Which system of linear inequalities is graphed? {y>2x+1x+y<−2 {y<2x+1x+y>−2 {y≤2x+1x+y≥−2 {y≥2x+1x+y≤−2 The image is
a system of linear inequalities graphed on a coordinate plane with increments of 1 and x and y axis ranging from negative 5 to 5. A dashed line passes through the points begin ordered pair 0 comma 1 end ordered pair and begin ordered pair 1 comma three end ordered pair. The shading is above the line. The other line passes through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 2 comma zero end ordered pair. The shading is below this line.
1 answer:
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Answer:
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.
<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>