A game is played using one die. If the die is rolled and shows 5​, the player wins $15. If the die shows any number other than ​5, the player wins nothing. Complete parts​ (a) through​ (b) below. a. If there is a charge of $3 to play the​ game, what is the​ game's expected​ value?
​$
​(Round to the nearest​ cent.)

b. What does this expected value​ mean? Choose the correct statement below.

A. This value represents the expected loss over the long run for each game played.
B. The player can expect to break even over the long run.
C. This value represents the expected win over the long run for each game played.

Damon makes 20 cups of lemonade by mixing lemon juice and water. the ratio of lemon juice to water is shown in the tape diagram. lemon juice\text{lemon juice} lemon juice water\text{water} water how much lemon juice did damon use in the lemonade? cups

In the picture below, line pq is parallel to line rs, and the lines are cut by a transversal, line tu. the transversal is not perpendicular to the parallel lines. note: figure is not drawn to scale. which of the following are congruent angles?

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.