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  8. <title>Algebra.Com New solved problems</title>
  9. <link>http://www.algebra.com</link>
  10. <description>New Solutions by tutors</description>
  11. <language>en-us</language>
  12. <copyright>Copyright Algebra.Com</copyright>
  13. <pubDate>Sat, 15 Mar 2025 19:58:00 +0000</pubDate>
  14. <lastBuildDate>Sat, 15 Mar 2025 19:58:00 +0000</lastBuildDate>
  15. <managingEditor>webmaster@algebra.com</managingEditor>
  16. <webMaster>webmaster@algebra.com</webMaster>
  17.  
  18. <item>
  19. <title>Problem 1171198 solved by CPhill</title>
  20. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171198</link>
  21. <description>This problem was solved by CPhill:
  22. Suppose that historically the average age at which Canadians have been happier than at any other time in their lives is 37 years. A random sample of 50 Canadians taken in 2020 indicated that the mean happiest age was 40 years with a standard deviation equal to 16 years. At the 10 percent level of significance, does this sample indicate that there has been a change in the average age when Canadians are happiest?
  23.  
  24.  
  25. a) State the null and alternative hypothesis.
  26.  
  27. b)State the decision rule
  28.  
  29. c)Compute the observed value of the test statistic.
  30.  
  31. d) What is your decision regarding the null hypothesis?   Dont forget your concluding statement.
  32.  
  33. e) Determine the p-value for this test. </description>
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  35. <pubDate>Sat, 15 Mar 2025 14:58:32 -0006</pubDate>
  36. </item>
  37. <item>
  38. <title>Problem 1171213 solved by CPhill</title>
  39. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171213</link>
  40. <description>This problem was solved by CPhill:
  41. Cricket World Cup (CWC) is considering a project proposal which requires an initial investment of $72,625 and it is expected to have net cash flows of $15,000 per year for 8 years. The firm cash flows are discounted at a rate of 12 percent.
  42. a. What is the projects Net Present Value (NPV)? (Rounded to 2 decimal places)
  43. b. What is the projects discounted payback period? (Rounded to 2 decimal places)
  44. </description>
  45. <guid isPermaLink="false">19aa775c-fff3-3377-8c27-b916f058590a</guid>
  46. <pubDate>Sat, 15 Mar 2025 14:58:03 -0006</pubDate>
  47. </item>
  48. <item>
  49. <title>Problem 1171229 solved by CPhill</title>
  50. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171229</link>
  51. <description>This problem was solved by CPhill:
  52. Suppose a company repacks cereal with the use of a machine that is calibrated so that the weight of cereal dispensed in a box is normally distributed with mean 0.40 kg and variance 0.01 kg2, although the weight stated in the cereal box is 0.45 kg. For quality control purposes, suppose a random sample of 15 cereal boxes is taken. What is the probability of selecting a random sample with mean weight less than the advertised weight?</description>
  53. <guid isPermaLink="false">751e9179-6b0f-3044-b271-ac459422a6d5</guid>
  54. <pubDate>Sat, 15 Mar 2025 14:57:32 -0006</pubDate>
  55. </item>
  56. <item>
  57. <title>Problem 1171230 solved by CPhill</title>
  58. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171230</link>
  59. <description>This problem was solved by CPhill:
  60. Suppose (X1,X2,,X9) is a random sample from Normal(2,42). Let X(bar) be the sample mean of X1,X2,,X9 and S2 be the sample variance of X1,X2,,X9. For items asking for the distribution of a statistic, do not forget to specify the parameters.
  61.  
  62.  
  63.  
  64. What is the distribution of the sample mean (X(bar))?</description>
  65. <guid isPermaLink="false">684d6129-55d9-3661-b772-64db4111791d</guid>
  66. <pubDate>Sat, 15 Mar 2025 14:57:03 -0006</pubDate>
  67. </item>
  68. <item>
  69. <title>Problem 1171244 solved by CPhill</title>
  70. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171244</link>
  71. <description>This problem was solved by CPhill:
  72. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
  73. The mean number of births per minute in a country in a recent year was about
  74. four.
  75. Find the probability that the number of births in any given minute is (a) exactly
  76. five,
  77. (b) at least
  78. five,
  79. and (c) more than
  80. five.
  81. </description>
  82. <guid isPermaLink="false">ca2a67b7-eb16-3b4d-8ce6-90c9c7389a82</guid>
  83. <pubDate>Sat, 15 Mar 2025 14:56:27 -0006</pubDate>
  84. </item>
  85. <item>
  86. <title>Problem 1171253 solved by CPhill</title>
  87. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171253</link>
  88. <description>This problem was solved by CPhill:
  89. Construct a grouped frequency distribution table below of the scores of 40 students on their Prelim Exam.
  90.  
