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3 years ago

In right triangle ABC, m B Em C. Let sin B = r and cos B = s.

Mathematics

1 answer:

tatyana61 [14]3 years ago

6 0

The expression that represents the value of sin C - cos C is s-r

From the triangle ABC, since sin B = r and cos B = s.=, hence;

Opposite side= r
Adjacent side = s
Hypotenuse = 1

If m<C is the reference angle, then;

Opposite side= s

Adjacent side = r

Hypotenuse = 1

Sin C = s and cos C = r

Hence the expression that represents the value of sin C - cos C is s-r

Learn more on trigonometry here: brainly.com/question/20519838

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The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5.

Natasha_Volkova [10]

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If $Z \leq -2$ or $Z \geq 2$ , the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1$

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{19 - 22}{1}$

$Z = -3$

$Z = -3 \leq -2$ , so yes, the sample mean being less than 19 days would be considered an unusual outcome.

7 0

3 years ago

F(x)=(x-2)-5 what is the transformation

Grace [21]

Down 5, right 2

If it's within the parentheses with the x, then it moves left/right. left if +, right if -

If it's outside the parentheses, you go up and down. up if +, down if -

5 0

3 years ago

1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26

statuscvo [17]

Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

Part A

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

Part B

The graph's function would be in the form of $y=acos(bx+c)+d$ where $a$ is the amplitude, $\frac{2\pi}{b}$ is the period, $-\frac{c}{b}$ is the phase/horizontal shift, and $d$ is the average/midline.

We already know our amplitude of $a=3$ from part A.

Since our period is given to us as 26 seconds, then we can use the equation $\frac{2\pi}{b}=26$ to find $b$ , which happens to be $b=\frac{\pi}{13}$ .

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity $sin(x)=cos(x-\frac{\pi}{2})$ which shifts the cosine graph $\frac{\pi}{2}$ units to the right. This means that $c=-\frac{\pi}{2}$ , making our phase shift $-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5$ , or 6.5 feet to the right

Our average/midline would be $d=12$ as given as the average height by the problem.

Therefore, the function is $f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12$

Part C

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

5 0

2 years ago

Read 2 more answers

HELP I WILL GIVE BRAINLIEST!

Hatshy [7]

Answer:

C. 8.1 Inches

Step-by-step explanation:

Take 100 Ib. and multiply it by 0.9. You get 90 lb. Now referring to the fraction rule, do the same to the "denominator": 9 In. x 0.9, and you get 8.1 Inches.

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3 years ago

Which store has the best deal?

ddd [48]

I believe it’s D. If it’s not I’m so sorry but D makes the most sense! <3

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3 years ago