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renee l.

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A child twirls a 0.17 kg mass attached to the end of a 19 cm long piece of string. He twirls the mass around at 2 revolutions per second in a vertical plane. Calculate the tension (in N) in the string when the mass is at the top of the circle.

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Gambler Campbell has created a simple new game for the local fair using a single fair 8-sided die and a fair coin. To play, you must pay $3. The outcomes of the game are below: \begin{itemize} \item If the coin flips tails, you lose. \item If the coin flips heads and the die rolls a 1 - 7, you receive $1. \item If the coin flips heads and the die rolls an 8, you receive the jackpot of $30. \end{itemize} Explain if you would like play the game in a couple of sentences. Use a mathematical calculation to justify your explanation.

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Peristalsis refers to Multiple Choice muscular movement of materials through the Gl tract. the opening and closing of sphincters. the action of bile on dietary fat. chewing and swallowing.

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2. Determine $\lim_{x \to 5^{+}} f(x)$, given that $f(x) = \begin{cases} x^2 + 3 & \text{if } 0 \le x \le 5\\ x^2 - 4 & \text{if } 5 < x < 6\\ x + 10 & \text{if } x > 6 \end{cases}$ [A] 14 [B] does not exist [C] 28 [D] 21 [E] 15

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Understanding the U.S. poverty line The following table shows the U.S. poverty thresholds for 2021 by size of family and number of related children under the age of 18. All figures are in dollars. For example, a family with two adults and three children is considered to be living in poverty if the family's income in 2021 is below $32,338. Use the table to answer the questions that follow. | Size of Family Unit | None | Related Children under 18 Years | Five | |---------------------|------|---------------------------------|------| | One person (unrelated individual) | | | | | Under 65 years | 14,097 | | | | | | 65 years and over | 12,996 | | | | | | Two persons | | | | | | | Households under 65 years | 18,145 | 18,667 | | | | | Households 65 years and over | 16,379 | 18,606 | | | | | Three persons | 21,196 | 21,811 | 21,831 | | | | Four persons | 27,949 | 28,406 | 27,479 | 27,575 | | | Five persons | 33,705 | 34,195 | 33,148 | 32,338 | 31,843 | | Six persons | 38,767 | 38,921 | 38,119 | 37,350 | 36,207 | 35,529 | | Seven persons | 44,606 | 44,885 | 43,925 | 43,255 | 42,009 | 40,554 | | Eight persons | 49,888 | 50,329 | 49,423 | 48,629 | 47,503 | 46,073 | | Nine persons or more | 60,012 | 60,303 | 59,501 | 58,828 | 57,722 | 56,201 | Source: "Poverty Thresholds for 2021 by Size of Family and Number of Related Children Under 18 Years," United States Census Bureau, https://www.census.gov/data/tables/time-series/demo/income-poverty/historical-poverty-thresholds.html. Juanita and Gilberto are married, under the age of 65, and have two children under the age of 18. Gilberto works full time and earns $19,000, while Juanita works part time and earns $9,000. Thus, in total, their family income is $28,000. Are Gilberto and Juanita living in poverty? Yes No Suppose that Gilberto divorces Juanita and leaves the family without paying alimony or child support. Juanita must now support her two children alone, so she begins working full time and earns a total of $18,000. Are Juanita and her children living in poverty? Yes No Again, consider Juanita, a single mother with two children under 18 who earns an annual income of $18,000. Suppose that Juanita qualifies for a welfare program for single mothers that provides her with $4,000 in food assistance. After receiving welfare, is Juanita's family living in poverty? Yes No Juanita and Gilberto are married, under the age of 65, and have two children under the age of 18. Gilberto works full time and earns $19,000, while Juanita works part time and earns $9,000. Thus, in total, their family income is $28,000. Are Gilberto and Juanita living in poverty? Yes No Suppose that Gilberto divorces Juanita and leaves the family without paying alimony or child support. Juanita must now support her two children alone, so she begins working full time and earns a total of $18,000. Are Juanita and her children living in poverty? Yes No

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4. A company has built six different size cell towers that vary in height and cost as shown below. Using this data, develop a linear regression equation, where Cost is your Y variable and Height is your X variable. Manually find the values of the parameters: $a$ (intercept) and $b$ (slope) for your linear regression equation. Plot the data and the line. Height (meters) Cost ($ x1000) 24 $265 31 $278 13 $134 16 $173 22 $203 19 $179

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4. (a) Given that 4% of the items in an incoming lot are defective. i. What is the probability that at most one defective item will be found in a random sample of size 30? ii. Repeat part i. with Poisson approximation.

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5. Multiply. Be sure to completely simplify your answer. \frac{x+3}{4x-2} \cdot (12x^2 + 2x - 4) a. \frac{3(x+3)}{3x+2} b. \frac{3(x+3)(2x-1)}{2} c. (x+3)(3x+2) d. (3x+1)(2x+3)

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(45%)3.Rod AB is pinned to ground at A. There is a prismatic joint between B and C. The housing of the prismatic joint is pinned to the rod AB at B. The distance between A and B is $L_1$ as shown below, i.e., $L_1$ is the length of rod AB. The angle $\theta_1$ shown below is measured counter-clockwise from the global/inertial horizontal to the directed line AB. The angle $\alpha$ shown below is measured from the global/inertial horizontal clockwise to the directed line CB. The following values are known/given: $L_1$=4m, R=3m, $\dot{R}$=9m/s², $\ddot{R}$=7m/s², $\theta_1$=30°, $\dot{\theta_1}$=5.5rad/s, $\ddot{\theta_1}$=3.8rad/s², $\alpha$=40°, $\dot{\alpha}$=7.5rad/s, $\ddot{\alpha}$=8.2rad/s². (Point C is not pinned to anything.) REQUESTED: At the instant shown, find the acceleration of point C, in m/s². HINTS: (1) Do *not* copy the solution for another problem and expect to get a bunch of partial credit. (2) Do not get too bogged down in your calculators. If you have n correct equations in n unknowns that uniquely determine the answer, you have 100% credit for the problem.

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Evaluate the sum $\sum_{k=1}^{6} k(3k+8)$. \begin{equation*} \sum_{k=1}^{6} k(3k+8) = \boxed{} \text{ (Simplify your answer.)} \end{equation*}

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