (0, \square] & {g(x)=x−5 g(x)=x-5 00} \\\newlineg(x)=x−5 g(x)=x-5 11 & g(x)=x−5 g(x)=x-5 22 & g(x)=x−5 g(x)=x-5 33 \\\newlineg(x)=x−5 g(x)=x-5 44 & & 33 \\\newline\hline\newline\end{tabular}
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33. There are only chicken and fish as non-veg items in a party. In a group of 200200 non-veg people, 8080 like only chicken and 6060 like only fish. If the number of people who do not like any of the two non-veg items is double of the number of people who like both items, answer the following questions.\newline(a) If the sets of people who like chicken and fish are represent by C \mathrm{C} and F \mathrm{F} respectively, what does n(CΔF) \mathrm{n}(\mathrm{C} \Delta \mathrm{F}) mean?\newline[1 K] [1 \mathrm{~K}] \newline(b) Illustrate the above information in a Venn-diagram.\newline[1U] [1 \mathrm{U}] \newline(c) Find the number of people who like at least one of the items.\newline[3 A] [3 \mathrm{~A}] \newline(d) How many people do not like chicken at all in each 100100 people?\newline[11HA]
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For Numbers 4646 - 5050: MULTIPLE-CHOICE\newlineINSTRUCTIONS: A if ONLY the FIRST statement is ALWAYS true, B if ONLY the SECOND statement is ALWAYS true, C \mathbf{C} if BOTH STATEMENTS are ALWAYS true and D if BOTH STATEMENTS are NOT always true.\newline4646. Functions expressed in the form of y=f(x) \mathrm{y}=\mathrm{f}(\mathrm{x}) can be solely differentiated explicitly. However, curves that fail both the vertical line test and the horizontal line test are not differentiable.\newline4747. In differentiating a function with respect to its independent variable, you take the derivative as it is (for example the derivative of y2 \mathrm{y}^{2} with respect to x \mathrm{x} is 2y 2 \mathrm{y} ) but you add it with the factor of the inner function's derivative (dy/dx), as encapsulated by the chain rule.\newlineThe dy/dx \mathrm{dy} / \mathrm{dx} is always a unique value, meaning the value of the slope never repeats for all (x,y) (x, y) that lie on a given curve.\newline4848. If f(x)=g(x) f(x)=g(x) , then f0(x)=g0(x) f_{0}(x)=g_{0}(x) . If f0(x)=g0(x) f_{0}(x)=g_{0}(x) , then f(x)=g(x) f(x)=g(x) .\newline4949. If a function is integrable over the interval y=f(x) \mathrm{y}=\mathrm{f}(\mathrm{x}) 11, then it is continuous.\newlineConversely, continuity implies integrability.\newline5050. Differentiability (over an interval) implies integrability.\newlineIf a function is integrable over an interval, then it is differentiable for all points between the endpoints of that interval.
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outlook\newlineSpotily: Węb Play\newlinero\newlineVour Sets\newlineA. Adobe Acróbat\newlineAlgebra II PD 77\newlineDeltaMath\newlineGiven the matrices A A and B B shown below, find B−16A B-\frac{1}{6} A .\newlineA=[−24246−30−1812−36−18]B=[4−961−12−11−40] A=\left[\begin{array}{cc} -24 & 24 \\ 6 & -30 \\ -18 & 12 \\ -36 & -18 \end{array}\right] \quad B=\left[\begin{array}{cc} 4 & -9 \\ 6 & 1 \\ -12 & -11 \\ -4 & 0 \end{array}\right] \newlineAnswer\newlineAttempt\newline22 out of\newlineRows: 44\newline⊖⊕ \ominus \oplus \newlineColumns: 22\newlineθ \boldsymbol{\theta} \newline[8−8.58] \left[\begin{array}{cc} 8 & -8 \\ .5 & 8 \end{array}\right]
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Equation of a Line : y=mx+b y=m x+b \newlineMTH 11W\newlineSection 44 Test: Modeling with Graphs (Modified)\newlineSlope =m= rise  run =y2−y1x2−x1 =m=\frac{\text { rise }}{\text { run }}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \newlinePage 55\newlineOptional Bonus Question [88 marks]\newline1313. A pattern of toothpicks is shown.\newline[22] (a) Complete the given table.\newline[11] (b) Apply first difference calculation on the table.\newline[11] (c) Is the pattern linear or non-linear?\newline[22] (d) Write the equation for the relation.\newline11 house\newline\begin{tabular}{|c|c|}\newline\hline \begin{tabular}{c} \newlinez of \\\newlineHouses\newline\end{tabular} & \begin{tabular}{c} \newlineFof \\\newlineToothpicks\newline\end{tabular} \\\newline\hline 11 & \\\newline\hline 22 & \\\newline\hline 33 & \\\newline\hline 44 & \\\newline\hline\newline\end{tabular}\newline[22] (e) Extrapolate the relation to predict the outcome for 1010 houses.
