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nikklg [1K]
3 years ago
8

In circle F with m∠EFG=54m∠EFG=54 and EF=19

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
3 0

Answer:

17.907082 unit

Step-by-step explanation:

According to the Question,

Given, A circle with centre F, ∠EFG=54 and EF=19 .

length of arc EG = Radius(EF) × ∠EFG(in Radian)

  • We Know, 1 degree = 0.0174533 Radian
  • 54 degree = 0.942478 Radian

length of arc EG = 19 x 0.942478 ⇔ 17.907082 unit

(For Diagram please find in attachment)

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Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to
attashe74 [19]

Answer:

a) Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

b) X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c) t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

p_v =P(t_{(49)}>2.81)=0.0035  

d) If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

\bar X=32.12 represent the sample mean  

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =30.2 represent the value that we want to test

\alpha 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)  

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-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".  

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c. Perform the test and calculate P-value

Calculate the statistic

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

t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

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

p_v =P(t_{(49)}>2.81)=0.0035  

d. State your conclusion.

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0
3 years ago
Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Serhud [2]

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

  • Find the mid-point of a diagonal whose endpoints are given
  • Use this mid-point to find the missing vertex
  • The mid point rule is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ x_{1} = -2 and x_{2} = 7

∴ y_{1} = -3 and y_{2} = 7

- Substitute them in the rule of the mid point to find the

   mid-point of XZ

∴ M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ x_{1} = x and x_{2} = 0

∴ y_{1} = y and y_{2} = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ 2.5=\frac{x+0}{2}

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ 2=\frac{y+5}{2}

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

4 0
3 years ago
Sally has completed 1/3 of her shift; Jerry has completed 5/6 of his shift; David has finished 1/2 of his shift; Mona has 7/8 of
Step2247 [10]
Sally = 1/3
Jerry = 5/6
David = 1/2
Mona = 1 - 7/8 = 1/8

So, the biggest fraction among them is 5/6.

Jerry has completed the most work time. 
3 0
3 years ago
PLEASE HELP ME ILL MARK AS BRAINLIEST
Gelneren [198K]

0.05 ---> 1/18

square root of 0.25 ------> 0.05

1/7------> 0.142857 repeating

0.6 -------> 2/3

5 0
3 years ago
Read 2 more answers
Which expression represents, 8 times the difference of two numbers?
tiny-mole [99]

Answer:

C, the difference is subtraction so 8 times the difference of two numbers is C

4 0
3 years ago
Read 2 more answers
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