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Fiesta28 [93]
3 years ago
15

The probability P of choosing an object at random from a group of objects is found by the fraction P(event) = Number of favorabl

e outcomes Total number of outcomes . Suppose the angle measures 30°, 60°, 120°, 150° are written on slips of paper. You choose two slips of paper at random. What is the probability that the measures you choose are complementary? The probability of choosing complementary measures is
Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

Answer:

P(c)  = 0,0833     or      P(c)  =  8.33 %

Step-by-step explanation:

Comlementary angles a thse which sum s 90⁰. xamles of complementay angles ae:

75⁰ and 15⁰

80⁰ and 10⁰

5⁰  and 85⁰

and s forth

From the group of given angles:

30⁰ ,  60⁰,  120⁰ , 150⁰

only the couple   30⁰ ,  60⁰ meet the request, that means are complementary (the sum is 90⁰).

So we only have one chance of chossing such a couple. The number of favorable outcomes is 1 )

Now we have 4 slips of paper (that means 4 elements, and the quantity of different pairs we can get combining these 4 elements is given by the combination of four (4) elements in group of two. That is:

C₄,₂  =  4! /  ( 4 - 2 )!     ⇒   C₄,₂  = 4*3*2*1 / 2*1    ⇒  C₄,₂  = 4*3  

C₄,₂  = 12  (Total number of outcomes)

Then the probability of chossing two slips of paper that the measure are complementary is:

P(c)  =  1 / 12       ⇒  P(c)  = 0,0833       ⇒     P(c)  =  8.33 %

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Which number produces a rational number when added to 0.5
Sladkaya [172]

Any number that you can completely write down on paper using digits ... and a fraction bar or decimal point if necessary ... is a rational number.  If you add it to 0.5, then the sum is another rational number.

5 0
3 years ago
Here are some values of sequence Q. Write a recursive definition for the sequence.
Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0
3 years ago
On Tuesday a local hamburger shop sold a combined total of 237 hamburgers and cheeseburgers. The number of cheeseburgers sold wa
AlekseyPX
Answer 79

Method trial and error until 158 cheeseburger and 79 hamburger
7 0
3 years ago
How do I solve this? I know it's easy but I don't understand clearly​
faltersainse [42]

The answer is r = p/2n - x/n

8 0
1 year ago
Haley draws one card from a standard deck of 52 playing cards. She draws one card, returns it to the deck, shuffles the deck, an
ipn [44]

Answer:

no

Step-by-step explanation:

because of the square she drawn

3 0
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