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e allowed: 22:4040 Hours\newline(Scien\newlineAttempt the following Questions.\newlineSECTION -\newline If A=[1112],B=[−2647] then find X when X+4A=7B S. x:A=[1112],B=[−2647]X+4A=7B4m′′×154m−2m−1×9n−2m102m×25m−220m \begin{array}{l} \text { If } A=\left[\begin{array}{ll} 1 & 1 \\ 1 & 2 \end{array}\right], B=\left[\begin{array}{cc} -2 & 6 \\ 4 & 7 \end{array}\right] \text { then find } X \text { when } \\ X+4 A=7 B \\ \text { S. } x: A=\left[\begin{array}{ll} 1 & 1 \\ 1 & 2 \end{array}\right], B=\left[\begin{array}{cc} -2 & 6 \\ 4 & 7 \end{array}\right] \\ X+4 A=7 B \\ \frac{4^{m \prime \prime} \times 15^{4 m-2 m-1} \times 9^{n-2 m}}{10^{2 m} \times 25^{m-2} 20 m} \\ \end{array} \newlineSimplify:
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11. If y=xsin⁡x y=x \sin x , then dydx= \frac{d y}{d x}= \newline(A) sin⁡x+cos⁡x \sin x+\cos x \newline(B) sin⁡x+xcos⁡x \sin x+x \cos x \newline(C) sin⁡x−xcos⁡x \sin x-x \cos x \newline(D) x(sin⁡x+cos⁡x) x(\sin x+\cos x) \newline(E) x(sin⁡x−cos⁡x) x(\sin x-\cos x) \newline22. Let f f be the function given by f(x)=300x−x3 f(x)=300 x-x^{3} . On which of the following intervals is the function f f increasing?\newline(A) dydx= \frac{d y}{d x}= 00 and dydx= \frac{d y}{d x}= 11\newline(B) dydx= \frac{d y}{d x}= 22\newline(C) dydx= \frac{d y}{d x}= 33 only\newline(D) dydx= \frac{d y}{d x}= 44 only\newline(E) dydx= \frac{d y}{d x}= 55\newlineUnauthorized copying or reuse of\newlineany part of this page is illegal.\newlineGO ON TO THE NEXT PAGE.\newlinedydx= \frac{d y}{d x}= 66\newlineA A A A A A A A A A A A A A A A A A A A A A A A A A A A\newline33. dydx= \frac{d y}{d x}= 77\newline(A) dydx= \frac{d y}{d x}= 88\newline(B) dydx= \frac{d y}{d x}= 99\newline(C) sin⁡x+cos⁡x \sin x+\cos x 00\newline(D) sin⁡x+cos⁡x \sin x+\cos x 11\newline(E) sin⁡x+cos⁡x \sin x+\cos x 22
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11. If y=xsin⁡x y=x \sin x , then dydx= \frac{d y}{d x}= \newline(A) sin⁡x+cos⁡x \sin x+\cos x \newline(B) sin⁡x+xcos⁡x \sin x+x \cos x \newline(C) sin⁡x−xcos⁡x \sin x-x \cos x \newline(D) x(sin⁡x+cos⁡x) x(\sin x+\cos x) \newline(E) x(sin⁡x−cos⁡x) x(\sin x-\cos x) \newline22. Let f f be the function given by f(x)=300x−x3 f(x)=300 x-x^{3} . On which of the following intervals is the function f f increasing?\newline(A) dydx= \frac{d y}{d x}= 00 and dydx= \frac{d y}{d x}= 11\newline(B) dydx= \frac{d y}{d x}= 22\newline(C) dydx= \frac{d y}{d x}= 33 only\newline(D) dydx= \frac{d y}{d x}= 44 only\newline(E) dydx= \frac{d y}{d x}= 55\newlineUnauthorized copying or reuse of\newlineany part of this page is illegal.\newlineGO ON TO THE NEXT PAGE.\newline−4-4-\newlineA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A\newline33. dydx= \frac{d y}{d x}= 66\newline(A) dydx= \frac{d y}{d x}= 77\newline(B) dydx= \frac{d y}{d x}= 88\newline(C) dydx= \frac{d y}{d x}= 99\newline(D) sin⁡x+cos⁡x \sin x+\cos x 00\newline(E) sin⁡x+cos⁡x \sin x+\cos x 11
