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3 years ago

Find the value of cos P rounded to the nearest hundredth, if necessary.

Mathematics

2 answers:

Lemur [1.5K]3 years ago

7 0

Answer:

$\cos P\approx 0.26$

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

In the given triangle, the adjacent side to angle P is marked as $\sqrt{7}$ and the hypotenuse of the triangle is $10$ . Therefore, we have:

$\cos P=\frac{\sqrt{7}}{10},\\\cos P=0.2645751311,\\\cos P \approx \boxed{0.26}$

Leni [432]3 years ago

3 0

Answer:

$\boxed {\boxed {\sf cos \ P \approx 0.26}}$

Step-by-step explanation:

There are three main trigonometric functions: sine, cosine, and tangent.

We are asked to find the cosine of angle P. The cosine is the ratio of the adjacent side to the hypotenuse.

$cos \theta = \frac{adjacent}{hypotenuse}$

In this triangle, the side measuring √7 is the adjacent side because it is next to angle P. The side measuring 10 is the hypotenuse because it is opposite the right angle.

adjacent = √7
hypotenuse= 10

$cos P= \frac{ \sqrt{7}}{10}$

$cos P=0.264575131106$

Round to the nearest hundredth. The 4 in the thousandths place to the right ( 0.264575131106) tells us to leave the 6 in the hundredths place.

$cos P \approx 0.26$

The cosine of angle P is approximately 0.26

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Answer:

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And replacing we got:

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Step-by-step explanation:

We have the following distribution

x 0 1 2 3 4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

$P(X=3) = 0.1$

Part b

We want this probability:

$P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

Part c

For this case we want this probability:

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Part d

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Part e

We can find the mean with this formula:

$E(X)= \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

Part f

We can find the second moment with this formula

$E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

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