6. The diameter delta(A) of a non-empty set A in a metric space (X, d) is defined to be
delta(A) = sup [x, y BELONGING_TO A] d(x,y).
A is said to be bounded if delta(A) < infinity. Show that A SUBSET B implies delta(A) <= delta(B).
Please see the attached image for proper description of the question with appropriate sym

A machine that produces ball bearings is set so that the average diameter is .50 inch. A sample of 10 ball bearings was measured with the results shown here. Assuming that the standard deviation is .05 inch, can we conclude at the 5% significance level that the mean diameter is not .50 inch?
.48 .50 .49 .52 .53 .48 .49 .47 .

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between th

Rotating Space Stations. One problem for human living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates "artificial gravity" at the outside of the station.
A) If the diameter of the space station is 8

For the metric space { N }, the set of all natural numbers, characterize whether or not it has the following properties: compact, totally bounded, has the Heine-Borel property, complete.
For compact, we are to show that every sequence converges. For totally bounded, we are to show that it can be covered by finitely many sets

Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings!
Let G be a connected graph and sq(G) be a graph which contains all vertices and edges of G and moreover edges joining every pair of vertices that were in G at distance 2. In other words, xy is

Please show calculations on how it's done.
Sun Love grapefruit growers have determined that the diameters of their grapefruits are normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. If a grapefruit is selected at random, what is the probability that its diameter:
a. is at least 4.14 in

A bolt hole in a brass plate has a diameter of 1.200 cm at 20oC. What is the diameter of the hole when the plate is heated to 220 oC? (The coefficient of linear thermal expansion for brass is 19 ? 10^-6 /oC.)

The Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.4 m in diameter. If the HST were to look down on Earth's surface (rather than up at the stars), what is the minimum separation of two objects that could be resolved using 550 nm light? [Note: The HST is used only for astr