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1ABC \sqrt{1} A B C adalah segitiga sama sisi dengan panjang sisi s s satuan dan persegi PQRS P Q R S panjang sisi 2m 2 m satuan.\newlinefininglah panjang segmen garis CD C D serta tentukan besar ∠CAB \angle C A B dan ∠DCA \angle D C A pada △ABC \triangle A B C serta panjang PR P R un besar ∠QPR \angle Q P R pada persegi PQRS P Q R S .\newlineCD=…∠CAB=…∠DCA=… \begin{array}{l} C D=\ldots \\ \angle C A B=\ldots \\ \angle D C A=\ldots \end{array} \newlinePR=…∠QPR=…. \begin{array}{l} P R=\ldots \\ \angle Q P R=\ldots . \end{array} \newlineDari ukuran sisi-sisi segitiga dan besarnya sudut di atas diapat ditentukan nilai-nilai perbandingan trigonometri, sinus, cosinus dan tangen sudut s s 11 dan ∠QPR \angle Q P R \newlines s 33\newlinecos⁡∠CAB=cos⁡….∘=±tan⁡∠CAB=tan⁡….∘=±cos⁡∠DCA=cos⁡….∘=tan⁡∠DCA=tan⁡…∘=±cos⁡∠QPR=cos⁡….∘=±tan⁡∠QPR=tan⁡…∘=± \begin{array}{ll} \cos \angle C A B=\cos \ldots .^{\circ}= \pm & \tan \angle C A B=\tan \ldots .^{\circ}= \pm \\ \cos \angle D C A=\cos \ldots .^{\circ}= & \tan \angle D C A=\tan \ldots{ }^{\circ}= \pm \\ \cos \angle Q P R=\cos \ldots .^{\circ}= \pm & \tan \angle Q P R=\tan \ldots{ }^{\circ}= \pm \end{array} \newlines s 44\newlinesin⁡∠QPR=sin⁡…∘= \sin \angle Q P R=\sin \ldots{ }^{\circ}= \newlineKemudian juga carilah di berbaga. sumber untuk menentukan nilai sinus, cosinus dan tangen sudut s s 55 dan s s 66\newlineDari hasil-hasil tersebut lengkapi tabel berikut :\newline\begin{tabular}{|c|c|c|c|c|c|}\newline\hlines s 77 & s s 55 & s s 99 & PQRS P Q R S 00 & PQRS P Q R S 11 & s s 66 \\\newline\hline PQRS P Q R S 33 & & & & & \\\newline\hline PQRS P Q R S 44 & & & & & \\\newline\hline PQRS P Q R S 55 & & & & & \\\newline\hline\newline\end{tabular}
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Review of 55.33, 55.44, and 55.55\newlinePerform the indicated operation.\newline11)\newlineg(a)=2a−4h(a)=−4a−26a−2 Find (g−h)(a) \begin{array}{l} g(a)=2 a-4 \\ h(a)=-4 a-2 \quad 6 a-2 \\ \text { Find }(g-h)(a) \end{array} \newline33)\newlineg(n)=2n−3f(n)=2n2+5n Find g(n)+f(n) \begin{array}{l} g(n)=2 n-3 \\ f(n)=2 n^{2}+5 n \\ \text { Find } g(n)+f(n) \end{array} \newline55)\newlinef(a)=−a3−3ag(a)=−4a+2 Find f(−3)+g(−3) \begin{array}{l} f(a)=-a^{3}-3 a \\ g(a)=-4 a+2 \\ \text { Find } f(-3)+g(-3) \end{array} \newline77)\newlineg(x)=−x−3f(x)=x2−5x Find g(x)⋅f(x) \begin{array}{l} g(x)=-x-3 \\ f(x)=x^{2}-5 x \\ \text { Find } g(x) \cdot f(x) \end{array} \newline99)\newlinef(n)=n+2g(n)=4n+4 Find f(−3)⋅g(−3) \begin{array}{l} f(n)=n+2 \\ g(n)=4 n+4 \\ \text { Find } f(-3) \cdot g(-3) \end{array}
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AA\newlineapp.educationperfect.com\newlineEducation P...\newlineBeach Form...\newlineep\newlineOnline Shop...\newline(1515)\newlineBeach Form...\newlineS s33.amazona...\newlineB\newlineBytelearn\newlineGaga\newlineGagaMia\newlineCalculating Surface Area of Prisms\newlineSebastyan A 238238\newlineEstelle B\newline240240\newlineAli I 240240\newlineYou 240240\newlineMookyungs 246246\newlineAlmaa M 247247\newlineRashid W 2424 s\newline=21×18=378 cm2 \begin{array}{l} =21 \times 18 \\ =378 \mathrm{~cm}^{2} \end{array} \newlineARectangle =lw A_{\text {Rectangle }}=l w \newline=21×27=567 cm2 \begin{array}{l} =21 \times 27 \\ =567 \mathrm{~cm}^{2} \end{array} \newlineARectangle =lw A_{\text {Rectangle }}=l w \newline=18×27=486 cm2SA=378+378+486+486+567+567SA=2862 cm2 \begin{array}{c} =18 \times 27 \\ =486 \mathrm{~cm}^{2} \\ S A=378+378+486+486+567+567 \\ S A=2862 \mathrm{~cm}^{2} \end{array}
