Answer:
w=4
Step-by-step explanation:
adding a negative is like subtracting so w=11-7
a.) A flat pattern that could be folded to make a 3-dimensional figure is called a "net." You can draw one for Tyler's bench by picking any surface of that rectangular prism and making a drawing of it. At any edge you choose, you can add the adjacent surface to your drawing. Keep doing this until all 6 surfaces are shown in their correct relationship to adjacent surfaces. An example is attached. (This is not the only way the net can be drawn.)
Interior lines of the net can be solid or dashed as you wish. I have shown some of them dashed so as to better illustrate how the area can be computed.
b.) The area of this figure represents the surface area of the rectangular prism. The dimensions of each surface will be 1×1.5, 1×5, or 1.5×5. There are two surfaces with each pair of dimensions. (Perhaps you can find each of these rectangles on the net diagram. Ones with the same dimensions are opposite faces of the rectangular prism.) We can add up the areas of the smaller rectangles to find the total, or we can take advantage of the drawing and divide the area into a smaller number of larger chunks that may make the computation easier.
For example, the rectangle AI that is shaded red is 5×4 in size, for a total of 20 ft². The rectangle KN that is shaded green is 8×1 in size, for a total of 8 ft². Then the total amount of cloth Tyler needs to reupholster his bench is
... 20 ft² + 8 ft² = 28 ft²
Answer:
3000miles
Step-by-step explanation:
(┛❍ᴥ❍)┛彡┻━┻
Given that a display allows a customer to hook together any selection of components, one of each type. These are the types:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette: Onkyo, Sony, Teac, Technics:
Part (a):
In how many ways can one component of each type be selected?
The number of ways one type of receiver will be selected is given by 5C1 = 5
The number of ways one type of CD player will be selected is given by 4C1 = 4
The number of ways one type of speakers will be selected is given by 3C1 = 3
The number of ways one type of cassette will be selected is given by 4C1 = 4
Therefore, the number of ways one component of each type can be selected is given by 5 x 4 x 3 x 4 = 240 ways
Part (b):
In how many ways can components be selected if both the
receiver and the compact disc player are to be Sony?
The number of ways of selecting a Sony receiver is 1
The number of ways of selecting a Sony CD player is 1
The number of ways one type of speakers will be selected is given by 3C1 = 3
The number of ways one type of cassette will be selected is given by 4C1 = 4
Therefore, the number of ways components can be selected if both the
receiver and the compact disc player are to be Sony is given by 1 x 1 x 3 x 4 = 12
Part (c)
In how many ways can components be selected if none of them are Sony?
The number of ways one type of receiver that is not Sony will be selected is given by 4C1 = 4
The number of ways one type of CD player that is not Sony will be selected is given by 3C1 = 3
The number of ways one type of speakers that is not Sony will be selected is given by 3C1 = 3
The number of ways one type of cassette that is not Sony will be selected is given by 3C1 = 3
Therefore, the number of ways that components can be selected if none of them are Sony is given by 4 x 3 x 3 x 3 = 108
Part (d):
In how
many ways can a selection be made if at least one Sony component is
to be included?
The total number of ways of selecting one component of each type is 240
The number of ways that components can be selected if none of them are Sony is 108
Therefore, the number of ways of selecting at least one Sony component is given by 240 - 108 = 132
Part (e):
If someone flips switches on the selection in a
completely random fashion, what is the probability that the system
selected contains at least one Sony component?
The total number of ways of selecting one component of each type is 240
The number of ways of selecting at least one Sony component is 132
Therefore, the probability that a system
selected at random contains at least one Sony component is given by 132 / 240 = 0.55
Part (f):
If someone flips switches on the selection in a
completely random fashion, what is the probability that the system
selected contains exactly one Sony
component? (Round your answer to three decimal places.)
The number of ways of selecting only a Sony receiver is given by 1 x 3 x 3 x 3 = 27
The number of ways of selecting only a Sony CD player is given by 4 x 1 x 3 x 3 = 36
The number of ways of selecting only a Sony cassette is given by 4 x 3 x 3 x 1 = 36
Thus, the number of ways of selecting exactly one Sony component is given by 27 + 36 + 36 = 99
Therefore, the probability that a system
selected at random contains exactly one Sony
component is given by 99 / 240 = 0.413
