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Write two-variable inequalities: word problems

A rancher wants to build a rectangular pen for her animals. She decides that the length, l l , of one side of the pen should be at most 6060 feet, the width, w w , of one side of the pen should be at least 3030 feet, and the perimeter of the pen should be at most 200200 feet. Which of the following systems of inequalities best models the situation described?\newlineChoose 11 answer:\newline(A) {l+w≤200w≥30l≤60 \left\{\begin{array}{l}l+w \leq 200 \\ w \geq 30 \\ l \leq 60\end{array}\right. \newline(B) {l+w≥200w≤30l≥60 \left\{\begin{array}{l}l+w \geq 200 \\ w \leq 30 \\ l \geq 60\end{array}\right. \newlinec) {l+w≤100w≥30l≤60 \left\{\begin{array}{l}l+w \leq 100 \\ w \geq 30 \\ l \leq 60\end{array}\right. \newline(D) {2l+2w≥200w≥30l≤60 \left\{\begin{array}{l}2 l+2 w \geq 200 \\ w \geq 30 \\ l \leq 60\end{array}\right.
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Thirty fast-food restaurant hourly employees were surveyed to see how many hours they worked per week, on average. The following data was obtained: {:[24,38,33,30,25,37,40,30,29,32,35,44,31,42,35,38,32,31,26,31,36,15,35,29,26,42,36,44,24,40]:} \{:[24, 38, 33, 30, 25, 37, 40, 30, 29, 32, 35, 44, 31, 42, 35, 38, 32, 31, 26, 31, 36, 15, 35, 29, 26, 42, 36, 44, 24, 40]:\} Assuming the population standard deviation is σ=7 \sigma=7 , construct a 9494% confidence interval for the mean number of hours per week that the population of fast-food restaurant employees work. xˉ=0.06 \bar{x}=0.06 , z92=1.8808σ∗ z_{\frac{9}{2}}=1.8808 \quad \sigma^{\ast} Margin of Error: E= E= We are 9494% confident that fast-food restaurant hourly employees, on average, work between hours and hours per week. Question Help: Submit Question
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Question 44\newline0.140.14//11 pt \newline2\sqrt{2}\newlineA scientific study was conducted to determine the hours of sleep that college students get per night. The study surveyed 3232 college students and obtained the following data:\newline\{:[7.1,\,7.4,\,7,\,8.1,\,7.6,\,6.3,\,7,\,6,\,6.8,\,6.4,\,7.5,\,7.5,\,8,\,6.1,\,8.4,\,7.3,\,8.5,\,6.6,\,7,\,7.5,\,6.6,\,7.1,\,7,\,6.2,\,6.6,\,7.5,\,],[5.9,\,7.7,\,6.7,\,6.4,\,7.7,\,6.9]:}\newlineConstruct a 95%95\% confidence interval for the average hours of sleep per night that college students get.\newline\{:[\bar{x}=\square],[\alpha=\square=\square],[t_{(9)}=\square]:}\newlineMargin of Error: \newlineE=E=\newlineWe are \newline95%95\% confident that college students get an average of between and hours of sleep per night. hours
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The amount of pollutants that are found in waterways near large cities is normally distributed with mean 99.88 ppm and standard deviation 11.77 ppm. 3535 randomly selected large cities are studied. Round all answers to 44 decimal places where possible.\newlinea. What is the distribution of X X ? X−N(9.8 X-\mathrm{N}(9.8 \newline11.77\newlineb. What is the distribution of xˉ?xˉ−N(9.8 \bar{x} ? \bar{x}-N(9.8 \newline11.77\newlinex) σ∘9.8 \sigma^{\circ} 9.8 \newlinec. What is the probability that one randomly selected city's waterway will have more than 9.8ppm 9.8 \mathrm{ppm} pollutants? 00.55\newlined. For the 3535 cities, find the probability that the average amount of pollutants is more than 99.88 ppm. 00.55\newlinee. For part d), is the assumption that the distribution is hormal necessary? ◯ \bigcirc Yes O O No\newlinef. Find the IQR for the average of 3535 cities.\newlineQ1=1.7ppmQ3=ppm \begin{array}{ll} \mathrm{Q} 1= & 1.7 \quad \mathrm{ppm} \\ \mathrm{Q} 3= & \mathrm{ppm} \end{array} \newlineIQR: ppm
