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3 years ago

Find the volume of each sphere. Round to the nearest tenth.. volume V=4/3

1 answer:

3 0

The complete question is
Find the volume of each sphere for the given radius. <span>Round to the nearest tenth

we know that
[volume of a sphere]=(4/3)*pi*r</span>³

case 1) r=40 mm
[volume of a sphere]=(4/3)*pi*40³------> 267946.66 mm³-----> 267946.7 mm³

case 2) r=22 in
[volume of a sphere]=(4/3)*pi*22³------> 44579.63 in³----> 44579.6 in³

case 3) r=7 cm
[volume of a sphere]=(4/3)*pi*7³------> 1436.03 cm³----> 1436 cm³

case 4) r=34 mm
[volume of a sphere]=(4/3)*pi*34³------> 164552.74 mm³----> 164552.7 mm³

case 5) r=48 mm
[volume of a sphere]=(4/3)*pi*48³------> 463011.83 mm³----> 463011.8 mm³

case 6) r=9 in
[volume of a sphere]=(4/3)*pi*9³------> 3052.08 in³----> 3052 in³

case 7) r=6.7 ft
[volume of a sphere]=(4/3)*pi*6.7³------> 1259.19 ft³-----> 1259.2 ft³

case 8) r=12 mm
[volume of a sphere]=(4/3)*pi*12³------>7234.56 mm³-----> 7234.6 mm³

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The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-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

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

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

3 years ago

Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline

alex41 [277]

The answer to this question is the letter "A" which is $20.70. The solution is shown below:

If the guy will solely use the car, his expenses for the gasoline per month is:
Guy alone = $ 2.76/gallon * 15 gallons = $ 41.4

If the guy will let his two officemates ride the car and contribute each quarter of the of a tank:
First officemate = 15/4 * $2.76 = $ 10.35
Second officemate = 15/4 * $2.76 = $10.35

The guy total savings is shown below:
Total savings = $41.4 - $10.35 -$10.35
Total savings = $20.70

The answer is the letter "A".

5 0

3 years ago

An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters abov

Hoochie [10]

Answer:

After 3 seconds

Step-by-step explanation:

Given

$h(t) = -5t^2 + 14t + 3$