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Yuk kita temukan perbandingan trigonometri pada kuadran II, menggunakan sumbu koordinat!\newlineCerminkan segitiga di Kuadran I Ke Kuadran II sehingga :\newlinex′=−xy′=yr′=r \begin{aligned} x^{\prime} & =-x \\ y^{\prime} & =y \\ r^{\prime} & =r \end{aligned} \newlinePerhatikan segitiga merah di Kuadran 22, aplikasikan perbandingan trigonometri pada segitiga siku-siku\newlinesin⁡(180∘−α)=…..…..=−…….cos⁡(180∘−α)=x′r′=−xr=−cos⁡αtan⁡(180∘−α)=…..…..=−=….. \begin{array}{l} \sin \left(180^{\circ}-\alpha\right)=\frac{\ldots . .}{\ldots . .}=-\ldots \ldots . \\ \cos \left(180^{\circ}-\alpha\right)=\frac{x^{\prime}}{r^{\prime}}=\frac{-x}{r}=-\cos \alpha \\ \tan \left(180^{\circ}-\alpha\right)=\frac{\ldots . .}{\ldots . .}=-=\ldots . . \end{array}
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The accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 00.0101 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels.\newline\begin{tabular}{lrrrrrrrr} \newlineMedium & 8383 & 8686 & 9292 & 7272 & 7777 & 9191 & 8282 & 4646 \\\newline& 9898 & 9393 & 114114 & 7979 & 7171 & 9090 & 111111 & 7878 \\\newline& & & & & & & & \\\newlineHigh & 101101 & 8585 & 8585 & 8282 & 7979 & 7676 & 104104 & 8888 \\\newline& 104104 & 9494 & 8989 & 8080 & 7575 & 9393 & 7575 &\newline\end{tabular}\newlineLet sample 11 be the sample with the larger sample variance, and let sample 22 be the sample with the smaller sample variance. What are the null and alternative hypotheses?\newlineA. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineB.\newlineH0:σ12=σ22H1:σ12≠σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array} \newlineH1:σ12<σ22 \mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \newlineC. H0:σ12=σ22 \mathrm{H}_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineH1:σ12>σ22 \mathrm{H}_{1}: \sigma_{1}^{2}>\sigma_{2}^{2} \newlineD.\newlineH0:σ12≠σ22H1:σ12=σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \end{array} \newlineIdentify the test statistic.\newlineThe test statistic is □ \square \newline(Round to two decimal places as needed.)
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The accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 00.0101 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels.\newlineC. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineH0:σ12=σ22H1:σ12≠σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array} \newlineH1:σ12>σ22 \mathrm{H}_{1}: \sigma_{1}^{2}>\sigma_{2}^{2} \newlineIdentify the test statistic.\newlineThe test statistic is 22.8282 .\newline(Round to two decimal places as needed.)\newlineIdentify the P-value.\newlineThe P-value is □ \square .\newline(Round to three decimal places as needed.)
