1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta).
2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta) and tan(theta).
3. Let (theta) be an angle in quadrant II such that csc(theta)=7/4. Find the exact values of tan(theta) and cos(theta).
4. Use a cofunction to write an expression equal to csc(3pi/8).
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The frequency table below shows the hourly wages of 22 factory workers.
How many are paid $10.50 per hour or more?
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1 point
Captionless Image
7
11
17
18
Adding up the frequency of the last two rows of the table, we get the total number of workers who are paid $10.50 per hour or more:
14 + 4 = 18
Therefore, 18 factory workers are paid $10.50 per hour or more. Answer: 18.
Researchers at Jackson Hospital asked 40 randomly selected patients about their sleep habits. Sixteen reported sleeping 8 hours or more each night. If there are 700 patients in the hospital, estimate the number of patients who sleep 8 hours or more each night.
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1 point
140
160
180
280
We can set up a proportion to estimate the number of patients who sleep 8 hours or more each night:
16/40 = x/700
Simplifying this proportion, we get:
0.4 = x/700
To solve for x, we can multiply both sides by 700:
x = 0.4 * 700 = 280
Therefore, we can estimate that 280 patients in the hospital sleep 8 hours or more each night. Answer: 280.
Which of the following types of information is suited for display on a double line graph?
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1 point
annual changes in Melody’s height and weight from 5 to 10 years old
number of Democrats and Republicans in the Senate during the past decade
monthly sales of two different types of cars during a one-year period
all of the above
Monthly sales of two different types of cars during a one-year period is suited for display on a double line graph as it allows us to compare and track the trends in sales between the two types of cars over time. Therefore, the correct answer is: Monthly sales of two different types of cars during a one-year period.
The list shows the final exam grades for Ms. Gold’s math class.
66, 98, 92, 91, 69, 55, 53, 90, 67, 74, 57, 58, 60, 59, 86, 92, 63, 55, 51, 84
Make a stem-and-leaf plot for the data.
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1 point
Option 1
Option 2
Option 3
Option 4
Here is the stem-and-leaf plot for the given data:
```
5 | 3 5 5 7 8
6 | 0 3 6 7 9
8 | 4 6
9 | 0 1 2
```
The stem-and-leaf plot below shows the number of miles run by members of the cross-country team.
How many students ran more than 30 miles?
Key= 1|2 = 12
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1 point
Captionless Image
3
5
8
9
To find the number of students who ran more than 30 miles, we need to look at the stem-and-leaf plot. We can see that there are 5 leaves (5, 7, 8, 8, and 9) in the rows with stems 3 and 4. Therefore, there are 5 students who ran more than 30 miles. Answer: 5.
The stem-and-leaf plot shows the ages of residents of a retirement home.
How many residents are older than 80?
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1 point
Captionless Image
Sandy Ridge, 14; Autumn Care, 12
Sandy Ridge, 8; Autumn Care, 9
Sandy Ridge, 13; Autumn Care, 11
Sandy Ridge, 6; Autumn Care, 4
The stem-and-leaf plot shows the ages of residents of a retirement home.
How many residents are older than 80?
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1 point
Captionless Image
a. Sandy Ridge, 14; Autumn Care, 12
b. Sandy Ridge, 8; Autumn Care, 9
c. Sandy Ridge, 13; Autumn Care, 11
d. Sandy Ridge, 6; Autumn Care, 4
We can see from the stem-and-leaf plot that there are no stems (tens digits) above 8, which means that there are no residents with ages above 80. So, the answer is zero. Answer: 0.
what answer do i choose
Choose option d. Sandy Ridge, 6; Autumn Care, 4.
Which survey question is biased?
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1 point
Which is your favorite, pizza or spaghetti?
Who do you live with: both parents, mother only, father only, or another guardian?
Should children be allowed to stay up as late as they would like?
Which subject is your favorite, math, which is easy, or English, which is difficult?
