If the z-score exceeds the critical value at a chosen level of significance, such as 0.05, the professor can reject the null hypothesis and conclude that the percentage of community college students owning smartphones is indeed higher than the national average of 40%
According to a Pew Research Center study in May 2011, 40% of all American adults had a smartphone, which allows users to read email and surf the internet.
A communications professor at a university believes that the percentage of community college students owning smartphones is higher than this national average. To test her hypothesis, she conducts a study by selecting 465 community college students at random and finds that 207 of them have a smartphone.
To test her hypothesis, the professor needs to perform a hypothesis test. The null hypothesis (H0) is that the percentage of community college students with smartphones is equal to the national average (40%). The alternative hypothesis (H1) is that the percentage is higher than 40%.
By using a sample proportion (p-hat) and a sample size (n) of 465, the professor can calculate the z-score and compare it to the critical value to determine if there's enough evidence to reject the null hypothesis. In this case, p-hat is equal to 207/465, which is approximately 44.52%.
If the z-score is below the critical value, she cannot reject the null hypothesis, and the difference between the national average and the community college students' smartphone ownership could be due to chance.
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Two random cards numbered from 1,2...100 are pulled from the deck. What is the probability that one number doubles the other from the deck
The probability that one number doubles the other from a deck of 1 to 100 numbered cards when two cards are drawn at random is 0.01 or 1%.
There are 100 cards in the deck numbered from 1 to 100, so there are 100 ways to choose the first card. For the second card, we have two cases to consider: either the second card is double the first or the first card is double the second.
If the first card is k, then the probability that the second card is 2k is 1/99, since there are 99 cards left in the deck and only one of them is 2k. Similarly, if the second card is k, then the probability that the first card is 2k is also 1/99.
Therefore, the probability that one number doubles the other is the sum of these probabilities, which is (100 * 1/99) * 2 = 2.02%. However, we have counted the case where the two cards are the same twice, so we need to subtract this probability (1/100) once, giving us a final probability of 2.02% - 1% = 1%.
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20ax - x= 5 in the equation above, a is a constant if the equation has no solution, what is the value of a ?
In a simple linear regression model, if all of the data points fall on the sample regression line, then the standard error of the estimate is
In a simple linear regression model, the standard error of the estimate (also known as the standard deviation of the residuals) measures the variability or scatter of the observed data points around the sample regression line.
It is an important measure of the accuracy of the regression model and helps us to estimate the uncertainty in making predictions.
If all of the data points fall exactly on the sample regression line, then the residuals (i.e., the differences between the observed values and the predicted values) will be zero for each data point. This means that there is no variability or scatter in the data points around the regression line, and hence the standard error of the estimate will also be zero.
However, this scenario is highly unlikely in real-world situations, as there will always be some random error or measurement noise that affects the observed data points. Therefore, it is important to interpret the standard error of the estimate in the context of the data and the regression model. A smaller standard error of the estimate indicates a better fit of the regression line to the data, whereas a larger standard error of the estimate indicates more variability or scatter in the data points around the regression line.
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A business student is interested in estimating the 99% confidence interval for the proportion of students who bring laptops to campus. He wants a precise estimate and is willing to draw a large sample that will keep the sample proportion within four percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available
The student needs to collect data from at least 665 students to estimate the 99% confidence interval for the proportion of students who bring laptops to campus with a precision of 4 percentage points.
To estimate the 99% confidence interval for the proportion of students who bring laptops to campus, the business student needs to ensure a certain level of confidence and precision in the estimate. Specifically, the student wants a confidence level of 99%, which means that there is a 99% chance that the true population proportion falls within the calculated interval. Additionally, the student wants a precision of 4 percentage points, which means that the sample proportion should be within 4 percentage points of the population proportion.
To determine the minimum sample size required to meet these criteria, the business student can use the following formula:
n = (Z^2 * p * (1 - p)) / E^2
where n is the sample size, Z is the Z-score for the desired confidence level (in this case, Z = 2.576 for a 99% confidence level), p is the estimated population proportion (since no prior estimate is available, the student can use 0.5 as a conservative estimate), and E is the desired margin of error (in this case, 0.04).
Plugging in the values, we get:
n = (2.576^2 * 0.5 * (1 - 0.5)) / 0.04^2
n = 664.76
Rounding up to the nearest whole number, the minimum sample size required by the student is 665. This means that the student needs to collect data from at least 665 students to estimate the 99% confidence interval for the proportion of students who bring laptops to campus with a precision of 4 percentage points.
