1. Intersection
2. complement
3. Union
4. finite set
5. disjoint sets
6. proper subset
7. subset
Answer:
30.2
Step-by-step explanation:
Answer:
Actually, what you said you have so far is not correct. The 2 correct answers are the 1st one (x + y = 15) and the 5th one (15x + 10y > 180)
Step-by-step explanation:
If tutoring French is x hours and scooping ice cream is y hours and he is going to work 15 hours for sure doing both, then we can add them together to get that x hours + y hours = 15 hours, or put simply: x + y = 15.
Now we are going to throw in the added fun of the money he makes doing each. The thing to realize here is that we can only add like terms. So looking at the equation above, we have x hours of tutoring and y hours of scooping, so if we want to add them, we will add those number of hours together to get the total number of hours he worked, which we know to be 15. The same goes for money. If we add money earned from tutoring to money earned from scooping, we need that to be greater than the money he wants to earn which is 180 at least. Because he wants to earn MORE than $180. we use the ">" sign. Since he earns $15 an hour tutoring, that expression is $15x; since he earns $10 an hour scooping, that expression is $10y. Now add them together (and you CAN because they are both expressions relating dollars to dollars) and set the sum > $180:
$15x + $10y > $180. That's why your answer is not correct. Use mine (with the understanding that you care about why yours is wrong and mine is correct) and you'll be fine.
Answer:
The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.
This means that 
95% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
