Two <em>possible answers</em> are:
5/16 and 3/8.
Explanation:
To create a fraction equivalent to a given fraction, you multiply the numerator and denominator by the same number. This means for 5/8, we could have:
5/8; (5*2)/(8*2)=10/16; (5*3)/(8*3)=15/24; etc.
For 1/2, we could have:
1/2; (1*2)/(2*2)=2/4; (1*3)/(2*3)=3/6; etc.
All transportation (bus, cab, train) are all similarly likely to be selected, and 1 of them must be selected at morning and evening, so we get: P (bus) = P (cab) = P (train) = 1/3. We also have P(no cab in evening) = P(no cab at morning) = 2/3
Now, P(using cab exactly once) = P(cab at morning and no cab in the evening) + P(no cab at morning and cab in the evening)
= P(cab, no cab) + P(no cab, cab)
= 1/3 * 2/3 + 2/3 * 1/3
= 2/9 + 2/9
= 4/9
Probability that Elizabeth uses a cab only once is 4/9.
The <em><u>correct answer</u></em> is:
She can determine that while there is an association between the variables, there is no correlation, and she cannot determine causation.
Explanation:
Since there is an arch shape to her graph, we know that as one variable changes, the other changes in the same manner. This means there is an association between the variables.
However, since the graph is not linear, there is no correlation between the variables. Since there is no correlation, we cannot determine causation.
Since the parabola passes by the center its equation is:
y = ax². But it opens downward, that means the coefficient a is negative.
Then the equation becomes:
y = - ax², with x = 0 as its axis of symmetry.
We are given that the height is 84 ft when the opening downward is 42 ft.
That means to the (height) y, corresponds x =+21 & x=-21 (due to symmetry).
In order to calculate a let's plug y & x with their related values:
y = - ax²
84 = - a(21)²
84 = - a(441) and a = - 84/441 ↔ a = - 4/21
And the final equation is : y = -4/21. x²
