Answer:
a) yes
b) ( 0.0280 , 0.1720 )
c) No
Step-by-step explanation:
A) Determine if the sample sizes are large enough
where :
ages between ( 18 to 29 )
p1 = 0.48 ,
n1 = 178 , ∴ n1 P1 = 85.44 also n1 ( 1 - p1 ) = 92.56
ages between ( 50 to 64 )
P2 = 0.03 ,
n2 = 427 ∴ n2p2 = 12.81 also n2( 1 -p2 ) = 414.19
<em>since all the values ae above 10 we can conclude that the sample sizes are large enough </em>
<em>answer = yes </em>
<u>B) Estimate the difference in the proportion of adult Americans aged 18 to 29</u>
= ( 0.0280 , 0.1720 )
attached below is the detailed solution
C) zero is not included in the interval
Answer:
See explanation
Step-by-step explanation:
Let 
be the coordinates of the point which has to be dilated with the scale factor of 
with the center of dilation at point 
(the origin).
The dilation with the scale factor and the center of dilation at the origin has the rule
So, you have simply to multiply each coordinate of the point by to get the image's coordinates.
The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL. This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.
Find the lengths of FM and ML. Then, FM + ML = FL
<u>FM</u>
ΔFKM (45°-45°-90°): FK is the hypotenuse so FM = 
<u>ML</u>
ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = 
, so KL = 
<u>FM + ML = FL</u>
= 
The answer is -7 because when you minus a negative number you add it, and -10 + 3 is -7. I hope this helps!
Answer: She would need 206 paper cups.
Step-by-step explanation: First of all, Monica has a 10-gallon container full of lemonade and this translates into 37850 cubic centimetres volume of lemonade. The conversion rate has been provided as one gallon equals 3785 cubic centimetres, therefore ten gallons would be 3785 times ten which gives you 37,850 cubic centimetres of lemonade.
Each cone shaped paper cup has a diameter measuring 8 centimetres and 11 centimetres in height. The radius of the cone shaped cup therefore is 4 centimetres (radius equals diameter divided by two). The volume of each cup therefore is given as;
Volume of a cone = (πr²h)/3
Volume of a cone = (3.14 * 4² * 11)/3
Volume of a cone = 552.64/3
Volume of a cone = 184.2
If each cone could hold 184 cubic centimetres of lemonade, then the entire ten gallons would require the following number of cone shaped cups;
Number of cups = Total volume/Volume of a cup
Number of cups = 37850/184.2
Number of cups = 205.48
Rounded to the nearest whole number, this becomes
Number of cups ≈ 206
Therefore Monica would need 206 cone shaped paper cups to empty the entire 10 gallons of lemonade.
