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3 years ago

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A restaurant owner is planning to have a courtyard area sodded. The sod comes in rolls that are 3 feet long by 1 foot wide. If t

he courtyard measures 60 feet by 50 feet, which of the following expressions represents the number of rolls of sod needed?

1 answer:

Andrews [41]3 years ago

6 0

Answer:

$(60\times 50)\div 3$

Step-by-step explanation:

We are given that

Length of roll of sod, l=3 feet

Width of roll of sod, b=1 feet

Length of courtyard, L=60 feet

Breadth of courtyard, B=50 feet

Area of rectangle= $Length\times breadth$

Using the formula

Area of roll of sod= $3\times 1 feet^2$

Area of roll of sod=3 square feet

Area of courtyard= $60\times 50$ square feet

Number of rolls of sod needed= $\frac{Area\;of\;courtyard}{area\;of\;roll\;of\;sod}$

Using the formula

Number of rolls of sod needed= $\frac{60\times 50}{3}$

Number of rolls of sod needed= $(60\times 50)\div 3$

This is required expression which represents the number of rolls of sod needed.

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Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that ar

Colt1911 [192]

Answer:

$z=\frac{0.0211-0.0132}{\sqrt{0.0141(1-0.0141)(\frac{1}{18440}+\frac{1}{2123})}}=24.827$

$p_v =P(Z>24.827)\approx 0$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of children with ASD in Utah is significantly higher than the proportion of children with ASD in Pennsylvania

Step-by-step explanation:

Data given and notation

$X_{P}=245$ represent the number of children with ASD in Pennsylvania

$X_{U}=45$ represent the number of children with ASD in Utah

$n_{P}=18440$ sample for Pennsylvania

$n_{U}=2123$ sample for Utah

$p_{P}=\frac{245}{18440}=0.0133$ represent the proportion of children with ASD in Pennsylvania

$p_{U}=\frac{45}{2123}=0.0212$ represent the proportion of children with ASD in Utah

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion for Utah is higher than the proportion for Penssylvania , the system of hypothesis would be:

Null hypothesis: $p_{U} \leq p_{P}$

Alternative hypothesis: $p_{U} > \mu_{p}$

We need to apply a z test to compare proportions, and the statistic is given by:

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

Where $\hat p=\frac{X_{U}+X_{P}}{n_{U}+n_{P}}=\frac{245+45}{18440+2123}=0.0141$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0211-0.0132}{\sqrt{0.0141(1-0.0141)(\frac{1}{18440}+\frac{1}{2123})}}=24.827$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one right tailed test the p value would be:

$p_v =P(Z>24.827)\approx 0$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of children with ASD in Utah is significantly higher than the proportion of children with ASD in Pennsylvania

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Dmitry_Shevchenko [17]

Answer:

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Step-by-step explanation:

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Cross multiply:
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zmey [24]

Answer:

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Answer:

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Step-by-step explanation:

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