According to the national institute on drug abuse, a u. s. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. a school official hopes to show the percentage is lower in his district, testing h0: p = 0.173 versus ha: p < 0.173. the health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
a. no, because () is less than 10. because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions.
b. yes, because the sample is random. it represents the 8th graders in the district.
c. yes, because () and (80)(1 ‑ 0.173) are both at least 10. this means we can use the normal distribution to model the distribution of sample proportions.
d. no, because 80 students is not enough to be representative of the students in the school district.
she needs to put the meal in the oven on or before 6: 55pm.
it is given that jasmine wants to eat at 8: 00pm.
the time she needs to cook her meal = 65 mins.
to find the time she needs to put the meal in the oven, we have to subtract 65 mins from 8: 00pm
65 mins = 1 hour and 5 mins.
so, 1 hour before 8: 00pm is 7: 00pm.
5 mins before 7: 00pm is 6: 55pm.
hence, she needs to put the meal in the oven on or before 6: 55pm so that she can't miss 800pm to eat.
c. 4√2 / 7 .
sin ф = 1/3.
cos ф = √(1 - (1/3)^2) note this will be the positive square root as
ф is in the first quadrant.
sin 2ф = 2 sin ф cos ф
= 2* 1/3 * √(1 - (1/3)^2)
= 2/3 * 2√2/3
= 4√2 / 9
cos 2ф = 1 -2 sin^2 ф = 1 - 2* (1/3)^2 = 7/9
tan 2 ф = sin 2ф / cos 2ф = 4√2/ 9 / 7/9
= 4√2 / 9 * 9 / 7
= 4√2 / 7 (answer).
|-14| is a module number, what it means? it will always be positive.
so, |-14| = 14