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3 years ago

5

An arc subtends a central angle measuring \dfrac{3\pi}{5} 5 3π start fraction, 3, pi, divided by, 5, end fraction radians. Wha

t fraction of the circumference is this arc?

1 answer:

alexgriva [62]3 years ago

8 0

Answer:

$\dfrac{3}{10}$

Step-by-step explanation:

Length of an arc $=\dfrac{\theta}{2\pi}X 2\pi r=\theta r$

If the central angle of the arc is $\dfrac{3\pi}{5}$

Length of an arc $=\dfrac{3\pi r}{5}$

Therefore:

Ratio of the length of the arc to the circumference

$=\dfrac{3\pi r}{5}:2\pi r\\=\dfrac{3\pi r}{5*2\pi r}\\=\dfrac{3}{10}$

Therefore, the arc is $\dfrac{3}{10}$ of the circumference is this arc.

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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

What’s the correct answer

n200080 [17]

The third one would be the correct answer. I separately multiplied each number in the first section by each number in the second section. For instance, 0 x 2 is 0, 4 x 5 is 20, 5 x 3 is 15, and 2 x 0 is 0. All of these numbers are in the third answer.

6 0

3 years ago

Sarah bought 18 boxes of 65 pens at $12 a box. She sold 378 of them at 3 for $1.00 and the rest at 4 for $1.00. Find her total p

KonstantinChe [14]

Answer:

$108

Step-by-step explanation:

1 box = $12

18 boxes = 12×18 = $216

Total = 18×65 = 1170 pens

Cost price, Cp = $216

3 = $1

378 = 378/3 = $126

1170-378= 792 pens remaining

4 = $1

792 = 792/4 = $198

Total selling price, sp = 126+198 = $324

Profit = Sp - Cp = 324 - 216 = $108

8 0

3 years ago

I need help ASAP can someone please help me right away

zysi [14]

Answer:

Smallest number would be 1^o

Step-by-step explanation:

Now with this one I can see the question now and the smallest* number of degrees to tilt it would be 1 degrees.

Have a good day. :)

Hope this helps!

<u>(brainliest would be appreciated)</u>

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3 years ago

Twenty-five percent of what number is 80?

tankabanditka [31]

The answer is 20
Hope this helps

3 0

3 years ago

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