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Alenkinab [10]
3 years ago
10

0 Xa The owner of a large electronic store building wants to install air-conditioning. The size of the air condicioner depends o

n the capacity of the building Below is a diagram with the dimensions of the building. The diagram is not drawn to scale. Notes canst out of a rectangular prism and a triangular prism Calculate the volume of the building ​
Mathematics
1 answer:
Softa [21]3 years ago
6 0

The volume of a shape is the amount of space in it.

<em>The volume of the building is </em>180m^3<em />

The given parameters are:

<u>Rectangular prism</u>

<u />Length = 3m; Width = 8m; Height = 5m<u />

<u />

<u>Triangular Prism</u>

<u />Base = 3m; Horizontal\ Height= 8m; Vertical\ Height = 5m<u />

<u />

<u />

The volume of the rectangular prism is:

<u />V_1 = Length \times Width \times Height<u />

<u />V_1 = 3m \times 8m \times 5m<u />

<u />V_1 = 120m^3<u />

<u />

<u />

The volume of the triangular prism is:

<u />V_2 = \frac 12 \times Base \times Horzontal \times Vertical\ Height<u />

<u />V_2 = \frac 12 \times 3m \times 8m \times 5m<u />

<u />V_2 =60m^3<u />

<u />

So, the volume of the building is:

V = V_1 + V_2

V = 120m^3 + 60m^3

V = 180m^3

Hence, the volume of the building is 180m^3

Read more about volumes at:

brainly.com/question/15861918

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3 years ago
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Two factories I and II produce phones for brand ABC. Factory I produces 60% of all ABC phones, and factory II produces 40%. 10%
denpristay [2]

Answer:

0.3721 or 37.21%

Step-by-step explanation:

P(I) = 0.60; P(II) = 0.40;

P(not defective I) = 0.90; P(not defective II) = 0.80

The probability that the phone came from factory II, given that is not defective, is determined by the probability of a phone from factory II not being defective divided by the probability of a phone not being defective.

P(II|not) = \frac{P(II)*P(not_{II})}{P(II)*P(not_{II})+P(I)*P(not_{I})}\\P(II|not) = \frac{0.40*0.80}{0.40*0.80+0.60*0.90}\\ P(II|not) =0.3721 = 37.21\%

The probability is 0.3721 or 37.21%.

4 0
3 years ago
Which of the following is an equation of a line perpendicular to the equation
arlik [135]
B is the answer ma brutha
5 0
2 years ago
Which of the following functions are homomorphisms?
Vikentia [17]
Part A:

Given f:Z \rightarrow Z, defined by f(x)=-x

f(x+y)=-(x+y)=-x-y \\  \\ f(x)+f(y)=-x+(-y)=-x-y

but

f(xy)=-xy \\  \\ f(x)\cdot f(y)=-x\cdot-y=xy

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.



Part B:

Given f:Z_2 \rightarrow Z_2, defined by f(x)=-x

Note that in Z_2, -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular f(x)=x

f(x+y)=x+y \\  \\ f(x)+f(y)=x+y

and

f(xy)=xy \\  \\ f(x)\cdot f(y)=xy

Therefore, the function is a homomorphism.



Part C:

Given g:Q\rightarrow Q, defined by g(x)= \frac{1}{x^2+1}

g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1}  \\  \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1}

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.



Part D:

Given h:R\rightarrow M(R), defined by h(a)=  \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)

h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\  \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)

but

h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\  \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.



Part E:

Given f:Z_{12}\rightarrow Z_4, defined by \left([x_{12}]\right)=[x_4], where [u_n] denotes the lass of the integer u in Z_n.

Then, for any [a_{12}],[b_{12}]\in Z_{12}, we have

f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\  \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)

and

f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)

Therefore, the function is a homomorphism.
7 0
3 years ago
In the adjoining figure, the parallel lines are marked by arrow lines. The value of angle 1 is:
dlinn [17]

Answer:

20°

Step-by-step explanation:

40°, 70° and 90° are the measures of the three angles of the quadrilateral.

Measure of fourth angle of the Quadrilateral

= 360° - (40° + 70° + 90°)

= 360° - 200°

= 160°

Measure of angle 1 will be equal to the measure of the linear pair angle of 160° as they are corresponding angles.

Thus,

m\angle 1 = 180\degree- 160\degree

\implies\huge\purple{\boxed{ m\angle 1 = 20\degree}}

Alternate method:

m\angle 1 = 180\degree- [360\degree-(40\degree+70\degree+90\degree)]

\implies m\angle 1 = 180\degree- [360\degree-200\degree]

\implies m\angle 1 = 180\degree- 160\degree

\implies m\angle 1 = 20\degree

6 0
2 years ago
Read 2 more answers
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