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1 month ago

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A swimming pool has about 603 cubic feet of water. The pool liner has a small hole and is leaking at a rate of 1.5 cubic feet ea

ch hour. Ruby wrote the equation V(h) = -1.5h + 603 to represent the scenario. Describe what each variable represents in the function, and how they relate to each other.

2 answers:

PIT_PIT [12.4K]1 month ago

3 0

Answer:

Ruby’s notation V(h) depicts the volume of the pool following h hours. In this context, hours serve as the independent variable and the total volume acts as the dependent variable.

Step-by-step explanation:

zzz [12.3K]1 month ago

3 0

Answer:

Ruby’s notation V(h) represents the pool's volume after h hours have passed. Here, hours are the independent variable, whereas the total volume is the dependent variable.

Step-by-step explanation:

sample response

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Read 2 more answers

At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

Leona [12618]

Answer:

a) Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

b) $r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

Additionally, the coefficient of determination is $r^2 = 0.657^2 =0.432$

Step-by-step explanation:

Definitions and data provided

The correlation coefficient is a measure that quantifies the strength of the relationship between two variable movements, denoted as r and ranging between -1 and 1.

The sum of squares refers to the total of the squared deviations, where deviation is defined as the difference between each value and the grand mean.

When performing multiple regression, the aim is to analyze the relationship between multiple independent variables and one dependent variable.

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9, sum y^2_i=\sum(y-\bar y)^2 =94228.8$

$\sum Y_i =17375, \sum X_i = 7665.5$

Part a

The slope can be calculated using this formula:

$\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}$

Following the substitutions, we have:

$\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

The intercept can be determined with this formula:

$\hat \beta_o = \bar y -\hat \beta_1 \bar x$

Average values for x and y can be calculated this way:

$\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955$

Replacing yields:

$\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

Part b

The correlation coefficient can be calculated using the following formula:

$r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}$

In our situation:

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9, sum y^2_i=\sum(y-\bar y)^2 =94228.8$

We can compute the correlation coefficient by substituting values:

$r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

The coefficient of determination is $r^2 = 0.657^2 =0.432$

6 0

2 months ago

A study1 conducted in July 2015 examines smartphone ownership by US adults. A random sample of 2001 people were surveyed, and th

Inessa [12570]

Answer:

a) Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

b) $z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

c) $z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

d) In this scenario, we notice that $\hat p_1 > \hat p_2$ thus the conclusion for this case would indicate

Step-by-step explanation:

Information provided

$X_{1}=688$ denote the number of men possessing smartphones

$X_{2}=671$ signify the number of women possessing smartphones

$n_{1}=989$ group of men sampled

$n_{2}=1012$ group of women sampled

$p_{1}=\frac{688}{989}=0.696$ symbolize the proportion of men with smartphones

$p_{2}=\frac{671}{1012}=0.663$ symbolize the proportion of women with smartphones

$\hat p$ denote the pooled estimate of p

z would denote the test statistic

$p_v$ signify the value

Part a

The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

Part b

The statistic relevant to this case is expressed as:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

Part c

By substituting the provided information, we find:

$z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

Part d

In this instance, it is evident that $\hat p_1 > \hat p_2$ thus the conclusion for this case would seem

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2 months ago