# The set of whole numbers and their opposites O Positive integer O Ratio O Absolute value O Integer

Question
Algebra foundations
The set of whole numbers and their opposites
O Positive integer
O Ratio
O Absolute value
O Integer

2021-03-08
Recall the set of whole numbers: 0,1,2,3...
The opposites of these are:...,-3,-2,-1
By combining, the set of whole numbers and their opposites is:
{...,-3,-2,-1,0,1,2,3...}
or the set of integers.

### Relevant Questions

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
$$\displaystyle≡{2}{\left(\text{mod}{3}\right)},{x}≡{3}{\left(\text{mod}{5}\right)},{x}≡{4}{\left(\text{mod}{11}\right)}$$ Find the smallest positive integer x.
Marty asked some of his classmates to rate their level ofstress out of 10, with 10 being very high. He also asked them tomeasure th enumber of minutes it took them to get from home toschool. A random selection of his results is listed below.

A.) Explain what a positive value for thecoefficient of correlation indicates.
Determine the absolute value of each of the following complex numbers:
z=-1-2i
Determine the absolute value of each of the following complex numbers:
z=3+4i
Airlines schedule about 5.5 hours of flying time for an A320 Airbus to fly from Dulles International Airport near Washington, D.C., to Los Angeles International Airport. Airlines schedule about 4.5 hours of flying time for the reverse direction. The distance between these airports is about 2,300 miles. They allow about 0.4 hour for takeoff and landing.
a. From this information, estimate (to the nearest 5 mph) the average wind speed the airlines assume in making their schedule.
b. What average airplane speed (to the nearest 5 mph) do the airlines assume in making their schedule?
Luis and raul are riding there bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows Luis position at two points during his ride to the beach. Write an equation in slope intercept form to represent Luis's Ride from his house to the beach. If raul lives 5 miles closer to the beach than Luis, At what speed must Raul ride for the plan to work?
1. The solutions of $$|u| < c$$ are the numbers that satisfy$$-c < u < c$$.
2. The solutions of $$|u| > c$$ are the numbers that satisfy$$u < -c\ or\ u < c$$.
These rules are valid if $$<$$ is replaced be $$\displaystyle\le$$ and $$>$$ is replaced by $$\displaystyle\ge$$