The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance, x, represe
2 answers:
You might be interested in
Answer:
B (0.312, 0.364)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence interval
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of
For this problem, we have that:
1289 randomly selected American adults responded to this question. This means that .
Of the respondents, 436 replied that America is doing about the right amount. This means that .
Determine a 95% confidence interval for the proportion of all the registered voters who will vote for the Republican Party.
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval is:
B (0.312, 0.364)
<span><span>1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.
</span>
The Law of Cosines is always preferable when there's a choice. There will be two triangle angles (between 0 and 180 degrees) that share the same sine (supplementary angles) but the value of the cosine uniquely determines a triangle angle.
To find a missing side, we use the Law of Cosines when we know two sides and their included angle. We use the Law of Sines when we know another side and all the triangle angles. (We only need to know two of three to know all three, because they add to 180. There are only two degrees of freedom, to answer a different question I just did.
<span>2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
</span>
We'll use the standard parabola, oriented in the usual way. In that case the directrix is a line y=k and the focus is a point (p,q).
The points (x,y) on the parabola are equidistant from the line to the point. Since the distances are equal so are the squared distances.
The squared distance from (x,y) to the line y=k is </span>
<span>
The squared distance from (x,y) to (p,q) is </span>
<span>
These are equal in a parabola:
</span>
<span>
</span>
Gotta go; more later if I can.
<span>3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.
4.A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.
5.Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross-sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.</span>
</span>
The Law of Cosines is always preferable when there's a choice. There will be two triangle angles (between 0 and 180 degrees) that share the same sine (supplementary angles) but the value of the cosine uniquely determines a triangle angle.
To find a missing side, we use the Law of Cosines when we know two sides and their included angle. We use the Law of Sines when we know another side and all the triangle angles. (We only need to know two of three to know all three, because they add to 180. There are only two degrees of freedom, to answer a different question I just did.
<span>2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
</span>
We'll use the standard parabola, oriented in the usual way. In that case the directrix is a line y=k and the focus is a point (p,q).
The points (x,y) on the parabola are equidistant from the line to the point. Since the distances are equal so are the squared distances.
The squared distance from (x,y) to the line y=k is </span>
<span>
The squared distance from (x,y) to (p,q) is </span>
These are equal in a parabola:
</span>
</span>
Gotta go; more later if I can.
<span>3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.
4.A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.
5.Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross-sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.</span>