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A new train goes 20% further in 20% less time than an old train. By what percent is the average speed of the new train greater than that of the old train
The average speed of the new train is greater than that of the old train by 50%.
Let's assume that the old train traveled a distance of "d" in "t" time, with an average speed of "s" (where s = d/t).
The new train travels 20% further than the old train, which means it travels a distance of 1.2d. It also travels this distance in 20% less time than the old train, which means it takes 0.8t time to cover the distance.
So, the average speed of the new train is (1.2d)/(0.8t) = 1.5d/t.
The percent increase in average speed of the new train compared to the old train is:
[(1.5d/t - s)/s] x 100%
Substituting s = d/t, we get:
[(1.5d/t - d/t)/(d/t)] x 100%
Simplifying the expression, we get:
(0.5d/t) x 100%
Therefore, the average speed of the new train is greater than that of the old train by 50%.
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The pattern follows the "add one dot to the top of each column and one dot to the right of each row" rule. What will the 6th term be? (1 point)
A pattern showing the square term number rule. The first term has one dot. The second term has four dots. The third term has nine dots. The fourth term has sixteen dots.
a
36
b
49
c
64
d
81
The pattern for the 6th term of the sequence is A₆ = 36
Given data ,
The first term has one dot (1² = 1)
The second term has four dots (2² = 4)
The third term has nine dots (3² = 9)
The fourth term has sixteen dots (4² = 16)
So , the fifth term A₅ = 25
And , from the pattern , the 6th term A₆ = 36
Hence , the 6th term is A₆ = 36
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Use the quadratic formula to solve the equation. Use a calculator to give solutions correct to the nearest hundredth
x² +
+ 8x = 8
stion 5 OT 5
Select the correct choice below and, if necessary, fill in the answer box
O A.
A. The solution set is
(Simplify your answer. Type an integer or a decimal rounded to
The solutions to the given equation correct to the nearest hundredth are approximate x ≈ -8.47 and x ≈ 0.47.
The given equation is x² + 8x = 8. To solve for x using the quadratic formula, we first need to rewrite the equation in the standard form ax² + bx + c = 0, where a, b, and c are constants.
x² + 8x = 8 can be rewritten as x² + 8x - 8 = 0, where a = 1, b = 8, and c = -8. Applying the quadratic formula, we have:
[tex]x = \frac{(-b \pm \sqrt{(b^2 - 4ac)) }}{ 2a}[/tex]
Simplifying the expression inside the square root, we get:
[tex]x = \frac{(-8 \pm \sqrt{(80)})}2\\x = \frac{(-8 \pm 8.94)}2[/tex]
Using a calculator to approximate the solutions to the nearest hundredth, we get:
x= -8.47
x = 0.47
Therefore, the solutions to the given equation correct to the nearest hundredth are approximately x ≈ -8.47 and x ≈ 0.47.
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The weights of 29 quarters are normally distributed about a mean of 0.75g with a standard deviation of 0.035g. Estimate the true standard deviation of the weights of pennies assuming a desired 99% level of confidence.
This means that we can be 99% confident that the true standard deviation of the weights of pennies is between 0.0216g and 0.0396g.
To estimate the true standard deviation of the weights of pennies with a 99% level of confidence.
we can use the formula for the confidence interval for a standard deviation, which is:
CI = (sqrt((n-1)*[tex]s^{2}[/tex]/[tex]X^{2}[/tex]_α/2), sqrt((n-1)*[tex]s^{2}[/tex]/[tex]X^{2}[/tex]_1-α/2))
Where CI is the confidence interval, n is the sample size (29 in this case).
s is the sample standard deviation (0.035g).
α is the significance level (0.01 for a 99% level of confidence).
[tex]X^{2}[/tex]_α/2 is the chi-square value at α/2 with n-1 degrees of freedom.
[tex]X^{2}[/tex]_1-α/2 is the chi-square value at 1-α/2 with n-1 degrees of freedom.
Substituting the values in the formula, we get:
CI = (sqrt((29-1)*0.035^2/[tex]X^{2}[/tex]_0.005/2), sqrt((29-1)*0.035^2/[tex]X^{2}[/tex]_0.995/2))
CI = (0.0216, 0.0396)
This means that we can be 99% confident that the true standard deviation of the weights of pennies is between 0.0216g and 0.0396g.
