A triangle is drawn. Three different squares are then drawn using the sides of the triangle as one side of each square. If the combined area of the squares on the two shorter sides is greater than the area of the square on the longest side, then the triangle is acute. 3 boxes outline a triangle. One box has an area of 100 inches squared and another box has an area of 36 inches squared. The third box has an area of question mark.

The area of the square on the shortest side is 36 square inches. The area of the square on the longest side is 100 square inches. Which is a possible value for the area of the square on the remaining side if the triangle is acute?

in.2

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.