Answer:
see image...
start with Graphing Form: y = a(x-h)²+ k
knowing that h is the x value (negative of it) of the vertex , and k is the y value of the vertex
Graphing Form Equation: y = a(x+3)²+32
you are also given that when the x value is 5 the y value has to be 0
0 = a(4)^2 + 32
a has to be - 1/2
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
=
[2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
=
[(2 × 5) + 2(n - 1) ]
= (10 + 2n - 2)
= (2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
Answer:
H 0 : μ = 3.1 H 1 : μ > 3.1
And this test is defined a a right tailed test since the symbol for the alternative hypothesis H1 is >.
The p value is:
The significance level is: 0.1 or 10%
And since the p value is very low compared to the significance level we have enough evidence to:
Reject the null hypothesis
Step-by-step explanation:
For this case we want to test the claim that mean GPA of night students is larger than 3.1 at the .10 significance level. The claim needs to be on the alternative hypothesis so then we have the following system of hypothesis:
H 0 : μ = 3.1 H 1 : μ > 3.1
And this test is defined a a right tailed test since the symbol for the alternative hypothesis H1 is >.
We have the following info given:
The statistic to check the hypothesis is given by:
Replacing the info given we got:
The degrees of freedom are given by:
The p value since is a right tailed ted is given by:
The significance level is 0.1 or 10%
And since the p value is very low compared to the significance level we have enough evidence to:
Reject the null hypothesis