In conclusion, to estimate the true standard deviation of the weights of pennies with a 99% level of confidence, we use the formula for the confidence interval for a standard deviation and substitute the sample size, sample standard deviation, and significance level. The resulting confidence interval gives us a range of values within which we can be confident that the true standard deviation lies.
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A store sells variety packs of granola bars. The table shows the types of bars in each pack . Mason says that for every 7 bars in a pack, there is 1 cinnamon bar. Do you agree? Explain.
It is not true that for every 7 bars in a pack, there is 1 cinnamon bar.
Let's assume that there are 7 packs, each containing 1 cinnamon bar, 4 honey bars, and 3 peanut butter bars.
Then, the total number of bars in the 7 packs would be:
1 (cinnamon) x 7 packs = 7 cinnamon bars
4 (honey) x 7 packs = 28 honey bars
3 (peanut butter) x 7 packs = 21 peanut butter bars
The total number of bars in the packs would be:
7 cinnamon bars + 28 honey bars + 21 peanut butter bars = 56 bars
So, the ratio of cinnamon bars to the total number of bars would be:
1 cinnamon bar : 56 total bars
This can be simplified to 1/56
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The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 5. Calculate the probability of a type II error if the true mean heat evolved is 103 and
To calculate the probability of a type II error, we need to first determine the critical value for the test. This can be found using the formula:
Critical value = mean + (z-score for desired level of significance) x (standard deviation/square root of sample size)
Assuming a 5% level of significance and a sample size of 25, the z-score for a one-tailed test is 1.645. Plugging in the values, we get:
Critical value = 100 + (1.645) x (5/sqrt(25)) = 101.645
Next, we need to determine the probability of failing to reject the null hypothesis (i.e. making a type II error) when the true mean heat evolved is actually 103. This can be found using a normal distribution table or calculator:
z-score = (critical value - true mean)/standard deviation = (101.645 - 103)/5 = -0.31
Using the normal distribution table, the probability of a z-score of -0.31 or less is 0.3783. Therefore, the probability of making a type II error is approximately 38%.
In summary, if the true mean heat evolved is 103 and we are using a one-tailed test with a 5% level of significance and a sample size of 25, there is a 38% chance that we will fail to reject the null hypothesis and make a type II error.
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In a survey of 100 students, 60% wake up with an alarm clock.
Of those who wake up with an alarm clock, 80% exercise to
begin the day. Among those who do not use an alarm clock,
25% exercise to begin the day. Construct a two-way frequency
table to display the data.
A two-way frequency table for the data:
How to solveHere's a two-way frequency table for the data:
| Alarm Clock | No Alarm Clock | Total
Exercise | 48 | 10 | 58
No Exercise | 12 | 30 | 42
Total | 60 | 40 | 100
A two-way frequency table, otherwise referred to as a contingency table, is a chart that showcases the frequencies or reckonings of two categorical variables.
The display has two columns and two or greater rows, with each row manifesting a single grouping of the primary element and each column demonstrating one type of the second constituent.
The cells of this array demonstrate the frequency or amount of appearances that abide by both categories. A two-way frequency table is perennially utilized in data analysis and statistics to investigate the association between two distinct categorical factors.
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Find the sample size required to make a 95% confidence interval estimate of the mean length of the bluejay bill so that the margin of error is 0.6 inches. Consider the standard deviation of the population to be 3 inches.
We will need a sample size of 35 bluejay bills to make a 95% confidence interval estimate of the mean length with a margin of error of 0.6 inches.
We find the sample size required for a 95% confidence interval estimate with a margin of error of 0.6 inches. Here are the terms we need to consider:
Confidence interval:
A range of values within which we can be confident the true population parameter lies.
Margin of error:
The amount added or subtracted from the sample mean to create the confidence interval.
Standard deviation:
A measure of the dispersion of a set of values, denoted as σ.
Sample size:
The number of observations in the sample, denoted as n.
Z-score:
The number of standard deviations a value is away from the mean.
Now let's calculate the sample size, n:
Identify the values from the problem.
- Confidence level: 95%
- Margin of error (E): 0.6 inches
- Population standard deviation (σ): 3 inches.
Find the Z-score for a 95% confidence interval.
For a 95% confidence interval, the Z-score is 1.96 (you can find this value in a Z-score table or through online calculators).
