Answer:
.
Step-by-step explanation:
In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are 
, 
, and 
:
,
, and
.
In this question, the length of the sides are 
, 
, and 
. The length of these sides should satisfty the following inequalities:
,
, and
.
Since 
, the inequality is guarenteed to be satisfied.
Simplify to obtain the inequality 
.
Similarly, simplify to obtain the inequality 
.
Since needs to be a whole number, the greatest that satisfies would be 
. Similarly, the least 
that satisfies would be 
. Thus, 
could be any whole number between 
and 
(inclusive.)
There are a total of 
distinct whole numbers between and (inclusive.) Thus, the number of possible whole number values for would be .
Answer:
95% confidence interval: (2.784,3.176)
Step-by-step explanation:
We are given the following information in the question:
Sample size, n = 25
Sample mean = $2.98
Standard error = $0.10
Alpha = 0.05
95% confidence interval:
Putting the values, we get,
Answer:
3) 67/441
Step-by-step explanation:
Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.
3x² +5x -7 = 0 . . . . . given equation
3x² +5x = 7 . . . . . . . add 7
x(3x +5) = 7 . . . . . . . factor
3x +5 = 7/x . . . . . . . . divide by x
Now, we can substitute into the expression you are evaluating to get ...
1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49
__
We know that when we divide the original quadratic by 3, we get
x² +(5/3)x -7/3 = 0
and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...
α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9
Then the value of the desired expression is ...
(67/9)/49 = 67/441
I believe it's 927/-125a^3)
Equivalent. Fractions that are equal are equivalent.
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