  91. 45 49 50 53 26 23 30 30 45 46
  92. 48 55 38 57 23 35 45 48 50 24
  93. 48 56 39 42 41 29 59 21 54 53
  94. 48 49 48 41 43 37 36 43 46 49
  95.  
  96. </description>
  97. <guid isPermaLink="false">4ff214b3-83f9-3702-bcdf-6aa89afda1a6</guid>
  98. <pubDate>Sat, 15 Mar 2025 14:54:48 -0006</pubDate>
  99. </item>
  100. <item>
  101. <title>Problem 1171286 solved by CPhill</title>
  102. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171286</link>
  103. <description>This problem was solved by CPhill:
  104. The value of an automobile over time is given in the following table:
  105.  
  106. Age ---  Value $
  107. 1   ---   14000
  108. 2   ---   9100
  109. 3   ---  6200
  110. 4   ---   4000
  111. 5   ---   3000
  112.  
  113. a) Use graphing technology to determine an equation that fits:
  114.  
  115. i)the linear model
  116. ii) the quadratic model
  117. iii) the exponential model
  118.  
  119. b) Use each model to predict the value of the car after 10 years
  120.  
  121. c) Which result is most reasonable? Give reasons for your answer
  122.  
  123. d) Which function provides the best model?</description>
  124. <guid isPermaLink="false">86c16af7-d894-3177-bbbe-940219484620</guid>
  125. <pubDate>Sat, 15 Mar 2025 14:51:29 -0006</pubDate>
  126. </item>
  127. <item>
  128. <title>Problem 1171303 solved by CPhill</title>
  129. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171303</link>
  130. <description>This problem was solved by CPhill:
  131. NASA is designing a new satellite to go on the international space station. The satellite disk is the shape of a parabola. The satellite will be attached to the station on a pole and will place the vertex of the satellite 4 feet away from the surface of the station. The receiver is to be positioned 7 feet above the roof. Write an equation that best models the parabolic cross section of the satellite dish.( can I see how you solve it please?)</description>
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  133. <pubDate>Sat, 15 Mar 2025 14:50:41 -0006</pubDate>
  134. </item>
  135. <item>
  136. <title>Problem 1171310 solved by CPhill</title>
  137. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171310</link>
  138. <description>This problem was solved by CPhill:
  139. Use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
  140. x 1 2 3 4 5 6 7 8 9      10
  141. f(x)   409.6 260.4 170.3 110.9 74.1 44.4 32.5 19.2 12.8   8.4</description>
  142. <guid isPermaLink="false">da61eff4-21ad-39ea-bfe5-8a2c92504b82</guid>
  143. <pubDate>Sat, 15 Mar 2025 14:43:24 -0006</pubDate>
  144. </item>
  145. <item>
  146. <title>Problem 1171313 solved by CPhill</title>
  147. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171313</link>
  148. <description>This problem was solved by CPhill:
  149. Inference (Two Populations), Chi-Squared Tests
  150. 1. A study comparing childrens reading age (in months) was developed using identical twin
  151. toddlers. One set of 6 twins played for 2 hours each day with educational toys
  152. (experimental group), the corresponding set of 6 twins played for 2 hours each day with
  153. non-educational toys (control group). The mean difference in reading age between the
  154. experimental group and control group of 6 sets of twins was -2.33 months and the
  155. standard deviation of the sample difference was 2.16 months. Set up a hypothesis test to
  156. determine if there is a difference between the 2 groups and use the appropriate sample
  157. test statistic to determine if the difference in reading age is significant at the 5% level</description>
  158. <guid isPermaLink="false">2b4d5c47-63e4-3ca5-9483-ba86547ddfd7</guid>
  159. <pubDate>Sat, 15 Mar 2025 14:42:11 -0006</pubDate>
  160. </item>
  161. <item>
  162. <title>Problem 1171314 solved by CPhill</title>
  163. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171314</link>
  164. <description>This problem was solved by CPhill:
  165. Time Series and Non-Parametric Tests
  166. 1. Perform a Trend and Seasonal analysis with the following data. Include the trend formula
  167. and the multiplicative indices for the seasons. Using the model forecast sales for the next
  168. year (all 4 seasons of year 4)
  169.  
