The long side of a rectangle is 3x+21 units, and it's area is 3x^2+33x+84. Find the width

You arrive at the airport at 1:50 pm and your flight leaves at 5:20 pm. How many MINUTES will you need to wait?

blsea [12.9K]

Answer:

you will need to wait 3 hours and 30 mins

Step-by-step explanation:

7 0

3 years ago

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The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A

Aloiza [94]

Answer:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

$\mu=37$ and $\sigma=28$ and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want to find this probability:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

4 0

3 years ago

10 points

Archy [21]

Answer:

16 books fit and theres .8 inches left

Step-by-step explanation:

16x2.2 = 35.2

36 - 35.2 + 0.8

7 0

3 years ago

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A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon. It was felt that gasoline price i

slava [35]

Answer:

alternative hypothesis : H₁ :

Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Alternative Hypothesis : H₁: μ < $1.298 a gallon

Step-by-step explanation:

Explanation:-

Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon

Population average μ= $1.298 a gallon

sample size 'n' = 37

Sample mean (x⁻) = $1.192 a gallon

Sample standard deviation 'S' = $0.0436

Null hypothesis :H₀ : μ = $1.298 a gallon

Alternative Hypothesis : μ < $1.298 a gallon

Degrees of freedom : ν = n-1= 37-1=36

t₀.₀₂₅ = 1.688

Test statistic

$t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }$

$t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }$

t = -14.8044

|t| = |-14.8044| > 1.688

Null hypothesis is rejected

Alternative hypothesis is accepted

Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

6 0

3 years ago

Last Tuesday, a parking lot had 80 cars. Of those 80 cars, 40% were tan, 20 were silver, and the rest were black. What perc

stepladder [879]

Answer:

Step-by-step explanation:

35%+28%=63%

37% of the cars were tan

7 0

3 years ago