Afacilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. he decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. in a sample of 15 students, he found the average time was 4.61 minutes and the standard deviation was 0.75 minutes. using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. assume normality.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.

Point r divides in the ratio 1 : 3. if the x-coordinate of r is -1 and the x-coordinate of p is -3, what is the x-coordinate of q? a. b. 3 c. 5 d. 6 e. -9