Alessandra tried to fill the prism with unit cubes but did not have enough. A rectangular prism has a length of 6, height of 4, and width of 5. Which statement would give a correct method for finding the volume of the prism? She knows there are 30 unit cubes in the bottom layer. Since the height is 4, there are 4 layers of 30 cubes each. She should multiply 4 times 30 = 120. The volume is 120 cubic units. She knows there are 11 cubes along the bottom and the height is 4, so she should multiply 4 times 11 = 44. The volume is 44 cubic units. She knows there are 30 unit cubes in the bottom layer. She will need 4 more layers, so she should add 30 + 30 + 30 + 30 + 30 = 150. The volume is 150 cubic units. She knows there are 11 cubes along the bottom, and she needs 3 more layers. She has 33 cubes already in the prism, so she should add 11 + 11 + 11 + 33 = 66. The volume is 66 cubic units.

When a formula is solved for a particular variable, several different equivalent forms may be possible. if we solved a=1/2bh for h, one possible correct answer is h=2a/b . which one of the following is not equivalent to this? a. h= 2(a/b) b. h= 2a(1/b) c. h= a/1/2b d. h= 1/2a/b

What can be said about the relationship between triangles and circles? check all that apply. a) many circles can be inscribed in a given triangle b) exactly one triangle can be inscribed in a given circle c) exactly one circle can be inscribed in a given triangle d) many triangular shapes can be circumscribed about a given circle

This task builds on important concepts you've learned in this unit and allows you to apply those concepts to a variety of situations. the task has several parts, each in its own section. mr. hill's seventh grade math class has been learning about random sampling and how it tends to produce samples that are representative of an entire population. they've also learned that if a sample is representative of the entire population, then estimates or predictions made based on the sample usually apply to the population as well. today, in class, they are also learning about variation in random sampling. that, although predictions and estimates about the population can be made from a random sample, different random samples will often produce slightly different predictions or estimates. to demonstrate this concept to his students, mr. hill is going to use simulation. he begins the lesson by explaining to the class that a certain university in the united states has a student enrollment of 19,100. mr. hill knows the percentage of students that are male and the percentage of students that are female. using simulation and random sampling, he wants his seventh grade students to estimate both the percentage of male students and the number of male students that are enrolled in this university. to conduct the simulation, mr. hill has placed one hundred colored chips in a bag, using the appropriate percentages of enrolled male and female university students. red chips represent males, and yellow chips represent females. each seventh grade student will randomly select twenty chips, record the colors they selected, and put the chips back in the bag. at this point, each seventh grade student will only know the results of their own random sample. before you begin, it's a good idea to look over each part to get oriented to the whole task. additionally, it's best to complete the sections in order, since they build on each other. finally, the work you complete will be a combination of computer-graded problems and written work that your teacher will grade. in some cases, you will need to complete work outside of the problem (in a word processing document or on paper, for example) and upload it for grading. to get started click work on questions. questions: 1. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the percentage of enrolled university students that are male? 2. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the number of enrolled university students that are male? 3. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. how many yellow chips were in their sample? 4. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. based on this sample, what is a good estimate for the number of enrolled university students that are female? 5. based on your dot plot, make a new estimate of both the percentage and number of males that attend this university. use complete sentences in your answer and explain your reasoning. 6. compare your estimates for the percentage of male university students from part a and part b. which estimate do you think is more representative of the population? use complete sentences in your answer and explain your reasoning. 7. once you have created both sets of numbers, complete the following tasks. in each task, make sure to clearly label which set you are identifying or describing. identify the elements of each set that you created. calculate the mean of each set. show your work in your answer. calculate the mean absolute deviation of each set. show your work in your answer. describe the process you used to create your sets of numbers under the given conditions.