A jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is odd- numbered given that the marble is blue

In the image, point a marks the center of the circle. which two lengths must form a ratio of 1 : 2? (options are in the images since thought they were harmful phrases)

70 points ! pls 2. given the following two sets of data what is the union of the two sets and what is the intersection of the two sets. set a = {1, 2, 3, 4, 5, 6, 7, 8, 9} set b = {2, 4, 6, 8, 10, 12, 14} 3. given a regular deck of cards. describe a way of pulling cards that would create a dependent event and then one that would create an independent event. 4. what is the probability of drawing a red card and then drawing a spade without replacing the card that was drawn first?

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.