# Tell whether the two quantities vary directly. Explain your reasoning. 23. the number of ounces of cereal and the number of Calories the cereal contains

Question
Linear equations and graphs
Tell whether the two quantities vary directly. Explain your reasoning. 23. the number of ounces of cereal and the number of Calories the cereal contains

2021-03-07
Two quantities, y and x, vary directly if y=kx where k is the constant of proportionality. The equation y=kx is a linear function with a y-intercept of 0 so two quantities vary directly if their relationship can be modeled by a linear function with a y-intercept of 0.
As the number of ounces of cereal increases, the number of Calories would also increase by a constant rate. The relationship between the two quantities can then be modeled by a linear function since there is a constant rate of change. If there are 0 ounces of cereal, there would be 0 Calories so the linear function has a yy-intercept of 0.
Therefore, the two quantities vary directly.

### Relevant Questions

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A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
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$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
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The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
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The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
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At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
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Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
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$$\mu_1 - \mu_2$$.
lower limit
upper limit
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Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
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1 [Graph] 2 [Graph]
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