(i forgot to put this in with the last question, sorry)
What is the volume of the triangular prism to the nearest whole unit?
[Image shows a triangular prism with a height of 4 ft, a width of 14 ft, and a length of 21 ft.]
A. 392 ft^2
B. 588 ft^2
C. 1,176 ft^2
D. 2,352 ft^2
Pup tent
area of triangle = (1/2) b h = (1/2)(4) (14) = 28 ft^2
28 ft^2 * 21ft = 588 ft^3
NOTE: Volume is CUBIC L^3, Area is squared L^2
Thank you! And yeah, I meant to put L^3 and not L^2, oops
Which choice correctly describes this event? I will pull a blue marble at random out of a jar with 49 red marbles and 1 blue marble
A) Certain event
B) Likely event
C) Unlikely event
D) Impossible event
D) Impossible event, since the event describes pulling a blue marble out of a jar with 49 red marbles and only 1 blue marble. The probability of selecting a blue marble in this case is 1/50, which is not impossible, but the question asks for a specific outcome with certainty. Therefore, the event as described is impossible.
Which THREE statements are correct when determining the likelihood of a chance event occurring?
Responses
A A chance event with a 0.35 probability is more likely to occur than an event with a 0.40 probability.A chance event with a 0.35 probability is more likely to occur than an event with a 0.40 probability.
B The closer the probability of a chance event is to 0, the less likely it is for the event to occur.The closer the probability of a chance event is to 0, the less likely it is for the event to occur.
C A probability of 12
means the event will more than likely occur.A probability of 1 2 means the event will more than likely occur.
D A chance event with a 0.95 probability of occurring is likely to occur.A chance event with a 0.95 probability of occurring is likely to occur.
E A chance event with a probability of 0.68 is more likely to occur than an event with a 0.55 probability.
A, B, and E are the correct statements:
A) A chance event with a 0.35 probability is more likely to occur than an event with a 0.40 probability. This is true, as the closer the probability is to 1, the more likely it is that the event will occur.
B) The closer the probability of a chance event is to 0, the less likely it is for the event to occur. This is also true, as a probability of 0 means the event is impossible.
E) A chance event with a probability of 0.68 is more likely to occur than an event with a 0.55 probability. This is true, as the closer the probability is to 1, the more likely it is that the event will occur.
A survey asked a group of teachers to choose their favorite type of lunch. The results of the survey are shown in the table.
Based on this data, what is the approximate probability that a teacher prefers soup? (round to the nearest hundredth)
Responses
A 0.270.27
B 0.210.21
C 0.330.33
D 0.240.24
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The approximate probability that a teacher prefers soup is 0.27.
To calculate this, we add up the number of teachers who prefer soup (27) and divide by the total number of teachers surveyed (100):
27/100 = 0.27
Therefore, the answer is option A) 0.27 (rounded to the nearest hundredth).
The table shows the frequency of colors in a bag of skittles. Based on this data, what is the approximate probability that a YELLOW skittle is pulled from a bag of skittles? (round to the nearest hundredth)
Responses
A 0.120.12
B 0.150.15
C 0.180.18
D 0.21
The approximate probability that a YELLOW skittle is pulled from a bag of skittles is 0.18.
To calculate this, we add up the number of yellow skittles (18) and divide by the total number of skittles (100):
18/100 = 0.18
Therefore, the answer is option C) 0.18 (rounded to the nearest hundredth).
Which describes a uniform probability model?
Responses
A drawing a red or black card from a deck of cardsdrawing a red or black card from a deck of cards
B selecting a ball from 2 red balls and 3 yellow ballsselecting a ball from 2 red balls and 3 yellow balls
C selecting a sock from 5 black socks and 10 white socksselecting a sock from 5 black socks and 10 white socks
D equally divided five section spinner with three colors
D) Equally divided five section spinner with three colors best describes a uniform probability model.
This is because in a uniform probability model, all possible outcomes have an equal chance or probability of occurring. The spinner described in option D has five equally divided sections, each with the same probability of being chosen, making it a uniform probability model.
Options A, B, and C describe situations where the probabilities of the outcomes are not necessarily equal, and therefore do not represent uniform probability models.
Eliza is rolling a die and recording whether she gets an even or an odd number. She rolls the die 250 times and records the number that she gets in the table. What is the experimental probability that she gets an even number?
Responses
A 153250
153 250
B 97250
97 250
C 127250
127 250
D 123250
The correct answer is B) 97/250 (or 0.388, rounded to the nearest thousandth).
To find the experimental probability of getting an even number, we need to calculate the number of times Eliza rolled an even number and divide it by the total number of rolls.
Looking at the table, we see that Eliza rolled an even number 97 times out of 250 total rolls.
Therefore, the experimental probability is 97/250 (or 0.388, rounded to the nearest thousandth).
A spinner that has 5 areas of equal size, blue, red, green, yellow, and purple, is spun 25 times. The results are shown in the table. Are all outcomes equally likely according to the results of the experiment?
