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2 years ago

Please help photos for my math

Mathematics

1 answer:

Talja [164]2 years ago

8 0

Answer:

1. Surface Area = 122 Volume = 84

2. Surface Area = 1632 Volume = 2880

3. Surface area = 168 Volume = 144

4. Volume = 1350 $\pi$

Step-by-step explanation:

1. This is a rectangular prism. To find the surface area it is the same thing. Find the area of all sides and add them together. Because this is a rectangular prism most of the sides are equal so we will only need to find the area of three sides. To find the area of the right side, just do 4*3=12. That would be the same for the opposite side. Then to find the front side, do 7*4= 28. That would also be the same for the opposite side. Then to find the top side, do 7*3= 21. That is the same for the bottom side. Add them all together and you will get your answer. 28+28+21+21+12+12 = 122.

To find the volume of a rectangular prism the formula is V = l*w*h.

Plug in: V = 7*3*4 and then you will get 84.

2. This is a triangular prism. First find the area of the the triangular surface by multiplying the base x height and dividing by 2. (16*12)/2 = 96. That is the same for the opposite side. Then find the area of the bottom rectangular surface. 12*30 = 360. Then find the area of the back rectangular surface. 16*30 = 480. Then find the area of the final base rectangle. 30*20 = 600. Add them together and you will get 1632. Basically, find the area of all sides and then add them together.

To find volume the formula is, V = (1/2)a*c*h

Fill that in: V = (1/2)16*12*30 and then you will get 2880.

3. This is a trapezoidal prism. To find the surface area you would find the area of all sides then add them together. To find the are of a trapezoid, the formula is: A = $\frac{a+b}{2}$ h

Fill that in: A = $\frac{4+12}{2}$ (6) and then you will get 48.

That is the same for the opposite side. Then you need to find the area of the rectangular side of the trapezoidal prism. 3*4= 12. This is also the same as the opposite side. The bottom side is 12*3= 36. The top side is 3*4= 12.

Add all of them together and you get 168.

1/2(4+12)*6

To find volume, V = $\frac{1}{2}$ h(b₁+b₂)h.

Fill in: V = $\frac{1}{2}$ 6(12+4)3 and then you will get 144.

4. This is a cylinder. The formula to find the volume is A= $\pi$ r²h. Because you are leaving the answer in terms of pi, do not multiply pi into the equation.

So you would do r²h. 15² = 225. 225*6= 1350. So your answer would be 1350 $\pi$ .

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P(-2<z<10)=0.7357-0.0228=0.7129

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So, the probability that the response time is less than 5 minutes is 0.0228

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3 years ago

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1 year ago

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Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

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So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

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Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$

P(1,2,0.16)=0.2688

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0.0256 + 0.2688 = 0.2944

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