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3 years ago

When Justin goes to work, he drives at an average speed of 60 miles per hour. It takes about 1 hour and 30

Mathematics

1 answer:

dexar [7]3 years ago

6 0

Answer:

$13.14

Step-by-step explanation:

60 mi/1 hour = x mi/1.5 hours

x = 90 mi to drive to work

25 mi/1 gallon = 90 mi/y gallons

y = 3.6 gallons to get to work

$3.65/1 gallon = $z/3.6 gallons

z = $13.14

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Find the slope and the y intercept.<br> Then use them to graph the line.

Margarita [4]

Answer:

The photo above show you how to graph it.

The equation is y=2x-3

Step-by-step explanation:

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3 years ago

10.) Kelly is flying a kite to which the angle of elevation is

jarptica [38.1K]

Answer:

61.08m

Step-by-step explanation:

Let " l " be the length of the rope and " θ " the angle at which it is raised. In other words:

l = 65m
θ = 70°

As you can see, there has been made a right angle triangle. So:

$sin70 = \frac{h}{l} \\ h = l \times sin70 \\ h = 65 \times 0.9397 = 61.08 \\ h = 61.08$

So the kite is approximately 61.08m above the ground.

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3 years ago

What is the surface area of the cube shown?<br><br> 6.5 lenth 6.5 hieght

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Answer:

253.5

Step-by-step explanation:

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3 years ago

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Solve the division problem. Round answer to the nearest hundredth. 9.252.063

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3 years ago

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Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compoun

aev [14]

Answer:

a) $29.4-1.96\frac{7}{\sqrt{10}}=25.06$

$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

So on this case the 95% confidence interval would be given by (25.06;33.74)

b) $z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988$

$p_v =P(z>1.988)=0.0234$

If we compare the p value and the significance level given $\alpha=Step-by-step explanation:Previous conceptsA confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". 
The margin of error is the range of values below and above the sample statistic in a confidence interval. 
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". 
Part a
Data given: 30 30 42 35 22 33 31 29 19 23
We can calculate the sample mean with the following formula:[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}= 29.4$ the sample mean

$\mu$ population mean (variable of interest)

$\sigma=7$ represent the population standard deviation

n=10 represent the sample size

95% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$29.4-1.96\frac{7}{\sqrt{10}}=25.06$

$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

So on this case the 95% confidence interval would be given by (25.06;33.74)

Part b

What are H0 and Ha for this study?

Null hypothesis: $\mu \leq 25$

Alternative hypothesis : $\mu>25$

Compute the test statistic

The statistic for this case is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988$

Give the appropriate conclusion for the test

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

$p_v =P(z>1.988)=0.0234$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

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3 years ago