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3 years ago

Integrate sec x ( sec x + tan x ) dx

1 answer:

8 0

<span> by taking integral we get
integral sec(x) (tan(x)+sec(x)) dx
applying integral we get
sec(x) (tan(x)+sec(x)) gives sec^2(x)+tan(x) sec(x)
= integral (sec^2(x)+tan(x) sec(x)) dx Integrate the sum term by term
= integral sec^2(x) dx+ integral tan(x) sec(x) dx For the integrand tan(x) sec(x), now we will use substitution

substitute u = sec(x) and du = tan(x) sec(x) dx
= integral 1 du+ integral sec^2(x) dx The integral of sec^2(x) is tan(x)
= integral 1 du+tan(x) The integral of 1 is u
= u+tan(x)+constant
Substitute the value of u which is equal to
= sec(x):
so our conclusion is
:tan(x)+sec(x)+constant
hope this helps</span>

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A population has mean 187 and standard deviation 32. If a random sample of 64 observations is selected at random from this popul

Zina [86]

Answer:

11.51% probability that the sample average will be less than 182

Step-by-step explanation:

To solve this question, we have 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 187, \sigma = 32, n = 64, s = \frac{32}{\sqrt{64}} = 4$

What is the probability that the sample average will be less than 182

This is the pvalue of Z when X = 182. So

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

By the Central Limit Theorem

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

$Z = \frac{182 - 187}{4}$

$Z = -1.2$

$Z = -1.2$ has a pvalue of 0.1151

11.51% probability that the sample average will be less than 182

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3 years ago

Take away the parentheses using distributive property.<br> −2(3v − 2x -1)

Alecsey [184]

You have to multiply -2 to all of the numbers inside the parenthesis and you will have your answer. -6v+4x+2

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3 years ago

The owners of a large pet store have determined that 65\ee, percent of their customers own dogs. They select 151515 customers at

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Answer:

D is a binomial random variable with $p = 0.65, n = 15$

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they have dogs, or they do not. The probability of a customer having a dog is independent of any other customer. This means that D is a binomial random variable.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

65% of the customers have dogs:

This means that $p = 0.65$

15 customers:

This means that $n = 15$

What type of variable is D?

D is a binomial random variable with $p = 0.65, n = 15$

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3 years ago

Which graph represents exponential decay?

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Answer: the first graph

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3 years ago

Read 2 more answers

What is the length of a ramp whose rise is 10 feet and slope is 5/12

polet [3.4K]

Answer:

120 feet

Step-by-step explanation:

Length/height =second number in ratio (here's it is 12)

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Therefore length will be 120

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4 years ago