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Mrrafil [7]
3 years ago
13

Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°

Mathematics
2 answers:
bezimeni [28]3 years ago
7 0
The answer is cos 67°.
VARVARA [1.3K]3 years ago
6 0

Answer:

<h3>cos 112° cos 45° + sin 112° sin 45° = cos(67)°</h3>

Step-by-step explanation:

Given trigonometric expression

cos 112° cos 45° + sin 112° sin 45°

We know, the trigonometric identity

<em>cos (A-B) = cos A cos B + sin A sin B.</em>

On comparing cos 112° cos 45° + sin 112° sin 45° and cos A cos B + sin A sin B, we can see that A= 112° and B = 45°.

Plugging value A= 112° and B = 45° in cos (A-B), we get

cos ( 112- 45) = cos(67)°

<h3>Therefore, cos 112° cos 45° + sin 112° sin 45° = cos(67)°</h3>
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Step-by-step explanation:

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If it 8 inch candle burns at 7/10 inch per hour and a 6 inch candle Burns at 1/5 inch per hour after how many hours would both c
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(1 point) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected p
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Answer:

a)

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

b) P(4

Step-by-step explanation:

For this case we have defined the cumulative distribution function like this:

F(X) = 0, x

F(X) = 0.4, 1 \leq x

F(X) = 0.6, 3 \leq x

F(X) = 0.8, 5 \leq x

F(X) = 1, x \geq 7

And we know that the general definition for the distribution function is given by:

F(x) = P(X \leq x) = \sum_{i\leq k} f(i)

Where f represent the density function.

Part a

For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

f(1) = P(X=1) = P(X \leq 1) - P(X=0) = F(1) -F(0) = 0.4-0=0.4

f(2) = P(X=2) = P(X \leq 2) - P(X=0)- P(X=1) = F(2) -F(1) = 0.4-0.4=0

f(3) = P(X=3) = P(X \leq 3) - P(X=0)- P(X=1) -P(X=2) = F(3) -F(2) = 0.6-0.4=0.2

f(4) = P(X=4) = P(X \leq 4) - P(X=0)- P(X=1) -P(X=2)-P(X=3) = F(4) -F(3) = 0.6-0.6=0

f(5) = P(X=5) = P(X \leq 5) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4) = F(5) -F(4) = 0.8-0.6=0.2

f(6) = P(X=6) = P(X \leq 6) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5) = F(6) -F(5) = 0.8-0.8=0

f(7) = P(X=7) = P(X \leq 7) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5)-P(X=6) = F(7) -F(6) = 1-0.8=0.2

And for any value higher than 7 we have that:

x_i \in [8,9,10,...]

f(x_i) = F(X_i) -F(X_i -1) = 1-1=0

So then we have our density function defined like this:

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

Part b

For this case we want to find this probability P(4

And since the random variable is discrete we can write this like that:

P(4

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Step-by-step explanation:

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