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erastovalidia [21]
2 years ago
11

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by

the equation g = 748u, where g is the total number of gallons of water used and u is the number of units.
Determine which statements about the relationship are true. Check all that apply.

g is the dependent variable.
u is the dependent variable.
g is the independent variable.
u is the independent variable.
The variables cannot be labeled without a table of values.
The variables cannot be labeled since any value can be selected for either.
Mathematics
2 answers:
Scorpion4ik [409]2 years ago
7 0

Answer:

option (a) and (d) is correct.

Step-by-step explanation:

Given : To bill customers for water usage, one city converts the number of gallons used into units.

This relationship is represented by the equation g = 748u

where, g is the total number of gallons of water used and u is the number of units.

We have to check out of given options which statement about the relationship is true.

Since, given relationship is  g = 748u.

We can put any value of u and find the corresponding value of g at that u.

For example

Since, u is the number of units used Let it be 30 units.

Then , we can find g , the total number of gallons of water used

By the relationship as g = 748u

Putting u = 30 , we get g = 748(30) = 22440 gallons.

So, here g depends on u and u is independent variable.

Thus, option (a) and (d) is correct.

Anastaziya [24]2 years ago
6 0

We are given equation g = 748u, where g is the total number of gallons of water used and u is the number of units.

We can see that the number of units of water being used by customers.

The number of units of water doesn't depend on the total number of gallons of water used.  

Therefore, the number of units u is an independent variable.

The value of the total number of gallons is totally depends on the number of units used.

Therefore,  the total number of gallons of water used g is a dependent variable.

So, we can conclude following statements:

1) g is the dependent variable.

2) u is the independent variable.

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Answer:

The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

Step-by-step explanation:

A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.

The (1 - <em>α</em>) % confidence interval for the population proportion (<em>p</em>) is given by:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

n = 6522\\\hat p=0.38\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a <em>z</em>-table for the critical value.

Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.38\pm 1.96\times \sqrt{\frac{0.38(1-0.38)}{6522}}\\=0.38\pm 0.0118\\=(0.3682, 0.3918)\\\approx (0.37, 0.40)

Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

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fredd [130]

Answer:

P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)

And we can find this probability using the complement rule and the normal standard distribution and we got:

P(z>6.302)=1-P(z

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 number of attacks of a population, and for this case we know the distribution for X is given by:

X \sim N(510,14.28)  

Where \mu=510 and \sigma=14.28

We are interested on this probability

P(X>600)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)

And we can find this probability using the complement rule and the normal standard distribution and we got:

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ANSWER:

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Step-by-step explanation:

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This gives us a total sum of squares of 1053.15

Sums of squares tell if a linear regression of one variable (or variables) on another is good or not.

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