If sin y° = 9 divided by c. and tan y° = 9 divided by d. ,what is the value of cos y°?

Mathematics

2 answers:

dybincka [34]3 years ago

5 0

Answer: The fraction d/c

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Explanation:

Check out the attached image. I've labeled the three sides of the triangle based on the reference angle y. The opposite side is 9, the adjacent is d, and the hypotenuse is c.

How did I get those values? Well

sine = opposite/hypotenuse = 9/c

tangent = opposite/adjacent = 9/d

matching terms we see that opposite = 9, adjacent = d, hypotenuse = c

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Now we compute the ratio for cosine

cosine = adjacent/hypotenuse

cos(y) = d/c

We don't have enough info to know the numeric value of d/c

Nady [450]3 years ago

4 0

$\bf sin(y)=\cfrac{\stackrel{opposite}{9}}{\stackrel{hypotenuse}{c}}\qquad \qquad \qquad tan(y)=\cfrac{\stackrel{opposite}{9}}{\stackrel{adjacent}{d}} \\\\\\ cos(y)=\cfrac{\stackrel{adjacent}{d}}{\stackrel{hypotenuse}{c}}$

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Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

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.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

$P(X < 4) + P(X \geq 4) = 1$