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3 years ago

Find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°

Mathematics

1 answer:

kati45 [8]3 years ago

6 0

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

(2a-32)°+(3a+22)° +x = 180°
(5a- 10)° +x= 180°
x= (180+10-5a)°
x= (190-5a)°

The third angle is: (190-5a)°

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Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0.80.80

wel

Answer:

0.99 probability that at least one trip will last less than an hour

Step-by-step explanation:

For each time that the machine is used, there are only two possible outcomes. Either it lasts more than an hour, or it does not. The probability of a trip lasting more than an hour is independent of other trips. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

0.8 probability of lasting more than one hour.

So $p = 0.8$

20 trips

So $n = 20$

Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour?

Either all the trips last for more than an hour, or at least one does not. The sum of the probabilities of these outcomes is decimal 1. So

$P(X = 20) + P(X < 20) = 1$

We want P(X < 20). So

$P(X < 20) = 1 - P(X = 20)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 20) = C_{20,20}.(0.8)^{20}.(0.2)^{0} = 0.0115$

$P(X < 20) = 1 - P(X = 20) = 1 - 0.0115 = 0.9885$

0.9885 probability that at least one trip will last less than an hour

Rouding to the nearest hundreth.

0.99 probability that at least one trip will last less than an hour

3 0

3 years ago

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Which expression is equivalent to 3(6m) + m? A. 19m B. 21m C. 7m + 3 D. 18m + 6m²

Lelechka [254]

Answer:

3(6m)+m=18m+m=19m so your answer would be A. 19m

Step-by-step explanation:

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3 years ago

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A group of 4 friends bought movie tickets. Each person also bought a large popcorn for $7.50. If they spent a total of $72, how

Andrew [12]

Answer:

$16.125 but i don't know if you have to round

Step-by-step explanation:

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3 years ago

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PLEASE I NEED HELP ASAP ITS ALMOST DUE

Liula [17]

I would THINK it’s 9???? I’m not sure

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3 years ago

Give the difinition, formula, and example problem of permutation, combination & probability... please asap huhu I'll mark yo

SSSSS [86.1K]

Answer:

Answer:

Permutation:

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Formula:

$nPr=\frac{n!}{(n-r)!}$

Example:

Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.

Combination:

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.

Formula:

$nCr=\frac{n!}{r!(n-r)!}$

Example:

Combination: Picking a team of 3 people from a group of 10.

C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Formula:

Conditional Probability P(A | B) = P(A∩B) / P(B)

Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)

Example:

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.

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Find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°​

Find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°