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s344n2d4d5 [400]
2 years ago
15

If b=4 units and h=5 units, the area of the triangle is _____ units2.

Mathematics
1 answer:
mestny [16]2 years ago
5 0

Answer:

Step-by-step explanation:

Area = 1/2 b h

= 1/2 * 4 * 5

= 10 unit^2.

You might be interested in
A hotel charges a $10,000 annual fee plus an additional $200 for each night you stay there. What is the average cost per night i
Anton [14]

Answer:

\$400

Step-by-step explanation:

GIVEN: A hotel charges a \$10000 annual fee plus an additional \$200 for each night you stay there.

TO FIND: average cost per night if you stay at the hotel for 50 nights.

SOLUTION:

Annual fee charged by hotel =\$10000

amount charged each night we stay there =\$200

Total number of nights we stay =50

Total amount paid for 50 nights=50\times\$200

                                                   =\$10000

Total amount paid =\text{annual fee}+\text{total amount paid for 50 nights}

                              =\$10000+\$10000

                              =\$20000

average cost per night =\frac{\text{total amount paid}}{\text{total number of nights of stay}}

putting values,

average cost per night =\frac{20000}{50}

                                      =\$400

Hence average cost per night if we stay at hotel for 50 days is \$400

6 0
3 years ago
PLZ HELP AND EXPLAIN !! Arron borrowed $200 from his cousin. He promised to repay the loan in 2 years at a simple annual interes
Dmitriy789 [7]
The first thing you have to do is know the equation. The equation is a(1+p)^t.
a= the amount of money p= the percent represented as a decimal and t=time ( the t is raised as an exponent)
so, in this case, it is represented as 200(1+0.05)^2\
200(1.05)^2
200(1.1025)
220.5 That is how much extra he would owe in interest fee's

5 0
3 years ago
What are all the subsets of {5,9,13}
Naddika [18.5K]
All The Subsets

For theset {a,b,c}:

<span>The empty set {} is a subset of {a,b,c}And these are subsets: {a}, {b} and {c}And these are also subsets: {a,b}, {a,c} and {b,c}And {a,b,c} is a subset of {a,b,c}</span>

And when we list all the subsets of S={a,b,c} we get the Power Set of {a,b,c}:

P(S) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} }

Think of it as all the different ways we can select the items (the order of the items doesn't matter), including selecting none, or all.

Example: The shop has banana, chocolate and lemon ice cream.

 

What do you order?

<span>Nothing at all: {}Or maybe just banana: {banana}. Or just {chocolate} or just {lemon}Or two together: {banana,chocolate} or {banana,lemon} or {chocolate,lemon}Or all three! {banana, chocolate,lemon}</span>

Question: if the shop also has strawberry flavor what are your options? Solution later.

How Many Subsets

Easy! If the original set has n members, then the Power Set will have <span>2n</span> members

Example: in the {a,b,c} example above, there are three members (a,b and c).

So, the Power Set should have 23 = 8, which it does!

Notation

The number of members of a set is often written as |S|, so when S has n members we can write:

|P(S)| = 2n

Example: for the set S={1,2,3,4,5} how many members will the power set have?

Well, S has 5 members, so:

|P(S)| = 2n = 25 = 32

You will see in a minute why the number of members is a power of 2

It's Binary!

And here is the most amazing thing. To create the Power Set, write down the sequence of binary numbers (using n digits), and then let "1" mean "put the matching member into this subset".

So "101" is replaced by 1 a, 0 b and 1 c to get us {a,c}

Like this:

<span><span> abcSubset</span><span>0000{ }</span><span>1001{c}</span><span>2010{b}</span><span>3011{b,c}</span><span>4100{a}</span><span>5101{a,c}</span><span>6110{a,b}</span><span>7111{a,b,c}</span></span>

Well, they are not in a pretty order, but they are all there.

Another Example<span>Let's eat! We have four flavors of ice cream: banana, chocolate, lemon, and strawberry. How many different ways can we have them?Let's use letters for the flavors: {b, c, l, s}. Example selections include:<span>{} (nothing, you are on a diet){b, c, l, s} (every flavor){b, c} (banana and chocolate are good together)etc</span></span>Let's make the table using "binary":<span><span> bclsSubset</span><span>00000{}</span><span>10001{s}</span><span>20010{l}</span><span>30011{l,s}</span><span>...... etc ..... etc ...</span><span>121100{b,c}</span><span>131101{b,c,s}</span><span>141110{b,c,l}</span><span>151111{b,c,l,s}</span></span>

And the result is (more neatly arranged):

P = { {}, {b}, {c}, {l}, {s}, {b,c}, {b,l}, {b,s}, {c,l}, {c,s}, {l,s}, {b,c,l}, {b,c,s}, 
{b,l,s}, {c,l,s}, {b,c,l,s} }


<span><span>SymmetryIn the table above, did you notice that the first subset is empty and the last has every member?But did you also notice that the second subset has "s", and the second last subset has everything except "s"?</span><span>  </span><span>In fact when we mirror that table about the middle we see there is a kind of symmetry.This is because the binary numbers (that we used to help us get all those combinations) have a beautiful and elegant pattern.</span></span>A Prime Example

The Power Set can be useful in unexpected areas.

I wanted to find all factors (not just the prime factors, but all factors) of a number.

I could test all possible numbers: I could check 2, 3, 4, 5, 6, 7, etc...

That took a long time for large numbers.

But could I try to combine the prime factors?

Let me see, the prime factors of 510 are 2×3×5×17 (using prime factor tool).

So, all the factors of 510 are:

<span>2, 3, 5 and 17,2×3, 2×5 and 2×17 as well, and2×3×5 and 2×3×17 and ..... aha! Just like ice cream I needed a Power Set!</span>

And this is what I got:

<span><span> 2,3,5,17SubsetFactors of 510</span><span>00000{ }1</span><span>10001{17}17</span><span>20010{5}5</span><span>30011{5,17}5 × 17 = 85</span><span>40100{3}3</span><span>50101{3,17}3 × 17 = 51</span><span> ... etc ...... etc ...... etc ...</span><span>151111{2,3,5,17}2 × 3 × 5 × 17 = 510</span></span>


And the result? The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255 and 510 (and −1, −2, −3, etc as well). See the All Factors Tool.

Automated

I couldn't resist making Power Sets available to you in an automated way.

So, when you need a power set, try Power Set Maker.

6 0
3 years ago
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geniusboy [140]

-1, maybe or maybe not this is my first time doing this

7 0
3 years ago
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
OverLord2011 [107]

Answer:

Here you go, I think

Step-by-step explanation:

5 0
3 years ago
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