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Ans:\newlineb3 b^{3} \newline\begin{tabular}{|c|l|c|c|}\newline\hline & & ( ) & () \\\newline\hline S & I am able to multiply a proper fraction and a whole number. & ✓ \checkmark \\\newline\hline S & I am able to express a mixed number in its simplest form. & \\\newline\hline T & You are able to multiply a proper fraction and a whole number. & \\\newline\hline T & You are able to express a mixed number in its simplest form. & \\\newline\hline\newline\end{tabular}\newline44. Find the value of 54×1210 \frac{5}{4} \times \frac{12}{10} . Give your answer as a mixed number in its simplest form.\newline5×124×10×1210×4=6040=2040 \begin{array}{l} \frac{5 \times 12}{4 \times 10} \times \frac{12}{10} \times 4 \\ =\frac{60}{40} \\ =2 \frac{0}{40} \end{array} \newlineAns:
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Consider the polynomial function h(x)=x6−3x5−17x3h(x)=x^{6}-3x^{5}-17x^{3}. \newlineWhat is the end behavior of the graph of hh?\newlineChoose 11 answer:\newline(A) As x→∞,h(x)→∞x \rightarrow \infty, h(x)\rightarrow \infty, and as x→−∞,h(x)→∞x \rightarrow -\infty, h(x)\rightarrow \infty.\newline(B) As x→∞,h(x)→−∞x \rightarrow \infty, h(x)\rightarrow -\infty, and as x→−∞,h(x)→∞x \rightarrow -\infty, h(x)\rightarrow \infty.\newline(C) As x→∞,h(x)→−∞x \rightarrow \infty, h(x)\rightarrow -\infty, and as x→−∞,h(x)→−∞x \rightarrow -\infty, h(x)\rightarrow -\infty.\newline(D) As x→∞,h(x)→∞x \rightarrow \infty, h(x)\rightarrow \infty, and as x→−∞,h(x)→−∞x \rightarrow -\infty, h(x)\rightarrow -\infty.
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Consider the function \newlinef(x)=x3−9x2−21x−2.f(x)=x^{3}-9x^{2}-21 x-2.\newlineIts derivative is \newlinef′(x)=3x2−18x−21.f^{\prime}(x)=3x^{2}-18 x-21. help (formulas)\newlineits second derivative is \newlinef′′(x)=6x−18f^{\prime\prime}(x)=6x-18\newlineThe graph that correctly displays \newlinef(z)f(z) (in black) and \newlinef′′(x)f^{\prime\prime}(x) (in orange) is\newlineA\newlineB\newlinec\newline00.\newlineB.\newlineUsing the graphs of \newlineff and \newlinef′′f^{\prime\prime}, indicate where \newlineff is concave up and concave down. Enter DNE if such an interval does not exist: \newlineff is concave up on \newline◻ help (intervals).\newlineff is concave down on
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33. Perhatikan matriks-matriks\newlineA=[30−1211],B=[4−102],C=[142315],D=[152−101324],E=[613−112413] A=\left[\begin{array}{rr} 3 & 0 \\ -1 & 2 \\ 1 & 1 \end{array}\right], \quad B=\left[\begin{array}{rr} 4 & -1 \\ 0 & 2 \end{array}\right], \quad C=\left[\begin{array}{lll} 1 & 4 & 2 \\ 3 & 1 & 5 \end{array}\right], \quad D=\left[\begin{array}{rrr} 1 & 5 & 2 \\ -1 & 0 & 1 \\ 3 & 2 & 4 \end{array}\right], \quad E=\left[\begin{array}{rrr} 6 & 1 & 3 \\ -1 & 1 & 2 \\ 4 & 1 & 3 \end{array}\right] \newlineHitunglah pernyataan berikut ini (jika mungkin).\newline(a) D+E D+E \newline(b) D−E D-E \newline(c) 5A 5 A \newline(d) −7C -7 C \newline(e) 2B−C 2 B-C \newline(f) 4E−2D 4 E-2 D \newline(g) −3(D+2E) -3(D+2 E) \newline(h) A−A A-A \newline(i) tr⁡(D) \operatorname{tr}(D) \newline(b) tr⁡(D−3E) \operatorname{tr}(D-3 E) \newline(k) D−E D-E 00\newline(l) D−E D-E 11
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