The survey question "Which subject is your favorite, math, which is easy, or English, which is difficult?" is biased because it presents a false dilemma or leading question that suggests that participants must choose between two options that are not necessarily mutually exclusive, and favors one option over the other. Therefore, the correct answer is: Which subject is your favorite, math, which is easy, or English, which is difficult?
A newspaper reporter wants to know how popular the hobby of bird watching is in the city. He asked people at the local bird refuge if they watched birds as a hobby. Which of the following best explains whether the reporter's data is valid or not?
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1 point
The data is valid for the entire city because the bird refuge is located in the city.
The data is not valid for the entire city because people can have more than one hobby.
The data is not valid for the entire city because bird watchers are more likely to visit a bird refuge.
The data is valid for the entire city because a bird refuge is a good place to find people who like to watch birds
The statement "The data is not valid for the entire city because bird watchers are more likely to visit a bird refuge" best explains whether the reporter's data is valid or not. The data could be biased because people who visit a bird refuge are more likely to have an interest in bird watching as a hobby, and therefore might not accurately represent the entire population of the city. Therefore, the correct answer is: The data is not valid for the entire city because bird watchers are more likely to visit a bird refuge.
What is the median of the data shown in the box and whisker plot below?
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1 point
Captionless Image
17
27
24
33
To find the median of the data shown in the box and whisker plot, we need to locate the middle value in the data set. We can see that the box stretches from about 22 to 30, which means that the middle value is somewhere between those two points. The median line inside the box indicates the median value, which appears to be closer to 24 than to 27. Therefore, the median of the data is approximately 24. Answer: 24.
The table shows the relationship between the number of roller coasters ridden at the fair and the amount spent at the fair. Graph the data in a scatter plot and describe the trend shown by the graph.
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1 point
The table shows the relationship between the number of roller coasters ridden at the fair and the amount spent at the fair. Graph the data in a scatter plot and describe the trend shown by the graph.
The scatter plot shows a negative trend. As the number of roller coasters increases, the total cost decreases.
The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
Option 4The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
Without the given table, it is not possible to graph the data. However, based on the description, the scatter plot shows a positive trend, meaning that as the number of roller coasters ridden at the fair increases, the amount spent at the fair also increases. Therefore, the correct answer is: The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
Jared drew a scatter plot comparing the number of hours worked and the amount of money earned over the course of a week. He graphed the ordered pairs (number of hours, amount paid) for each day worked. Which of the three scatter plots below most likely represents the data?
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1 point
Option 1
Option 2
Option 3
Option 4
There are no scatter plots provided to choose from. Please include the scatter plots or re-propose the question.
David wants to survey his friends about their favorite animal. He distributes the following survey. Is this an appropriate survey for David to use?
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1 point
Captionless Image
Yes, with this survey David can tell what his friends’ favorite animals are.
Yes, even though this survey doesn’t show what other types of animals students like, it does show how many students at the school like dogs.
No, this survey only shows student results using one type of data display.
No, this survey encourages students to choose dogs as their favorite animal and doesn’t allow them to choose another type of animal.
Option 5
The survey presented by David is inappropriate because it does not allow his friends to choose their own favorite animals and instead encourages them to choose dogs. This could lead to biased results. Moreover, the survey only asks for one type of animal, which limits the range of possible responses and may not accurately capture the variety of favorite animals among David's friends. Therefore, the correct answer is: No, this survey encourages students to choose dogs as their favorite animal and doesn’t allow them to choose another type of animal.
no
1. (-7,4) is in quadrants II,
so x=-7, y = 4
by Pythagoras, r = √(49 = 16) = √65
sinØ = y/r = 4/√65
cscØ = r/y = √65/4
cotØ = x/y = -7/4
2. since sinØ = -2/5 and Ø is in IV,
y = -2, r = 5, then x^2 + 4 = 25
x = √21
etc.
can you finish the rest?