1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stells [14]
3 years ago
10

Find the general indefinite integral. (use c for the constant of integration.) (7θ − 6 csc(θ) cot(θ)) dθ

Mathematics
1 answer:
KiRa [710]3 years ago
8 0
\int \! 70 - 6 \csc(\theta) \cot(\theta) \ \mathrm{d}\theta = \int \! 70 - 6 \cdot \frac{1}{\sin(\theta)} \cdot \frac{\cos(\theta)}{\sin(\theta)} \ \mathrm{d}\theta = \int \! 70 \ \mathrm{d}\theta - \int \! \frac{6 \cos(\theta)}{\sin^2(\theta)} \ \mathrm{d}\theta = 70 \theta + \frac{6}{\sin(\theta)} + C, \ C \in \mathbb{R}.
You might be interested in
Rahim purchases a new car for $24,000 and finances it with a 5-year simple interest loan at a rate of 3.75%. What are Rahim’s mo
worty [1.4K]

Answer:

900 if your its 3.75% of 24000

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Segment EF is a mid segment of triangle ABC. IF BC = 12 cm, what is the measure of segment EF?
Effectus [21]
The answer is 6 cm. The mid segment is half of BC
8 0
2 years ago
Read 2 more answers
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9
Eva8 [605]

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that \mu = 8.9, \sigma = 2.9

Sample of 37:

This means that n = 37, s = \frac{2.9}{\sqrt{37}}

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

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

By the Central Limit Theorem

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

Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}

Z = -0.53

Z = -0.53 has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

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

Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}

Z = -3.08

Z = -3.08 has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

7 0
2 years ago
Two fractions have a common denominators of 8. What could the two fractions be?
Anna71 [15]
4 and 8 would be the anwser because 4 x 2 = 8 and then 8x1=8
3 0
3 years ago
Read 2 more answers
The inverse of the linear function y=1/2x+3
GarryVolchara [31]
The inverse would be y=-1/2x+3 because the inverse is the negative of the function.  to make the function negative make the slope negative and keep the y-intercept.

I hope I've helped!
6 0
3 years ago
Other questions:
  • 3 kids where practicing their jumping Fred jumped 11/12 of a yard Lilly jumped 2/3 of Freds distance Tad jumped 4/5 of Lillys di
    8·1 answer
  • What is 15/50 written in percent
    6·1 answer
  • 604703.472883 rounded to nearest hundred
    15·2 answers
  • Evaluate numerical expression
    9·2 answers
  • Work out these questions without a calculator and showing all working out
    12·1 answer
  • A survey of us adults found that 11% think that congress is a good reflection of american views. you rnadomly select 35 us adult
    7·1 answer
  • Find the sum of 10x^2-10x-610x 2 −10x−6 and x+6x+6.
    6·1 answer
  • Bruce flipped a penny 5 times. It landed on heads 2 times and tails 3 times. If he flips the coin a 6th time, which of the follo
    15·1 answer
  • Y=7-3x. is it a linear or nonlinear
    15·2 answers
  • What’s life about and why are we here on this earth
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!