Use the formula to calculate the sample size, n:
n = (Z * σ / E)²
n = (1.96 * 3 / 0.6)²
Calculate n:
n = (5.88)²
n ≈ 34.5744
Round up to the nearest whole number, since we can't have a fraction of a sample.
n ≈ 35.
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Values that are computed from a complete census, which are considered to be precise and valid measures of the population, are referred to as:
Parameters are the values that are computed from a complete census, which are considered to be precise and valid measures of the population. So, option(b) is right one.
In statistics, a population parameter is a number that identifies an entire group of people or population. This should not be confused with arguments in other forms of mathematics that refer to values that remain constant for a mathematical function. Note that the population parameter is not a statistic, it refers to data for a sample or group of the population. With good research, we can get statistics that accurately estimate the population. Statistics is a numerical measure described with sample data. Therefore, the parameter is a numerical description of the characteristic of population.
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Complete question:
Values that are computed from a complete census, which are considered to be precise and valid measures of the population, are referred to as:
a) statistic
b) parameters
At the local college, a study found that students had an average of 0.70.7 roommates per semester. A sample of 133133 students was taken. What is the best point estimate for the average number of roommates per semester for all students at the local college
We estimate that the average number of roommates per semester for all students at the local college is 0.7.
The best point estimate for the average number of roommates per semester for all students at the local college would be the sample mean, which is calculated as the sum of the number of roommates for all students in the sample divided by the number of students in the sample.
Using the information given in the problem, we have:
Sample size (n) = 133
Sample mean ([tex]\bar X[/tex]) = 0.7
Therefore, the best point estimate for the population mean (μ) is the sample mean:
μ ≈ [tex]\bar X[/tex] = 0.7
So, we estimate that the average number of roommates per semester for all students at the local college is 0.7.
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If a many-to-many-to-many relationship is created when it is not appropriate to do so, how can the problem be corrected?
If a many-to-many-to-many relationship is created when it is not appropriate to do so, the problem can be corrected by re-designing the database schema to remove the unnecessary relationship.
Here are some steps you can follow to correct the problem:
Analyze the existing database schema to identify the many-to-many-to-many relationship and the tables involved in it.
Evaluate the relationship to determine whether it is necessary or not. If it is not, remove it from the schema.
If the relationship is necessary, analyze the tables and their attributes to identify the primary keys and foreign keys involved in the relationship.
Create a new table to serve as an intermediary between the tables involved in the relationship.
Update the foreign keys in the related tables to point to the primary keys in the new intermediary table.
Migrate the data from the existing tables to the new intermediary table.
Test the new database schema to ensure that it functions correctly and that all data is correctly retrieved and stored.
Overall, the process of correcting a many-to-many-to-many relationship involves re-evaluating the database schema and modifying it as necessary to ensure that it is properly designed to store and retrieve data efficiently and accurately.
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Find all possible values of rank(A) as a varies. (Enter your answers as a comma-separated list.) [\begin{array}{cc} a&2&-1\\3&3&2\\-2&-1&a\end{array}\right]
The only possible value of rank(A) is 3, and it does not depend on the value of a. Therefore, the answer is: 3
The rank of a matrix is the dimension of the row space or column space of the matrix. To find all possible values of rank(A) as a varies, we can use the determinant of the matrix and the rank-nullity theorem.
The determinant of A is given by:
|A| = a(9a + 2) - 6a + 6(2 + 2a) = 9a^2 + 12a + 12
We can see that |A| is a quadratic polynomial in a, and it is never equal to zero. Therefore, the matrix A is always invertible, and its rank is 3.
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if a jaguar has traveled 25.5 miles in an hour if it continues at the same speed how far will it travel in 10 hours ps: this is due in about 60 seconds please hurry with explnation
Answer:255
Step-by-step explanation:
25.5 * 10 = 255 so the answer would be 255
Answer: 255 miles
Step-by-step explanation: 25.5 miles times 10 hours will get you 255 miles away.
Math help please ! No bots.
An equation that best models the graph shown above is [tex]y = 2(\frac{1}{3} )^x[/tex]
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, base, or constant.Based on the graph, we would calculate the value of a and b as follows;
f(x) = a(b)^x
2 = a(b)⁰
a = 2
Next, we would determine value of b as follows;
6 = 2(b)⁻¹
6 = 2/b
b = 2/6
b = 1/3
Therefore, the required exponential function is given by;
[tex]f(x) = y = 2(\frac{1}{3} )^x[/tex]
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Variability between groups is due to ______. Group of answer choices the level of the dependent variable the F ratio the grouping factor chance Flag question: Question 4
Variability between groups is due to the grouping factor.