  170. Year   Season    Sales
  171. 1       sp      140
  172. 1       su      50
  173. 1       w       130
  174. 1       f       520
  175. 2       sp      200
  176. 2       su      110
  177. 2        w      190
  178. 2        f      550
  179. 3        sp     260
  180. 3        su     220
  181. 3        w      210
  182. 3        f       570
  183. </description>
  184. <guid isPermaLink="false">857a6e6e-7f2c-354f-9785-fb856baaff99</guid>
  185. <pubDate>Sat, 15 Mar 2025 14:32:37 -0006</pubDate>
  186. </item>
  187. <item>
  188. <title>Problem 1171361 solved by CPhill</title>
  189. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171361</link>
  190. <description>This problem was solved by CPhill:
  191. Q1) Let U={a,b,c,d,e,f,g,h,i,j},A={a,b,c,d,e},B={a,b,d,f,g},C={a,d,e} Findl
  193.  
  194.  
  195. (AC)\B  
  196. (A\C)(B\C)
  197. n(A^cB^c )
  198.  
  199. </description>
  200. <guid isPermaLink="false">537ebace-2cc4-32d1-a5b6-97ae4a899eea</guid>
  201. <pubDate>Sat, 15 Mar 2025 14:31:32 -0006</pubDate>
  202. </item>
  203. <item>
  204. <title>Problem 1171385 solved by CPhill</title>
  205. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171385</link>
  206. <description>This problem was solved by CPhill:
  207. a family is planning an 8-hr road trip and is going to take along a porrtable video game system for the kids to play. The father is worried that the batteries will go dead before the end of the trip so he takes along an extra set.  From experience he know the batteries will typically need replaced once every 10 hr. Assuming that the number of times the batteries need to be replaced in 1 hour has a poisson distribution and that the kids play the video game for all 8 hours, find the probability that the two sets of batteries last the entire trip.</description>
  208. <guid isPermaLink="false">23b5c715-7b87-3fb5-a2d4-8b6cf7c673c3</guid>
  209. <pubDate>Sat, 15 Mar 2025 14:30:33 -0006</pubDate>
  210. </item>
  211. <item>
  212. <title>Problem 1171394 solved by CPhill</title>
  213. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1171394</link>
  214. <description>This problem was solved by CPhill:
  215. 27 % adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
  216. (a) P(3)=</description>
  217. <guid isPermaLink="false">a33f7c74-0426-3d93-acf7-f282c2d8a65c</guid>
  218. <pubDate>Sat, 15 Mar 2025 14:29:29 -0006</pubDate>
  219. </item>
  220. <item>
  221. <title>Problem 1209876 solved by CPhill</title>
  222. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209876</link>
  223. <description>This problem was solved by CPhill:
  224. Find the largest value of x where the plots of
  225. f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}
  226. intersect.
  227. </description>
  228. <guid isPermaLink="false">8f0455c8-0643-3205-b030-00e9123e2ffe</guid>
  229. <pubDate>Sat, 15 Mar 2025 14:28:44 -0006</pubDate>
  230. </item>
  231. <item>
  232. <title>Problem 1209877 solved by CPhill</title>
  233. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209877</link>
  234. <description>This problem was solved by CPhill:
  235. Fill in the blanks, to make a true equation:
  236.  
  237. \frac{2x^4 - 3x^3 - x^2 + 4x - 4}{x^2 + x} = ___x^2 + ___x + ___ + ___/x + ___/(x + 1).</description>
  238. <guid isPermaLink="false">6a67f3a1-a4ed-3052-a6a1-e93d60c3fd1a</guid>
  239. <pubDate>Sat, 15 Mar 2025 14:27:45 -0006</pubDate>
  240. </item>
  241. <item>
  242. <title>Problem 1209878 solved by CPhill</title>
  243. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209878</link>
  244. <description>This problem was solved by CPhill:
  245. Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of y = 0 as x approaches positive infinity, where
  246. f(x) = \frac{2x^4 - 3x^3 - 8x^2 + 4x - 4}{x^2 + x}.
