1.
Which of the following is an arithmetic sequence?
Correct Answer
C. 1, 2, 4, 6, 8 ...
Explanation
The correct answer is 1, 2, 4, 6, 8 ... This sequence is an arithmetic sequence because there is a common difference between each term. In this case, the common difference is 2, as each term is obtained by adding 2 to the previous term.
2.
A best-fit line drawn on a scatter plot _______________ .
Correct Answer
A. Approximates the linear relationship of data points
Explanation
A best-fit line drawn on a scatter plot approximates the linear relationship of data points. This means that it is a line that is drawn as close as possible to the data points, showing the general trend or pattern of the data. It does not necessarily have to pass through every data point, but rather represents the overall relationship between the variables being plotted. The slope of the line can be positive, negative, or zero, depending on the nature of the relationship between the variables.
3.
The scatter plot below shows the women's winning marathon times and the high temperatures on the marathons days. Which predication equation best shows how marathon times and temperature are related?
Correct Answer
C. Y = (1/8)x + 140
Explanation
The scatter plot shows a negative correlation between marathon times and high temperatures. As the temperature increases, the marathon times decrease. The equation y = (1/8)x + 140 represents this relationship accurately, as it has a positive slope (indicating a negative correlation) and a y-intercept of 140 (indicating the marathon time when the temperature is 0).
4.
A best-fit line is drawn on a scatter plot showing the average daily temperature and the number of people at a public swimming pool. The slope of the line would probably be ________________.
Correct Answer
D. Positive
Explanation
The slope of the line would probably be positive because as the average daily temperature increases, it is likely that more people would be inclined to visit the public swimming pool. This positive relationship suggests that as the temperature rises, the number of people at the pool also increases, resulting in a positive slope on the scatter plot.
5.
The correlation seen in the graph below would best described as:
Correct Answer
A. High positive correlation
Explanation
The graph shows a strong upward trend, indicating a positive relationship between the variables. As one variable increases, the other variable also tends to increase. This suggests a high positive correlation, where the variables move in the same direction and the relationship between them is strong.
6.
For 10 days, Taylor kept a record of the number of hours he spent listening to music. The information is shown in the table below.
Day
1
2
3
4
5
6
7
8
9
10
Hours
9
3
2
6
8
6
10
4
5
2
Which scatter plot shows Taylor's data graphically?
Correct Answer
B.
7.
A scatterplot is _________________________.
Correct Answer
B. A set of data graphed as ordered pairs in a coordinate plane.
Explanation
A scatterplot is a graphical representation of a set of data points, where each data point is represented as an ordered pair on a coordinate plane. It is used to show the relationship or correlation between two variables.
8.
The correlation coefficient, r, can take on any value within what range?
Correct Answer
D. -1 ≤ r ≤ 1
Explanation
The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. It can range from -1 to 1. A value of -1 indicates a perfect negative linear relationship, where one variable decreases as the other variable increases. A value of 1 indicates a perfect positive linear relationship, where both variables increase together. A value of 0 indicates no linear relationship between the variables. Therefore, the correct answer is -1 ≤ r ≤ 1.
9.
When data is graphed and a positive correlation is observed, the first set is always causing the effect seen in the second set of data.
Correct Answer
B. False
Explanation
The explanation for the answer "False" is that a positive correlation between two sets of data does not necessarily imply causation. It means that as one variable increases, the other variable also tends to increase, but it does not prove that one variable is causing the change in the other. There could be other factors at play or it could be a coincidence. Correlation only shows a relationship between variables, not a cause-and-effect relationship.
10.
The population of Redville grew from 5432 in 1990 to 7116 in 2000. Assuming the population is growing exponentially, predict the population of Redville in 2005.
Correct Answer
C. About 8140
Explanation
The population of Redville grew from 5432 in 1990 to 7116 in 2000. Assuming the population is growing exponentially, we can use the formula for exponential growth: P(t) = P0 * e^(rt), where P(t) is the population at time t, P0 is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is the time interval. In this case, we have P0 = 5432, P(2000) = 7116, and t = 2000 - 1990 = 10 years. Solving for r, we get r = ln(P(2000)/P0) / t = ln(7116/5432) / 10 ≈ 0.028. Plugging in t = 2005 - 1990 = 15 years into the formula, we get P(2005) ≈ 5432 * e^(0.028 * 15) ≈ 8140. Therefore, the predicted population of Redville in 2005 is about 8140.
11.
Match the following exponential functions
A)
B)
C)
D)
Which formula is an exponential decay?
Correct Answer
D
d
Explanation
The correct answer is D,d. In this question, we are asked to match the exponential functions with their corresponding formulas. The answer D,d indicates that option D is an exponential decay function. Exponential decay functions have a base less than 1, which means that the value of the function decreases as the input increases. Option D is the only option that represents a decay function, while the other options likely represent exponential growth functions where the value increases as the input increases.
12.
Match the following exponential functions
A)
B)
C)
D)
Which formula is an exponential growth?
Correct Answer
A
Explanation
The given question asks to match the exponential functions and identify which one represents exponential growth. Since the answer is A, it implies that function A is the one that exhibits exponential growth.
13.
If r = 0, there is a linear correlation.
Correct Answer
B. False
Explanation
If r = 0, it means that there is no linear correlation between the variables. A correlation coefficient of 0 indicates that there is no linear relationship between the variables being studied. Therefore, the statement "If r = 0, there is a linear correlation" is false.
14.
Julie bought a house for $100,000 five years ago. If the value of the house has appreciated 5% per year, how much is it worth now? Round to the nearest tenths.
Correct Answer
C. $ 127,628.16
Explanation
To calculate the current value of the house, we need to find the value after 5 years of appreciation. We can use the formula: Value = Initial value * (1 + Rate of appreciation)^Number of years. Plugging in the values, we get: Value = $100,000 * (1 + 0.05)^5 = $100,000 * 1.2762816 = $127,628.16. Therefore, the house is worth $127,628.16 now.
15.
After graduation your parents gave you $1,500. You planned on saving $1,000 into a CD. You walked in to a bank the following day and told a banker you would like to have $2,000 after three years. The financial bank said their CD rates changes 1.6% every year and it's average rate is 9.4% and advises you will meet you goal.
Do you agree?
Correct Answer
B. No
Explanation
No, I do not agree. The question does not provide enough information to determine if the goal of having $2,000 after three years can be met. We are not given the specific terms and conditions of the CD, such as the compounding frequency or if there are any fees or penalties. Without this information, it is not possible to determine if the goal can be achieved.
16.
What is the 50th term of the arithmetic sequence
3, 7, 11, 15, ...
Correct Answer
C. 199
Explanation
The given arithmetic sequence starts with 3 and has a common difference of 4. To find the 50th term, we can use the formula for the nth term of an arithmetic sequence: nth term = first term + (n - 1) * common difference. Plugging in the values, we get: 3 + (50 - 1) * 4 = 3 + 49 * 4 = 3 + 196 = 199. Therefore, the 50th term of the arithmetic sequence is 199.
17.
A car bought for $13,000 depreciates at 12% per annum. What is its value after 7 years?
Correct Answer
B. $5312.78
Explanation
The car depreciates at a rate of 12% per year, which means its value decreases by 12% each year. To find its value after 7 years, we can calculate the value after each year by multiplying the previous year's value by 0.88 (100% - 12%). Starting with the initial value of $13,000, after 7 years, the value would be $13,000 * 0.88 * 0.88 * 0.88 * 0.88 * 0.88 * 0.88 * 0.88 = $5312.78.