The F ratio is a measure of the variability between groups relative to the variability within groups, but it is not the cause of the variability between groups.
In an experimental design, researchers often manipulate an independent variable to observe its effects on a dependent variable.
The independent variable is often a grouping factor, which means that participants are assigned to different groups based on some characteristic or condition.
Participants may be assigned to a treatment group or a control group, or they may be grouped based on age, gender, or some other factor.
The experiment is conducted, the dependent variable is measured in each group, and the researcher is interested in whether there are significant differences between the groups.
Variability between groups refers to the differences in the mean scores of the dependent variable between the different groups.
The grouping factor is the reason for the variability between groups.
This is because the different groups are defined by the levels of the grouping factor, and the participants within each group are assumed to be similar with respect to the dependent variable.
Any differences between the groups must be due to the effect of the grouping factor.
The F ratio, which is calculated by dividing the variability between groups by the variability within groups, is used to test whether the differences between the groups are statistically significant.
The F ratio is a measure of the extent to which the grouping factor explains the variability in the dependent variable, and a significant F ratio indicates that there are significant differences between the groups.
Variability between groups is due to the grouping factor, and the F ratio is used to test whether the differences between the groups are statistically significant.
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A single number cube is rolled twice determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.
The number of possible outcomes on rolling a cube twice is 36
The possible number of outcomes of an experiment are the number of elements in the sample space.
The sample space of rolling a cube twice is given as:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Hence, there are 36 elements in the sample space.
Hence, the number of possible outcomes on rolling a cube twice is 36
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What is the smallest of 3 consecutive positvie integers if the product of the smaller two integers is 8 less than 4 times the largest integer?
Suppose the true proportion of high school juniors who skateboard is 0.18. If many random samples of 250 high school juniors are taken, by how much would their sample proportions typically vary from the true proportion
Thus, the sample proportions we get would be close to the true proportion of 0.18, with most of the sample proportions falling within a range of 0.151 to 0.209.
The variation of sample proportions from the true proportion can be measured using the standard deviation of the sampling distribution.
In this case, since the population proportion is known (0.18) and the sample size is large (250), we can use the normal approximation to the binomial distribution.
The standard deviation of the sampling distribution of sample proportions is given by the formula sqrt(p*(1-p)/n), where p is the population proportion and n is the sample size. Plugging in the values, we get sqrt(0.18*(1-0.18)/250) = 0.029.
Therefore, we can expect the sample proportions to vary from the true proportion by about 0.029 on average.
In other words, we can be fairly confident that if we take many random samples of 250 high school juniors, the sample proportions we get would be close to the true proportion of 0.18, with most of the sample proportions falling within a range of 0.151 to 0.209.
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A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag,
find the probability that a blue marble will be drawn.
Answer:
3/14
Step-by-step explanation:
The probability of drawing a blue marble can be found by dividing the number of blue marbles by the total number of marbles in the bag.
The total number of marbles in the bag is:
4 (red) + 3 (blue) + 7 (green) = 14
The number of blue marbles is 3.
So, the probability of drawing a blue marble is:
3/14
Answer:
Step-by-step explanation: d
In how many different ways can five women and three men stand in a line if no two men stand next to each other
There are 24,000 different ways to arrange five women and three men in a line if no two men stand next to each other.
If no two men can stand next to each other, we can first arrange the women in the line, and then insert the men in the spaces between the women.
There are 5! ways to arrange the 5 women in the line.
We can visualize the 5 women standing like this:
W W W W W
To ensure that no two men stand next to each other, we need to insert the 3 men into the 4 spaces between the women. We can use the stars and bars method to count the number of ways to do this.
We can represent the spaces between the women with 4 bars:
| | | | |
To insert the 3 men into these spaces, we need to place 3 stars in these 4 spaces. We can use the stars and bars formula to calculate the number of ways to do this:
C(3 + 4 - 1, 3) = C(6, 3) = 20
So there are 20 ways to arrange the 3 men in the spaces between the 5 women.
Therefore, the total number of ways to arrange 5 women and 3 men such that no two men stand next to each other is:
5! × 20 = 24,000
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in 1940 john atansoff a physicist from iows state university wanted to solvve a 29 x 29 linear system of equations. how many arithmetic operations would this have required.