  247. </description>
  248. <guid isPermaLink="false">861206b5-c32b-376b-a390-acc85cb13d21</guid>
  249. <pubDate>Sat, 15 Mar 2025 14:26:57 -0006</pubDate>
  250. </item>
  251. <item>
  252. <title>Problem 1209880 solved by CPhill</title>
  253. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209880</link>
  254. <description>This problem was solved by CPhill:
  255. Find the all real numbers that are not in the domain of f(g(x)), where
  256. f(x) = \frac{3x^2 - 10x - 25}{x + 1} and g(x) = \frac{14x - 6}{3x^2 + 5x + 15}</description>
  257. <guid isPermaLink="false">a5a499d3-2106-3c4b-a2ff-434178f21953</guid>
  258. <pubDate>Sat, 15 Mar 2025 14:26:08 -0006</pubDate>
  259. </item>
  260. <item>
  261. <title>Problem 1209882 solved by CPhill</title>
  262. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209882</link>
  263. <description>This problem was solved by CPhill:
  264. Find the values of x where the vertical asymptotes of f(g(x)) are located, where
  265. f(x) = \frac{2x - 8}{x^2 - 2x - 3} and g(x) = \frac{x^3 + 2x + 9}{x^2 + 4}.</description>
  266. <guid isPermaLink="false">3c4a729a-8506-30ff-b922-523f43b923ce</guid>
  267. <pubDate>Sat, 15 Mar 2025 14:25:31 -0006</pubDate>
  268. </item>
  269. <item>
  270. <title>Problem 1209885 solved by CPhill</title>
  271. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209885</link>
  272. <description>This problem was solved by CPhill:
  273. Let f be the piecewise function such that
  274. f(x) =
  275. x^2 - 5x - 64 &#x26; \text{if} \ x \le 0, \\
  276. x^2 + 3x - 38 &#x26; \text{if} \ x &#x3E; 0.
  277.  
  278. Find all x such that f(x) = 50.
  279. </description>
  280. <guid isPermaLink="false">1bf5fa5e-19d0-38ee-a72b-d43c3d4257ba</guid>
  281. <pubDate>Sat, 15 Mar 2025 14:24:57 -0006</pubDate>
  282. </item>
  283. <item>
  284. <title>Problem 1209886 solved by CPhill</title>
  285. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209886</link>
  286. <description>This problem was solved by CPhill:
  287. Find the area of the region determined by the system
  288. y \ge |x|, \\
  289. y \le -|2x + 1| + 6.</description>
  290. <guid isPermaLink="false">013b482d-a153-390d-84b3-863bf925a034</guid>
  291. <pubDate>Sat, 15 Mar 2025 14:24:03 -0006</pubDate>
  292. </item>
  293. <item>
  294. <title>Problem 1209884 solved by greenestamps</title>
  295. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209884</link>
  296. <description>This problem was solved by greenestamps:
  297. What is the horizontal asymptote as x approaches positive infinity of the graph of
  298. y = \sqrt{4x^2 + 5x} - \sqrt{4x^2}?
  299. The horizontal asymptote is in the form y = mx + k.
  300. </description>
  301. <guid isPermaLink="false">da459ce0-6efa-3a4b-a550-1dce1243d49d</guid>
  302. <pubDate>Sat, 15 Mar 2025 01:18:10 -0006</pubDate>
  303. </item>
  304. <item>
  305. <title>Problem 1209883 solved by greenestamps</title>
  306. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209883</link>
  307. <description>This problem was solved by greenestamps:
  308. Find all real x where
  309. 2 \cdot \frac{x - 5}{x - 3} &#x3E; \frac{2x - 5}{x + 2} + 20.
  310. Give your answer in interval notation.
  311. </description>
  312. <guid isPermaLink="false">be42555d-5072-3494-b118-6e97d6c29f62</guid>
  313. <pubDate>Sat, 15 Mar 2025 00:35:52 -0006</pubDate>
  314. </item>
  315. <item>
  316. <title>Problem 1209881 solved by Edwin McCravy</title>
  317. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209881</link>
  318. <description>This problem was solved by Edwin McCravy:
  319. Fill in the blanks, to make a true equation:
  320.  
  321. (8x^3 + 24x^2 + 15x + 1)/((x^2 - 1)(x^2 + 3x)) = ___/(x - 1) + ___/(x + 3) + ___/x + ___/(x + 1)</description>
  322. <guid isPermaLink="false">ab26489e-c90c-3804-b800-5e21ef93451b</guid>
  323. <pubDate>Fri, 14 Mar 2025 22:02:27 -0006</pubDate>
  324. </item>
  325. <item>
  326. <title>Problem 1209879 solved by ikleyn</title>
  327. <link>http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=1209879</link>
  328. <description>This problem was solved by ikleyn:
  329. . If one adult is randomly selected from these 700 adults, find
  330. the probability that this adult
  331. i. likes chocolate ice cream
  332. ii. is a woman
  333. iii. likes vanilla ice cream given that this adult is a woman
  334. iv. is a man given that this adult likes chocolate ice cream
  335. b. Are events men and vanilla ice cream mutually exclusive?
  336. What about chocolate ice cream and vanilla ice cream?
  337. c. Are events women and chocolate ice cream independent?
  338. Why or why not?</description>
  339. <guid isPermaLink="false">a098cd0d-c892-39cb-9d0a-94409e737ffa</guid>
  340. <pubDate>Fri, 14 Mar 2025 12:02:12 -0006</pubDate>
  341. </item>
  342. </channel>
  343. </rss>

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