Answer:
y = - 3x² - 24x - 60
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 4, - 12 ), thus
y = a(x + 4)² - 12
To calculate a substitute (- 7, - 39) into the equation
- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )
- 27 = 9a ( divide both sides by 9 )
- 3 = a
y = - 3(x + 4)² - 12 ← in vertex form
Expand (x + 4)²
y = - 3(x² + 8x + 16) - 12
= - 3x² - 24x - 48 - 12
y = - 3x² - 24x - 60 ← in standard form
= - 3(x²
Answer:
42 gallons.
Step-by-step explanation:
count every inch *2 and calculate gallons
Answer:
x³ - 6x² + 18x - 10
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
= x³ - 2x² + 12x - 6 - (4x² - 6x + 4)
= x³ - 2x² + 12x - 6 - 4x² + 6x - 4 ← collect like terms
= x³ - 6x² + 18x - 10
Answer:
a) H0: 
H1: 
b) 
And the critical values with 
on each tail are:
c) ![t=(10-1) [\frac{1.186}{1.34}]^2 =7.05](https://tex.z-dn.net/?f=%20t%3D%2810-1%29%20%5B%5Cfrac%7B1.186%7D%7B1.34%7D%5D%5E2%20%3D7.05)
d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
Step-by-step explanation:
Information provided
n = 10 sample size
s= 1.186 the sample deviation
the value that we want to test
represent the p value for the test
t represent the statistic (chi square test)
significance level
Part a
On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:
H0:
H1:
The statistic is given by:
![t=(n-1) [\frac{s}{\sigma_o}]^2](https://tex.z-dn.net/?f=%20t%3D%28n-1%29%20%5B%5Cfrac%7Bs%7D%7B%5Csigma_o%7D%5D%5E2%20)
Part b
The degrees of freedom are given by:
And the critical values with on each tail are:
Part c
Replacing the info we got:
Part d
For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
Answer:
Yes
Step-by-step explanation:
First, suppose that nothing has changed, and possibility p is still 0.56. It's our null hypothesis. Now, we've got Bernoulli distribution, but 30 is big enough to consider Gaussian distribution instead.
It has mean μ= np = 30×0.56=16.8
standard deviation s = √npq
sqrt(30×0.56×(1-0.56)) = 2.71
So 21 is (21-16.8)/2.71 = 1.5494 standard deviations above the mean. So the level increased with a ˜ 0.005 level of significance, and there is sufficient evidence.
