A circle is centered at N(-6, -2). The point E(-1,1) is on the circle.
2 answers:
Answer:
Outside the circle
Step-by-step explanation:
Let's first write the equation of this circle: , where (h, k) is the center and r is the radius. Here, the center is (-6, -2). We need to find the radius, which will just be the distance from N to E:
NE =
The radius is √34, which means that r² = 34. So, our equation is:
(x + 6)² + (y + 2)² = 34
Plug in -10 for x and -7 for y:
(x + 6)² + (y + 2)² = 34
x² + 12x + 36 + y² + 4y + 4 = 34
x² + 12x + y² + 4y + 40 = 34
x² + 12x + y² + 4y + 6 = 0
(-10)² + 12 * (-10) + (-7)² + 4 * (-7) + 6 = 7
Since 7 > 0, we know that H lies outside the circle.
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Answer:
A. 23+x=140
Step-by-step explanation:
The angle addition postulate states that the measure of a larger angle formed by two or more smaller angles placed side by side is the the sum of the smaller angles. The angle addition postulate states that if B is in the interior of AOC , then:
m∠AOB + m∠BOC = m∠AOC.
From the image:
∠NOP = ∠NOQ + ∠QOP
∠NOP = 140, ∠NOQ = x, ∠QOP = 23
substituting:
140 = x + 23
x = 140 - 23 = 117
∠NOQ = 117°
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c)
d) If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.
Step-by-step explanation:
Data given and notation
The sample mean is given by:
And the sample deviation is:
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(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".
Part b Calculate the statistic
We can replace in formula (1) the info given like this:
Part c P-value
The degrees of freedom are given by:
Since is a right tailed test the p value would be:
Part d Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.