Plz help me i need this in simplest form or in a decimal
2 answers:
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Answer:
One possible equation is , which is equivalent to
.
Step-by-step explanation:
The factor theorem states that if (where
is a constant) is a root of a function,
would be a factor of that function.
The question states that and
are
-intercepts of this function. In other words,
and
would both set the value of this quadratic function to
. Thus,
and
would be two roots of this function.
By the factor theorem, and
would be two factors of this function.
Because the function in this question is quadratic, and
would be the only two factors of this function. In other words, for some constant
(
):
.
Simplify to obtain:
.
Expand this expression to obtain:
.
(Quadratic functions are polynomials of degree two. If this function has any factor other than and
, expanding the expression would give a polynomial of degree at least three- not quadratic.)
Every non-zero value of corresponds to a distinct quadratic function with
-intercepts
and
. For example, with
:
, or equivalently,
.
Answer:
The hippocampus volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm³
Step-by-step explanation:
Let x= the hippocampus volumes in the alcoholic adolescents
We'll conduct a hypothesis test at the 0.01 significance level with
Null hypothesis: x = 9.02 cm³
Alternate hypothesis: x < 9.02 cm³
A sample of 13 alcoholic adolescents gives the parameters
size=N= 13
mean=M= 8.12 cm³
standard deviation= s= 0.8 cm³
According to the sample, with 99% confidence, t statistic for the value X=9.02 can be found using the formula:
t= where
- M is the sample mean (8.12)
- s is the standard deviation of the sample (0.8)
- N is the sample size (13)
If we put these numbers in the formula:
t= =4.056
One tailed critical value for the sample with 12 degrees of freedom (sample size-1) in 99% confidence level is 2.681.
Since t value (4.056) is bigger than the critical value, we fail to reject the alternate hypothesis, therefore reject the null hypothesis and accept alternate hypothesis.