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-Dominant- [34]
3 years ago
15

A gas pump fills 2^-2 gallon of gasoline per second. how many gallons does the pump fill in one minute?

Mathematics
1 answer:
astraxan [27]3 years ago
6 0

Answer:

The gas pump filling the gallons in 1 minute will be: 15

Step-by-step explanation:

  • Given that a gas pump fills 2^-2 gallon of gasoline per second.

As there are 60 seconds in 1 minute.

Thus,

Gas pump filling the gallons in 1 minute will be:

60\:\times 2^{-2}

=60\times \frac{1}{2^2}             ∵ a^{-b}=\frac{1}{a^b}

\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}

=\frac{1\times \:60}{2^2}

=\frac{60}{2^2}

=\frac{2^2\times \:3\times \:5}{2^2}

=3\times \:5

=15 gallons in one minute

Therefore, the gas pump filling the gallons in 1 minute will be: 15

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ehidna [41]

Answer:

Null hypothesis:p_{1} = p_{2}    

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

z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688    

p_v =2*P(Z>2.688)= 0.0072    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

Step-by-step explanation:

Data given and notation    

X_{1}=410 represent the number of people indicating that their financial security was more than fair  in 2012

X_{2}=315 represent the number of people indicating that their financial security was more than fair in 2010

n_{1}=1000 sample 1 selected  

n_{2}=900 sample 2 selected  

p_{1}=\frac{410}{1000}=0.410 represent the proportion estimated of people indicating that their financial security was more than fair in 2012

p_{2}=\frac{315}{900}=0.350 represent the proportion estimated of people indicating that their financial security was more than fair in 2010  

\hat p represent the pooled estimate of p

z would represent the statistic (variable of interest)    

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

\alpha=0.05 significance level given  

Part a: Concepts and formulas to use    

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:    

Null hypothesis:p_{1} = p_{2}    

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

Hypothesis testing

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

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{410+315}{1000+900}=0.382  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.    

Calculate the statistic  

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

z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688    

Statistical decision  

Since is a two sided test the p value would be:    

p_v =2*P(Z>2.688)= 0.0072    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

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4 years ago
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Answer:

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Step-by-step explanation:

3a - p = m

→ First plus p to both sides to isolate 3a

3a = m+p

→ Divide both sides by 3 to isolate a

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Answer:

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Step-by-step explanation:

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See attached graph.

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Find the area of the trapezoid with a base of 19 inches, height 12.6 inches and base 29.2 inches
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Height: h=12.6 inches
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