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andriy [413]
3 years ago
12

The number of swings in use on average is.

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
7 0

Answer:

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Step-by-step explanation:

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How do you work this out?
Katarina [22]
Because ABCD is a rectangle, the length of CD is 12 cm.

We need to determine the length of DE.  If we can do that, then the sum of the lengths of CD and DE represents the unknown:  the length of CE.

To find the length of CE, we have to "solve" the upper triangle.

Here's an outline of what to do:

1.  Show that BC=AD and find the length.
2.  Note that angle CAD is 60 degrees.  Why?
3.  Note that angle EAD is 30 degrees.  Why?
4.  Find the length of ED
5.  Add ED and DC, that is, ED + 12 cm.  This is your answer.

Please ask questions if need be.
5 0
3 years 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
Reducing Fractions<br> 30/90
fgiga [73]

Answer: 1/3

<u>Divide</u>

30/90÷30/30=1/3

Since we are simplifying fractions we divide the numerator and the denominator by a number the fraction can go into.

We could use 10 then divide by 3. You can also just divide by 30 and get the answer.

Let's try dividing by 10 then 3!

30/90÷10/10=3/9

3/9÷3/3=1/3

As you can see we still get 1/3 when we divide by 3. Even tho you have to divide twice you still get 1/3. That's all that matters.

3 0
3 years ago
It is believed that 36% of the US population has never been married, 32% are divorced, 27% are married, and 5% are widowed. You
Katena32 [7]

Answer: the smallest number of people required for the sample to meet the conditions for performing inference is 100

Step-by-step explanation:

Given that;

36% of US population has never been married

32% are divorced

27% are married

5% are widowed

Taking a simple random sample of individuals to test this claim;

we need expected count in each cell to be at least 5, here the smallest proportion is 5% = 0.05

so we only need to satisfy condition for its expected count;

n × 0.05 ≥ 5

n = 5 / 0.05 = 100

Therefore the smallest number of people required for the sample to meet the conditions for performing inference is 100

6 0
2 years ago
How do you find the area of the sector of the circle with a radius of 4in and a central angle θ of pi/3? Please explain procedur
Lena [83]

It is generally useful to use the formula. The procedure is to substitute the given values for the variables in the formula, then do the arithmetic.

... A = (1/2)r²·θ . . . . r is the radius, θ is the central angle in radians

Put the numbers in ...

... A = (1/2)(4 in)²·(π/3)

... A = 8π/3 in² ≈ 8.37758 in²

6 0
3 years ago
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