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3 years ago

Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

Mathematics

1 answer:

makkiz [27]3 years ago

8 0

Answer:

$390ft^2\\$

Step-by-step explanation:

Ok so we have 2 (congruent) triangles and 3 rectangles.

Your main approach to this problem should be to find the area of each of the faces and adding them up to get to your final answer. Your question makes a point of including the correct unit in your answer. Since this is surface area, the unit would be $ft^2$

Now let's start:

First, I am going to start with finding the area of the rectangles.

$12\cdot11=132\\13\cdot11=143\\5\cdot11=55\\\\55+143+132=330$

Alright, next lets move on to the triangles.

They are both the same, if you notice. So find one and double it.

$12\cdot5=60\\\frac{60}{2}=30\\30\cdot2=60$

now lets add em all

330+60

= 390 and thats your final answer, dont forget to include the unit, ft^2

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shtirl [24]

The answer is 1. Yeah

5 0

3 years ago

Read 2 more answers

Learning Thoery In a learning theory project, the proportion P of correct responses after n trials can be modeled by p = 0.83/(1

elena-s [515]

Answer:

a) $P(n=3) = \frac{0.83}{1+e^{-0.2(3)}}= \frac{0.83}{1+ e^{-0.6}} = 0.536$

b) $P(n=7) = \frac{0.83}{1+e^{-0.2(7)}}= \frac{0.83}{1+ e^{-1.4}} = 0.666$

c) $0.75 =\frac{0.83}{1+e^{-0.2n}}$

$1+ e^{-0.2n} = \frac{0.83}{0.75}= \frac{83}{75}$

$e^{-0.2n} = \frac{83}{75}-1= \frac{8}{75}$

$ln e^{-0.2n} = ln (\frac{8}{75})$

$-0.2 n = ln(\frac{8}{75})$

And then if we solve for t we got:

$n = \frac{ln(\frac{8}{75})}{-0.2} = 11.19 trials$

d) If we find the limit when n tend to infinity for the function we have this:

$lim_{n \to \infty} \frac{0.83}{1+e^{-0.2t}} = 0.83$

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

Step-by-step explanation:

For this case we have the following expression for the proportion of correct responses after n trials:

$P(n) = \frac{0.83}{1+e^{-0.2t}}$

Part a

For this case we just need to replace the value of n=3 in order to see what we got:

$P(n=3) = \frac{0.83}{1+e^{-0.2(3)}}= \frac{0.83}{1+ e^{-0.6}} = 0.536$

So the number of correct reponses after 3 trials is approximately 0.536.

Part b

For this case we just need to replace the value of n=7 in order to see what we got:

$P(n=7) = \frac{0.83}{1+e^{-0.2(7)}}= \frac{0.83}{1+ e^{-1.4}} = 0.666$

So the number of correct responses after 7 weeks is approximately 0.666.

Part c

For this case we want to solve the following equation:

$0.75 =\frac{0.83}{1+e^{-0.2n}}$

And we can rewrite this expression like this:

$1+ e^{-0.2n} = \frac{0.83}{0.75}= \frac{83}{75}$

$e^{-0.2n} = \frac{83}{75}-1= \frac{8}{75}$

Now we can apply natural log on both sides and we got:

$ln e^{-0.2n} = ln (\frac{8}{75})$

$-0.2 n = ln(\frac{8}{75})$

And then if we solve for t we got:

$n = \frac{ln(\frac{8}{75})}{-0.2} = 11.19 trials$

And we can see this on the plot attached.

Part d

If we find the limit when n tend to infinity for the function we have this:

$lim_{n \to \infty} \frac{0.83}{1+e^{-0.2t}} = 0.83$

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

5 0

3 years ago

What are the coordinates of the vertex of the graph of

vesna_86 [32]

The vertex is (3,0). The 3 inside the abs val bar tells you the x value of the vertex is 3. No number outside the abs value bar is a +0 which is the y value of the vertex.

4 0

3 years ago

What is the point slope equation of a line with slope -5 that contains the point (6,3)

ehidna [41]

Step-by-step explanation:

Given

Slope (m) = -5

Point

(x1 , y1) = ( 6 , 3)

So the equation is

y - y1 = m ( x - x1)

y - 3 = -5 ( x - 6)

y - 3 = -5x +30

5x + y = 30 + 3

5x + y = 33

5x + y - 33= 0

Which is the required equation.

Hope it will help you :)

3 0

3 years ago

Jason begins at the start of a path and rides his bike 11 12 miles on the path. The path is 12 14 miles long. Enter the distance

nikitadnepr [17]

Answer:

Number of miles remaining for Jason to reach end of the path = 3/4 miles

Step-by-step explanation:

Total distance of the path = 12 1/4 miles

Distance reached by Jason's bike on the path = 11 1/2 miles

Enter the distance, in miles, Jason must ride to reach the end of the path.

Number of miles remaining for Jason to reach end of the path = Total distance of the path - Distance reached by Jason's bike on the path

= 12 1/4 miles - 11 1/2 miles

= 49/4 - 23/2

= (49-46) / 4

= 3/4 miles

Number of miles remaining for Jason to reach end of the path = 3/4 miles

6 0

3 years ago