In which group of statements is the conclusion not justified by the previous pair of statements?

Find the missing angle measures marked with question marks.

slavikrds [6]

Answer:

First one- The ? across from 70 degrees is 70 degrees, and the ones on the side are both 110 degrees.

The second one- The one across 53 degrees is 53 degrees and the ones are the side are both 127 degrees.

Step-by-step explanation:

Take the shown angle and subract that by 180 degrees to get your answer for the missing angles. And the one across from the shown angle is the same number.

Hope this helped im not sure if its right though.

6 0

4 years ago

Government data show that 9% of the American population are at least 75 years of age. To test a random-digit dialing device, you

Lubov Fominskaja [6]

Answer: 9% parameter, 3% statistic

Step-by-step explanation: Parameter and statistic are are statistical terms used to describe a group or observation.

However, the distinction between a parameter and a statistic is in the measured observation.

Parameter is used to describe an entire population while statistic is used to describe a sample.

Where a population refers to the entire number of people or inhabitant of a particular country while a sample refers to a subset of observation drawn randomly from a population which serves a representative of the entire population.

In the question above, 9% is used to make a description of the whole American population who are at least 75 years of age. While,

3% is used to describe a subset of the American population (sample) who are 75 years or older.

7 0

4 years ago

Set up the integral that uses the method of cylindrical shells to find the volume V of the solid obtained by rotating the region

Ganezh [65]

Answer:

first exercise

V = 16 π

second exercise

V= 68π/15

Step-by-step explanation:

Initially, we have to plot the graph x = (y − 5)2 rotating around y = 3 and the limitation x = 4

vide picture 1

The rotation of x = (y − 5)2 intersecting the plane xy results in two graphs, which are represented by the graphs red and blue. The blue is function x = (y − 5)2. The red is the rotated cross section around y=3 of the previous graph. Naturally, the distance of "y" values of the rotated equation is the diameter of the rotation around y=3 and, by consequence, this new red equation is defined by x = (y − 1)2.

Now, we have two equations.

x = (y − 5)2

xm = (y − 1)2 (Rotated graph in red on the figure)

The volume limited by the two functions in the 1 → 5 interval on y axis represents a volume which has to be excluded from the volume of the 5 → 7 on y axis interval integration.

Having said that, we have two volumes to calculate, the volume to be excluded (Ve) and the volume of the interval 5 → 7 called as V. The difference of V - Ve is equal to the total volume Vt.

(1) Vt = V - Ve

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(2) V=\int\limits^{y_{1} }_{y_{2}}{2*pi*y*f(y)} \, dy$

f(y) represents the radius of the infinitesimal cylinder.

Replacing (2) in (1), we have

$V= \int\limits^{5 }_{{3}}{2*pi*y*(y-5)^{2} } \, dy - \int\limits^{7 }_{{5}}{2*pi*y*(y-5)^{2} } \, dy$

V = 16 π

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Second part

Initially, we have to plot the graph y = x2 and x = y2, the area intersected by both is rotated around y = −7. On the second image you can find the representation.

vide picture 2

As the previous exercise, the exclusion zone volume and the volume to be considered will be defined by the interval from x=0 and y=0, to the intersection of this two equations, when x=1 and y = 1.

The interval integration of equation y = x2 will define the exclusion zone. By the other hand, the same interval on the equation x=y2 will be considered.

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(3) V=\int\limits^{x_{1} }_{x_{2}}{2*pi*x*f(x)} \, dx$

Notice that in the equation above, x and y are switched to facilitate the calculation. f(x) is the radius of the infinitesimal cylinder

Having this in mind, the infinitesimal radius of equation (3) is defined by f(x) + radius of the revolution, which is 7. The volume seeked is the volume defined by the y = x2 minus the volume defined by x=y2. As follows:

$V= \int\limits^{1 }_{{0}}{2*pi*x*(\sqrt{x} + 7) } \, dy - \int\limits^{1 }_{{0}}{2*pi*x*(x^{2}+7) } \, dy$