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TiliK225 [7]
3 years ago
7

According to this diagram what is cos 16

Mathematics
2 answers:
myrzilka [38]3 years ago
8 0
<h2>Answer:</h2>

Option: B is the correct answer.

         B)    \dfrac{24}{25}

<h2>Step-by-step explanation:</h2>

We know that the cosine trignometric ratio corresponding to a angle theta(θ) is defined as the ratio of the adjacent side to the angle theta to the hypotenuse of the triangle containing θ as one of the angle.

By looking at the figure we observe that the triangle is a right angled triangle and the length of the side adjacent to angle 16° is: 24 and the hypotenuse of the triangle is: 25.

Hence, we get:

\cos 16=\dfrac{24}{25}

Ahat [919]3 years ago
5 0

Answer:

B: 24/25

Step-by-step explanation:

cos16° = adj/hyp

=24/25

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3 years ago
If 20% of the people in a community use the emergency room at a hospital in one year, find
Pie

Answer:

a) 87.91% probability that at most three used the emergency room

b) 20.13% probability that exactly three used the emergency room.

c) 3.28% probability that at least five used the emergency room​

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution 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.

Sample of 10 people:

This means that n = 10

20% of the people in a community use the emergency room at a hospital in one year

This means that p = 0.2

a) At most three used the emergency room

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684

P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020

P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791

87.91% probability that at most three used the emergency room

b) Exactly three used the emergency room

P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013

20.13% probability that exactly three used the emergency room.

c) At least five used the emergency room​

P(X \geq 5) = 1 - P(X < 5)

In which

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

From 0 to 3, we already have in a).

P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328

3.28% probability that at least five used the emergency room​

4 0
3 years ago
M∠1=(3x+8)°​, m∠2=(3x+18)°​, and m∠3=(7x+9)°. What is m∠​3?
deff fn [24]

Answer:

87.4°

Step-by-step explanation:

(3x + 8) + (3x + 18) + (7x + 9) = 180

3x + 8 + 3x + 18 + 7x + 9 = 180

add the common numbers

13x + 35 = 180

subtract 35

13x = 145

divide 13

x = 11.2

then plug it back in to m<3

7(11.2) + 9

78.4 + 9

= 87.4°

8 0
4 years ago
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