Answer:
B
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
To obtain this form use the method of completing the square
Given
x² - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )
x² - 8x + y² - 2y = 8
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1
(x - 4)² + (y - 1)² = 25 → B
The formulas for conditional probability are:


.
Since

and

, you have the equation

.
Therefore,

.
Answer: The correct choice is D.
T= C(7+AB)
T = 7C + ABC
T - 7C = ABC
(T - 7C)/BC = A
Answer:
The answer is (A.)
Step-by-step explanation:
4 x 9 = 36
6 x 9 = 54
8 x 9 = 72
Step 1: Writing Null and Alternate HypothesisFirst we need to write the Null and Alternate Hypothesis for this problem.
Researcher claims that mileage will be increased on addition of Fuel additive. So the null and alternate hypothesis will be:
: μ ≤ 25.1 (Null Hypothesis)
: μ > 25.1 (Alternate Hypothesis)This is a Right Tailed Test. Since population standard deviation is not know, we will use t-test to check the researchers claim.
Step 2: Finding Test StatisticSample Mean = x = 26.8
Standard Deviation = s = 3.9
Sample Size = n = 35
Degrees of Freedom = df = n - 1 = 34
Test statistic(t) is given by:
Step 3: Finding p valueUsing t table or calculators find the p value for t=2.579 with 34 degrees of freedom for one tailed test.
P value comes out to be:
p = 0.0072
Step 4: ConclusionSince the p value is lesser than the significance level of 0.05, we reject the Null Hypothesis.
We have enough evidence to support the researcher's claim that the new additive increases the miles per gallon of the cars.