In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.
In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.
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If in a city of 1000 households, 100 are watching ABC, 80 are watching CBS, 50 are watching NBC, 70 are watching Fox, 500 are watching everything else, and 200 do not have the TV set on, what is CBS's share
CBS's share of households in the city is 8%.
Out of the 1000 households in the city:
100 are watching ABC
80 are watching CBS
50 are watching NBC
70 are watching Fox
500 are watching everything else
200 do not have the TV set on
To calculate CBS's share, we need to find the percentage of households that are watching CBS out of the total number of households:
CBS's share = (number of households watching CBS / total number of households) x 100%
CBS's share = (80 / 1000) x 100%
CBS's share = 8%
Therefore, CBS's share of households in the city is 8%.
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Trignometric Functions and Unit Circle
Would someone be so kind as to help me with this? I got the first part down but im confused about the rest
(Solve trignometric function for all possible values in radians)
I tried myself but im really stuck
The solutions to the trigonometric equation 4sin(θ) - 1 = 2sin(θ) + 1 using unit circle are π/2 or 3π/2 (in radians).
To solve the equation 4sin(θ) - 1 = 2sin(θ) + 1, we need to isolate the sine term on one side of the equation.
Here, start by combining like terms
4sin(θ) - 2sin(θ) = 1 + 1
2sin(θ) = 2
Next, we can isolate sin(θ) by dividing both sides by 2
sin(θ) = 1
Now we need to find all possible values of θ for which sin(θ) = 1. Since sine is positive in the first and second quadrants, the solutions will be angles in these quadrants that have a sine value of 1.
In the first quadrant, the reference angle for sin(θ) = 1 is π/2 radians (90 degrees). Therefore, the solution is
θ = π/2
It is in the first quadrant.
In the second quadrant, the reference angle for sin(θ) = 1 is also π/2 radians (90 degrees), but the angle itself is in the range pi to 3π/2. Therefore, the solution is
θ = π + π/2 = 3π/2
It is in the second quadrant.
So the solutions to the equation 4sin(θ) - 1 = 2sin(θ) + 1 are
θ = π/2 or 3π/2 (in radians)
Note that these solutions correspond to the x-coordinates of the points on the unit circle where the sine value is 1.
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Solve for x, rounding to the nearest hundredth
68x3^x/2=136
The solution of the given expression 68 × [tex]3^{(x/2)}[/tex] = 136 for x is equal to 1.26 ( rounded to the nearest hundredth ).
The expression is equal to ,
68 × [tex]3^{(x/2)}[/tex] = 136
Divide both the side of the expression by 68 we get,
⇒ [ 68 × [tex]3^{(x/2)}[/tex] ] / 68 = ( 136 ) / 68
⇒ [tex]3^{(x/2)}[/tex] = 2
Take logarithmic function on both the side of the expression we get,
⇒ ( x / 2) log 3 = log 2
⇒ ( x / 2) = log 2 / log 3
⇒ x = 2 × ( log 2 / log 3 )
⇒ x = 2 × ( 0.3010 / 0.4771 )
⇒ x = 2 × 0.6309
⇒ x = 1.2618
Therefore, the solution of the expression for x rounded to the nearest hundredth is x ≈ 1.26.
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The given question is incomplete, I answer the question in general according to my knowledge:
Solve the expression for x, rounding to the nearest hundredth
68 × 3^( x/2 ) = 136
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Increasing the significance level of a hypothesis test (say, from 1% to 5%) will cause the p-value of an observed test statistic to:___________
Increasing the significance level of a hypothesis test, for example from 1% to 5%, does not directly affect the p-value of an observed test statistic. The p-value is determined by the data and the test statistic, not the significance level.
However, changing the significance level will affect your decision about whether to reject or fail to reject the null hypothesis.
The significance level, denoted by alpha (α), represents the probability of making a Type I error, which occurs when you incorrectly reject the null hypothesis when it is true. By increasing the significance level, you are allowing for a higher probability of making a Type I error, making the test less stringent.
The p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the significance level, you reject the null hypothesis in favor of the alternative hypothesis.
In conclusion, increasing the significance level of a hypothesis test will not cause the p-value of an observed test statistic to change. Instead, it will change the threshold at which you decide to reject the null hypothesis, making the test more likely to reject the null hypothesis, and increasing the chance of making a Type I error.
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