Answer:
The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).
Step-by-step explanation:
The formula for estimating the population proportion by a confidence interval is given by:
Where:
is the sample's proportion of success, which in this case is the people that regularly lie during surveys,
is the critical value needed to find the tails of distribution related to the confidence level,
is the sample's size.
<u>First</u> we compute the value:
<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):
Now we can replace in the formula with the obtained values to compute the confidence interval:
Answer:
$3.20
Step-by-step explanation:
I hope this helps.
Sorry if I'm wrong.
Answer:
π
V-foam = 4r³( 2 - ----- )
3
Step-by-step explanation:
Let the radius of the sphere be r. Then the volume of the sphere is
V = (4/3)(π)(r³).
Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus
V = (2r)³, or 8r³.
Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:
V-foam = 8r³ - (4/3)(π)(r³). This could be factored into
π
V-foam = 4r³( 2 - ----- )
3
The area of the trapezoid is the product of the height and the average of the two bases:
<span>30 (25 + 33)/2 = 30 (58)/2 = 30 (29) = 870 square yd. </span>
<span>But we want to exclude the area of the fountain. </span>
<span>Since it's circular its area is π times the square of its radius, or 16π square yd. </span>
<span>So the area of the park, excluding the fountain, is </span>
<span>870 - 16π square yd, </span>
<span>or about 820 square yd.</span>
