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prisoha [69]
3 years ago
6

Equation with angle addition can someone please answer please help

Mathematics
1 answer:
marishachu [46]3 years ago
8 0

Answer:

57°

Step-by-step explanation:

We can see that LOM is MON + LON so we can set up an equation to find the value of x then substitute that back into MON to find the value of that angle.

→ In equations its important to keep both sides equal and do operations to both sides and not one because then if you do an operation to only one side then you have changed the equation so it's important to do operations on both sides and that's an important rule to bare in mind.

2x + 33 + 3x + 20 = 113

→ Simplify

5x + 53 = 113

→ Minus 53 from both sides to isolate 5x

5x = 60

→ Divide both sides by 5 to isolate x

x = 12

But we are not finished, we have only found the value of x not the value of MON as we were asked so we have to substitute x back into the expression to find the value of MON

2x + 33

→ Substitute x = 12 back into the expression

2 × 12 + 33

→ Simplify

24 + 33 = 57

The value of MON is 57°

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andreev551 [17]

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<u>Step-by-Step Explanation:</u>

Pythagorean Theorem is: a² + b² = c²  , <em>where "c" is the hypotenuse</em>

5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}

Note: (15)² + (3√11)² = hypotenuse²   →   hypotenuse = 18

6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}

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7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}

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Answer:

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Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:

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\mu_{\bar X} = 61

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So then is appropiate use the normal distribution to find the probabilities for \bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean \bar X is also normal and given by:

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