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A company manufactures cellular phones and laptop computers. The company's daily production of cellular phones, cc, must be more than 500,000500,000, and its daily production of laptop computers, ll, must be more than 300,000300,000. If the maximum capacity of the company's manufacturing center is no more than 950,000950,000 total cellular phones and laptop computers, which of the following systems of inequalities best models the situation described?\newlineChoose 11 answer:\newline(A) {c−l>950,000c≥500,000l≥300,000\begin{cases} c-l > 950,000 \\ c \geq 500,000 \\ l \geq 300,000 \end{cases}\newline(B) {c−l≤950,000c>500,000l>300,000\begin{cases} c-l \leq 950,000 \\ c > 500,000 \\ l > 300,000 \end{cases}\newline(C) {c+l<950,000c≥500,000l≥300,000\begin{cases} c+l < 950,000 \\ c \geq 500,000 \\ l \geq 300,000 \end{cases}\newline(D) {c+l≤950,000c>500,000l>300,000\begin{cases} c+l \leq 950,000 \\ c > 500,000 \\ l > 300,000 \end{cases}
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Ty tried to solve the differential equation dydx=4xey \frac{d y}{d x}=\frac{4}{x e^{y}} . This is his work:\newlinedydx=4xey \frac{d y}{d x}=\frac{4}{x e^{y}} \newlineStep 11: ∫eydy=∫4xdx \quad \int e^{y} d y=\int \frac{4}{x} d x \newlineStep 22: ey=4ln⁡∣x∣+C \quad e^{y}=4 \ln |x|+C \newlineStep 33: ln⁡(ey)=ln⁡(4ln⁡∣x∣+C) \quad \ln \left(e^{y}\right)=\ln (4 \ln |x|+C) \newlineStep 44: y=ln⁡(4ln⁡∣x∣+C) \quad y=\ln (4 \ln |x|+C) \newlineIs Ty's work correct? If not, what is his mistake?\newlineChoose 11 answer:\newline(A) Ty's work is correct.\newline(B) Step 11 is incorrect. The separation of variables was done incorrectly.\newline(C) Step 33 is incorrect. The right-hand side of the equation should be ln⁡(4ln⁡∣x∣)+C \ln (4 \ln |x|)+C .\newline(D) Step 44 is incorrect. The left-hand side of the equation should be ∣y∣ |y| .
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Eleanor tried to find all the equations of vertical lines tangent to the curve given by\newline3x2+24x−y2+2y=−44.  3 x^{2}+24 x-y^{2}+2 y=-44 \text {. } \newlineThis is her solution:\newlineStep 11: Finding an expression for dydx \frac{d y}{d x} .\newlinedydx=y−13(x+4) \frac{d y}{d x}=\frac{y-1}{3(x+4)} \newlineStep 22: Forming a system of equations.\newline{3x2+24x−y2+2y=−443(x+4)=0y−1≠0 \left\{\begin{array}{l} 3 x^{2}+24 x-y^{2}+2 y=-44 \\ 3(x+4)=0 \\ y-1 \neq 0 \end{array}\right. \newlineStep 33: Solving the system.\newlineThere are no solutions to the system of equations, so there are no vertical lines tangent to the graph.\newlineIs Eleanor's solution correct? If not, at which step did she make a mistake?\newlineChoose 11 answer:\newline(A) The solution is correct.\newline(B) Step 11 is incorrect.\newline(C) Step 2 \mathbf{2} is incorrect.\newline(D) Step 33 is incorrect.
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Anjali was given this problem:\newlineA person stands at a distance of 1212 meters east of an intersection and watches a car driving away from the intersection to the north at 44 meters per second. At a certain instant t0 t_{0} , the car is at distance n(t0) n\left(t_{0}\right) of 99 meters from the intersection. What is the rate of change of the distance d(t) d(t) between the car and the person at that instant?\newlineWhich equation should Anjali use to solve the problem?\newlineChoose 11 answer:\newline(A) tan⁡[d(t)]=n(t)12 \tan [d(t)]=\frac{n(t)}{12} \newline(B) d(t)=12⋅n(t)2 d(t)=\frac{12 \cdot n(t)}{2} \newline(C) d(t)+12+n(t)=180 d(t)+12+n(t)=180 \newline(D) [d(t)]2=122+[n(t)]2 [d(t)]^{2}=12^{2}+[n(t)]^{2}
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