Responses
A Yes, since the areas of each colored section has the same area.Yes, since the areas of each colored section has the same area.
B No, it seems more likely to spin a blue or red than a green or yellow.No, it seems more likely to spin a blue or red than a green or yellow.
C No, all of the probabilities do not add to equal one.No, all of the probabilities do not add to equal one.
D Yes, all of the probabilities add to equal one.
Based on the table of results, we cannot definitively conclude that all outcomes are equally likely.
Option B is a possible conclusion based on the results, as it appears that blue and red were spun more often than green and yellow, which may suggest that these outcomes are not equally likely.
Option C is also a possible conclusion based on the results, as the probabilities for each outcome do not add up to equal one.
Option A is not a correct conclusion since having equal areas of the colored sections doesn't guarantee that all outcomes are equally likely.
Option D is incorrect since the sum of probabilities is less than one (0.08+0.16+0.28+0.12+0.24=0.88).
Therefore, the best answer is B) No, it seems more likely to spin a blue or red than a green or yellow, based on the results of the experiment.
Mary Jane spins the spinner 15 times. The arrow lands 6 times on a star and 9 times on the heart. Which THREE statements are correct when comparing the experimental and theoretical probabilities?
Responses
A The theoretical probability for landing on the star is greater than the experimental probability.The theoretical probability for landing on the star is greater than the experimental probability.
B The experimental probability for landing on the heart is less than the theoretical probability.The experimental probability for landing on the heart is less than the theoretical probability.
C As the number of spins increases, the closer the experimental probability will get to the theoretical probability.As the number of spins increases, the closer the experimental probability will get to the theoretical probability.
D The experimental probability for landing on the star is greater than the theoretical probability.The experimental probability for landing on the star is greater than the theoretical probability.
E The experimental probability for landing on the heart is greater than the theoretical probability.
B), C), and D) are the correct statements when comparing the experimental and theoretical probabilities.
B) The experimental probability for landing on the heart is less than the theoretical probability. We can calculate the theoretical probability of landing on the heart by dividing its sector size (3/5) by the total number of sectors (2), which gives us 3/10. The experimental probability is calculated by dividing the number of times the arrow landed on the heart (9) by the total number of spins (15), which gives us 9/15, which simplifies to 3/5. Since 3/5 is greater than 3/10, the statement is false.
C) As the number of spins increases, the closer the experimental probability will get to the theoretical probability. This statement is true because the Law of Large Numbers states that as the number of trials increases, the experimental probability will converge to the theoretical probability.
D) The experimental probability for landing on the star is greater than the theoretical probability. Using the same calculations as in statement B, we see that the theoretical probability of landing on the star is 2/10 or 1/5. The experimental probability is calculated as 6/15, which simplifies to 2/5. Since 2/5 is greater than 1/5, the statement is true.
Therefore, the answer is B, C, and D.
When you press Enter on the keyboard, a computer program outputs a random odd number greater than 1 and less than 9.
Question 1
What is the sample space for the given situation?
Responses
A {3, 5, 7}{3, 5, 7}
B {1, 3, 5, 7, 9}{1, 3, 5, 7, 9}
C {2, 3, 4, 5, 6, 7, 8, 9}{2, 3, 4, 5, 6, 7, 8, 9}
D {3, 4, 5, 6, 7, 8, 9}
A) {3, 5, 7} is the sample space for the given situation.
This is because the program outputs a random odd number greater than 1 and less than 9, which means that the possible outcomes are 3, 5, and 7.
Option B is incorrect because it includes the number 1, which is not a possible outcome in this situation.
Option C is incorrect because it includes even numbers, which are also not possible outcomes.
Option D is incorrect because it includes the number 4, which is an even number and not a possible outcome.
Therefore, the answer is A) {3, 5, 7}.
A book club is trying to decide a day and time to meet. They can meet either Monday or Wednesday. The possible times are 2 p.m. or 6 p.m. What is the sample space for this situation?
Responses
A {(M, W), (2, 6)}
B {(M, 2), (M, 6), (W, 2), (W, 6)}
C {(M, 6), (W, 2)}
D {(M, 2), (W, 6)}
B) {(M, 2), (M, 6), (W, 2), (W, 6)} is the sample space for this situation.
This is because there are two possible days (Monday or Wednesday) and two possible times (2 pm or 6 pm) for each day. Therefore, the sample space consists of all possible combinations of the two days and two times:
(M, 2) - meeting on Monday at 2 pm
(M, 6) - meeting on Monday at 6 pm
(W, 2) - meeting on Wednesday at 2 pm
(W, 6) - meeting on Wednesday at 6 pm
Option A is incorrect because it does not include all the possible combinations of day and time.
Option C is incorrect because it only includes two of the possible combinations.
Option D is incorrect because it only includes two of the possible combinations and does not include the other two.
Therefore, the answer is B) {(M, 2), (M, 6), (W, 2), (W, 6)}.
