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Kobotan [32]
3 years ago
14

A new school banner is to be 4 1/2 feet wide by 7 1/4 feet long. what is the area? if a fabric for the banner costs $6 a square

foot , how much will the banner cost to make?
Mathematics
1 answer:
lilavasa [31]3 years ago
3 0

The area is 32 5/8 ft squared and It would cost$ 195.75


how to slove: you take the to fractions and mulitply them and get 32 5/8 for the area then you multiply 32 5/8 by 6 to find the price of the banner.

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A bag contains 25 balls 20 of which are blue what percentage of balls are not blue
Artist 52 [7]

Answer:

20%

Step-by-step explanation:

20/25 = blue

This means 5/25 of the balls in the bag are NOT blue

(25-20 = 5)

We need to convert 5/25 to a percentage

\dfrac{5}{25} = \dfrac{5\times4}{25\times4}=\dfrac{20}{100}

% = per cent

"per" means "out of"

"cent" means "one hundred"

so

20/100 = 20%

7 0
1 year ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
What is the product?<br><br> Enter your simplified answer in the box.<br> −14⋅(−611)−14⋅(−611)
allochka39001 [22]
The answer i got is 17108.
8 0
3 years ago
Read 2 more answers
Look at the figure. Classify the pair of angles: 2 and 7
FromTheMoon [43]
Consecutive exterior angles
7 0
3 years ago
Read 2 more answers
-8 ( y + 4 ) = 10y + 4
maks197457 [2]
Let's solve your equation step-by-step.<span><span>−<span>8<span>(<span>y+4</span>)</span></span></span>=<span><span>10y</span>+4

</span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>8<span>(<span>y+4</span>)</span></span></span>=<span><span>10y</span>+4

</span></span><span>Simplify: </span><span><span><span><span>(<span>−8</span>)</span><span>(y)</span></span>+<span><span>(<span>−8</span>)</span><span>(4)</span></span></span>=<span><span>10y</span>+4</span></span>(Distribute)<span><span><span><span>−<span>8y</span></span>+</span>−32</span>=<span><span>10y</span>+4</span></span><span><span><span>−<span>8y</span></span>−32</span>=<span><span>10y</span>+4

</span></span>Step 2: Subtract 10y from both sides.<span><span><span><span>−<span>8y</span></span>−32</span>−<span>10y</span></span>=<span><span><span>10y</span>+4</span>−<span>10y</span></span></span><span><span><span>−<span>18y</span></span>−32</span>=4

</span>Step 3: Add 32 to both sides.<span><span><span><span>−<span>18y</span></span>−32</span>+32</span>=<span>4+32</span></span><span><span>−<span>18y</span></span>=36

</span>Step 4: Divide both sides by -18.<span><span><span>−<span>18y</span></span><span>−18</span></span>=<span>36<span>−18</span></span></span><span>y=<span>−2

</span></span>Answer:<span>y=<span>−<span>2

Good luck mate :P
</span></span></span>
7 0
3 years ago
Read 2 more answers
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