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saw5 [17]
3 years ago
9

Simplify sinø + cosø × cotø

Mathematics
1 answer:
insens350 [35]3 years ago
3 0
That would be 
                        cos x
sin x + cos x * --------
                        sin x
               
                        sin x
Mult sin x by ----------
                        sin x

to obtain 

(sin x)^2
------------
   sin x

and then add

(cos x)^2
-------------
   sin x

with the outcome being 

(sin x)^2 + (cos x)^2        1
--------------------------- = --------- = cos x (answer)
              sin x                sin x
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In science class, students are mixing water and a citric acid solution. The table shows how much water and acid solution two stu
rusak2 [61]

Answer:

the one with the most parts citric acid

Step-by-step explanation:

no tables were provided but if a cup is 3/4 water and 1/4 citric acid and the other is 1/4 water and 3/4 citric acid then it's the second one. Basically it the one with the most citric acid.

4 0
3 years ago
The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation
fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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.

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 = 197.5, \sigma = 8.3

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

Z = \frac{210.9 - 197.5}{8.3}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{196 - 197.5}{2.14}

Z = -0.7

Z = -0.7 has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

5 0
3 years ago
What are the answer to both of these. I am confused. Please Help. I will give Brainliest Answer.
Mumz [18]

Answer:

The First 1 is B. And the Second 1 is B. As well.

Step-by-step explanation:

8 0
3 years ago
Help ASAP plssssssssss
mr_godi [17]

Answer:

Length of three dimensions of the cube is

<u>6</u>cm.

What is the area of the base of a cube of sides 2.5m?

<u>37.5m²</u>

5 0
3 years ago
Alvin's age is two times Elga's age. The sum of their ages is 63. What is Elga's age?
lawyer [7]

Answer: Alvin = 42 yrs , Elga = 21 yrs

Step-by-step explanation:

Let Elga's age be x , and Alvin's age be y ,since Alvin is two times Elga's age , then

Alvin's age = 2x , that is

y = 2x ............... equation 1

The sum of their ages is 63 implies

x + y = 63 .............. equation 2

Solving the resulting linear equations by substitution method.

Substitute equation 1 into equation 2 , we have

x + 2x = 63

3x = 63

x = 63/3

x = 21

Therefore : Elga is 21 years old , then Alvin will be 21 x 2, which will be 42

8 0
3 years ago
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