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3 years ago

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.

Mathematics

1 answer:

tankabanditka [31]3 years ago

8 0

Answer:

lateral area ≈ 668 m²

surface area ≈ 740 m²

Step-by-step explanation:

The lateral area of a triangular prism = perimeter of the base × height of the prism

lateral area = ph

where

p = perimeter of the base

h = height or altitude

Base edges are 8m , 9m and 12.04m and height is 23 m.

lateral area = ph

lateral area = (8 + 9 + 12.04) × 23

lateral area = 29.04 × 23

lateral area = 667.92 m²

lateral area ≈ 668 m²

Surface area

surface area = lateral area + 2B

where

B = area of it triangular bases

surface area = lateral area + 2B

surface area = 667.92 + 2(1/2 × base × height)

surface area = 667.92 + 2(1/2 × 8 × 9)

surface area = 667.92 + 2(1/2 × 72)

surface area = 667.92 + 2(36)

surface area = 667.92 + 72

surface area = 739.92

surface area ≈ 740 m²

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If a < 0 then the graph opens_____

telo118 [61]

Answer:

down

Step-by-step explanation:

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4 0

3 years ago

Read 2 more answers

Number 8 only please

givi [52]

Answer:

Should be roughly 79.76% if I'm doing this right.

Step-by-step explanation:

Looking at the problem, you're given 3 things:

1) 6.8 million tonnes are recycled;

2) 6.8 million tonnes is 27% of the total household waste;

3) 20.1 million tonnes could be recycled.

Since they're asking for what percentage of total household waste could be recycled, you're looking at a multi-step cross multiplication problem.

It's not very difficult though, don't worry.

So I'm gonna start by telling you to just forget that the word "million" exists for the moment. You only need 6.8, 20.1, and 27%.

Setting up the first part of the problem requires you to convert 27% into a fraction. That's $\frac{27}{100}$ .

6.8 is 27% of some mysterious number that we need to figure out what percent of household waste could be recycled, so that'll be set up on the opposite side of the equal sign as the equivalent to 27.

So we're starting out with this: $\frac{6.8}{?} =\frac{27}{100}$

Since you're trying to initially find the total household waste, we're setting x as the variable to solve for.

$\frac{6.8}{x} =\frac{27}{100}$

Cross-multiplying** means you multiply the numerator of one side of the equal sign to the denominator of the other side of the equal sign, and vice versa (denominator of one side to numerator of other). So multiply 6.8 to 100, and 27 to x.

$680=27x$

Now that you have this, you have to isolate x. Divide both sides by 27 to do this.

$25.185185...=x$

I'm gonna round that for simplicity's sake, because 185 repeats.

$25.2=x$

So we have 25.2 million tonnes of total household waste. Great! Now we can find the percentage of household waste that could be recycled.

Since we have how much could be recycled and the total, we just need to solve for the percent this time. So this is what the set-up will look like:

$\frac{20.1}{25.2} =\frac{x}{100}$

x being the percent we're solving for.

Cross-multiply again:

$2010=25.2x$

Divide both sides by 25.2:

$79.761904761904...=x$

Then round for simplicity's sake:

$79.76=x$

And you get 79.76% of household waste could be recycled.

Hope this helped!

**Be careful with cross-multiplying when you get to higher level math though. Not every situation allows for cross-multiplying. In fact, you can only cross-multiply when there's an equal sign.

6 0

3 years ago

Can you help me with number 6? Confused abit Please

Sunny_sXe [5.5K]

You can see the three diagram attached. Each link is labeled with the probability: you have probability 1/6 that a six is rolled, and 5/6 that it is not rolled.

To answer the questions, find the path that brings you to the desired outcome, and multiply all the labels you meet.

First question:

To get three sixes, you have to choose the left path at each roll. The probability is always 1/6, so the answer is

$\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{6^3}$

Second question:

To get no sixes, you have to choose the right path at each roll. The probability is always 5/6, so the answer is

$\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} = \frac{5^3}{6^3}$

Third question:

To get exactly one six, it can either be the first, second or third roll.

In all cases, you have to choose the left path once and the right path twice: left-right-right mean that you get the six in the first roll, right-left-right means that you get the six in the second roll, right-right-left means that you get the six in the third roll.

In every case, the left turn has probability 1/6, and the right turn has probability 5/6. The probability of each combination is thus

$\frac{1}{6} \times \frac{5}{6} \times \frac{5}{6} = \frac{5^2}{6^3}$

And since there are three of these combinations, The answer is

$3\frac{5^2}{6^3}$

Fourth question:

Since the question suggests to use what we already achieved, let's do it: having at least one six is the complementary event of having no sixes at all. If an event has probability p, its complementary has probability 1-p. So, since the probability of no sixes is known, the probability of at least one six is

$1 - \frac{5^3}{6^3}$