Kateri draws a square. She wants to draw one line to draw one line to divide the square into 2 triangles. Is it possible for her
1 answer:
You might be interested in
The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = one twelfth (x - 5)² ⇒ 1st answer
Step-by-step explanation:
The form of the equation of the parabola is (x - h)² = 4p(y - k), where
- The vertex of the parabola is (h , k)
- The focus is (h , k + p)
- The directrix is at y = k - p
∵ The focus of the parabola is at (5 , 3)
- Compare it with the 2nd rule above
∴ h = 5
∴ k + p = 3 ⇒ (1)
∵ The directrix is at y = -3
- By using the 3rd rule above
∴ k - p = -3 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = 0
- Divide both sides by 2
∴ k = 0
- Substitute the value of k in equation (1) to find p
∵ 0 + p = 3
∴ p = 3
Substitute the values of h , k , and p in the form of the equation above
∵ (x - 5)² = 4(3)(y - 0)
∴ (x - 5)² = 12 y
- Divide both sides by 12
∴ (x - 5)² = y
- Switch the two sides
∴ y = (x - 5)²
The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = (x - 5)²
Learn more:
you can learn more about the quadratic equations in brainly.com/question/8054589
#LearnwithBrainly
Answer:
(a) NULL HYPOTHESIS, :
3.5%
ALTERNATE HYPOTHESIS, :
> 3.5%
(b) We conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.
Step-by-step explanation:
We are given that a random sample of seven Ohio banks is selected.The bad debt ratios for these banks are 7, 4, 6, 7, 5, 4, and 9%.The mean bad debt ratio for all federally insured banks is 3.5%.
We have to test the claim of Federal banking officials that the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.
(a) Let, NULL HYPOTHESIS, :
3.5% {means that the the mean bad debt ratio for Ohio banks is less than or equal to the mean for all federally insured banks}
ALTERNATE HYPOTHESIS, :
> 3.5% {means that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks}
The test statistics that will be used here is One-sample t-test;
T.S. = ~
where, = sample mean debt ratio of Ohio banks = 6%
s = sample standard deviation = = 1.83%
n = sample of banks = 7
So, test statistics = ~
= 3.614
(b) Now, at 1% significance level t table gives critical value of 3.143. Since our test statistics is more than the critical value of t so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.
Hence, Federal banking officials claim was correct.