Hannah is getting dressed for a party. She plans to wear either shorts or jeans, a red, blue or green shirt, and flip flops or tennis shoes. According to the tree diagram, how many possible outfits can she make?
Responses
A 88
B 1010
C 1616
D 1414
E 12
According to the tree diagram, Hannah can make 12 possible outfits.
To calculate this, we start at the top of the tree and follow each branch until we reach the end of each path. We then multiply the number of options at each level of the tree, following each branch down to the end:
- For the first level, there are 2 options: shorts or jeans
- For the second level, there are 3 options: red, blue, or green shirt
- For the third level, there are 2 options: flip flops or tennis shoes
Multiplying the number of options at each level, we get:
2 options x 3 options x 2 options = 12 possible outfits
Therefore, the answer is E) 12.
Reliable source def
A reliable source is one that is trustworthy, accurate, and objective. It is a source that provides information that is factual, verifiable, and can be supported by evidence and research. Reliable sources are important in academic and professional settings as they help to ensure the accuracy and credibility of the information being used or shared. Examples of reliable sources include peer-reviewed journals, reputable news organizations, and government or educational institutions.
Conduct a short research project using the chart below. Refer to the chart on page 4 of 10 for specific information. Then once you reach page 10, complete the chart.
Research Project Steps
Details to Include
My (short) Research Project
Identify a research question
A question that identifies the topic and the specific focus of your research
Research question:
Use sources to conduct research
Use several reliable sources to find facts and details that specifically address your question
g
Analyze sources and draw conclusions that answer the research question
Determine what your research explains about your topic and draw conclusions that answer your question.
My (short) Research Project
Identify a research question: How has the number of international tourists to the United States changed over the past 10 years?
Research question: What is the trend in the number of international visitors to the United States over the last decade?
Use sources to conduct research:
- Visit the U.S. Department of Commerce, National Travel and Tourism Office website and review the annual international visitation reports.
- Research articles from reputable news organizations, such as CNN and The New York Times, to see how the number of international visitors has been reported over time.
Analyze sources and draw conclusions that answer the research question:
- According to the National Travel and Tourism Office, the number of international visitors to the United States increased from 60.7 million in 2010 to 79.3 million in 2019, representing a 30.7% increase over the decade.
- However, this increase was not steady year to year. In fact, there were declines in 2014 and 2015, and then again in 2020 due to the COVID-19 pandemic.
Conclusion:
The number of international visitors to the United States has been generally increasing over the last decade, with some fluctuations. However, the COVID-19 pandemic had a significant impact on international travel in 2020.
Conduct a short research project using the chart below. Refer to the chart on page 4 of 10 for specific information. Then once you reach page 10, complete the chart.
Research Project Steps
Details to Include
My (short) Research Project
Identify a research question
A question that identifies the topic and the specific focus of your research
Research question: What is the trend in the number of international visitors to the United States over the last decade?
Use sources to conduct research
Use several reliable sources to find facts and details that specifically address your question
Sources and relevant information from each source:
1.
2.
3.
4.
Analyze sources and draw conclusions that answer the research question
Determine what your research explains about your topic and draw conclusions that answer your question.
My (short) Research Project
Identify a research question: What is the trend in the number of international visitors to the United States over the last decade?
Use sources to conduct research:
1. Visit the U.S. Department of Commerce, National Travel and Tourism Office website and review the annual international visitation reports.
2. Research articles from reputable news organizations, such as CNN and The New York Times, to see how the number of international visitors has been reported over time.
Sources and relevant information from each source:
1. According to the National Travel and Tourism Office, the number of international visitors to the United States increased from 60.7 million in 2010 to 79.3 million in 2019, representing a 30.7% increase over the decade.
2. A CNN article from August 2020 reported that international tourism to the United States was down 75% due to the COVID-19 pandemic.
3. A New York Times article from January 2020 reported that the number of visitors from China, previously the largest source of international tourists to the United States, had declined due to trade
Conduct a short research project using the chart below. Refer to the chart on page 4 of 10 for specific information. Then once you reach page 10, complete the chart.
Research Project Steps
Details to Include
My (short) Research Project
Identify a research question
A question that identifies the topic and the specific focus of your research
Research question: What is the trend in the number of international visitors to the United States over the last decade?
Use sources to conduct research
Use several reliable sources to find facts and details that specifically address your question
Sources and relevant information from each source:
Visit the U.S. Department of Commerce, National Travel and Tourism Office website and review the annual international visitation reports.
Research articles from reputable news organizations, such as CNN and The New York Times, to see how the number of international visitors has been reported over time.
A New York Times article from January 2020 reported that the number of visitors from China, previously the largest source of international tourists to the United States, had declined due to trade
A CNN article from August 2020 reported that international tourism to the United States was down 75% due to the COVID-19 pandemic.
Analyze sources and draw conclusions that answer the research question
Determine what your research explains about your topic and draw conclusions that answer your question.
Analysis of research:
Conclusions that answer my research question:
What is the trend in the number of international visitors to the United States over the last decade?
Analysis of research:
Conclusions that answer my research question: