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3 years ago

Find the measure of

Mathematics

2 answers:

UkoKoshka [18]3 years ago

5 0

Answer:

20°

Step-by-step explanation:

In circle geometry, one of the theorem States that angle at the center of a circle is twice angle at the circumference.

Let x be the angle at the centre and y be angle at the circumference. The theorem can be expressed mathematically as;

x = 2y

According to the diagram <BOC is the angle at the center represented as x which is 40°

Angle<BAC is at the circumference of the circle represented as y.

To find <BAC, note that

<BOC = 2<BAC

40° = 2<BAC

<BAC = 40°/2

<BAC = 20°

Ivenika [448]3 years ago

3 0

Answer:

The measure of angle BAC is 20°

Step-by-step explanation:

step 1

Find the measure of arc BC

we have that

m∠BOC=arc BC ------> by central angle

we have

m∠BOC=40°

therefore

arc BC=40°

step 2

Find the measure of angle BAC

we know that

The inscribed angle is half that of the arc it comprises

m∠BAC=(1/2)[arc BC]

we have

arc BC=40°

substitute

m∠BAC=(1/2)[40°] =20°

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3 years ago

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:

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

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3 years ago

Can you fine the cube root of a negative number? If so, is it positive or negative? Explain your answer.

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Answer:

Yes, you can find the cube root of a negative number. The answer will be negative!

Step-by-step explanation:

Example: Find the cube root of -27

We know that a cube root is a number multiplied by itself 3 times (NOT MEANING THE NUMBER TIMES 3)

For example, The cube root of 27 positive is 3 because 3 x 3 x 3 = 27

But if we are using a negative number: It is really different because we got to know the rules.

The setup: -3 x -3 x -3 = -27

If we started with -3 x -3 first we know that a negative times a negative equals positive so the answer will be 9 positive, then we have this equation left:

9 x -3 = -27

The rule with this is a number times a negative is negative, so the answer of the question "Find the cube root of -27 is -3"

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