To write the equation of an ellipse in standard form with the center at the origin, we need to use the following equation:
x^2/a^2 + y^2/b^2 = 1
where (0, 0) is the center of the ellipse, a is the length of the semi-major axis (half the length of the longer axis), and b is the length of the semi-minor axis (half the length of the shorter axis).
From the given characteristics, we know that the vertex is (-5,0) which means that a = 5 (since the distance from the center to a vertex is the length of the semi-major axis). We also know that the co-vertex is (0,4) which means that b = 4 (since the distance from the center to a co-vertex is the length of the semi-minor axis).
Using these values, we can plug them into the standard form equation and simplify:
x^2/5^2 + y^2/4^2 = 1
x^2/25 + y^2/16 = 1
Therefore, the equation of the ellipse in standard form with the center at the origin and with the given characteristics is A. x^2/25 + y^2/16 = 1.
Show your work
1. write an equation of an ellipse in standard form with the center at the orgin and with the given characteristics.
Vertix (-5,0) and co-vertex at (0, 4)
A. x^2/25 + y^2/16 = 1
B. x^2/4 + y^2/5= 1
3 answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.
Of all those who participated in the study, 80% received medication A.
Of those who received medication A, 76% reported an improvement.
Of those who received the placebo, 62% reported no improvement.
Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.
Of all those who participated in the study, 80% received medication A.
Of those who received medication A, 76% reported an improvement.
Of those who received the placebo, 62% reported no improvement.
To find P(placebo and improvement), we need to use the formula:
P(placebo and improvement) = P(placebo) * P(improvement | placebo)
From the given information, we know that:
- P(placebo) = 1 - P(medication A) = 1 - 0.8 = 0.2
- P(no improvement | placebo) = 0.62 (since 62% reported no improvement, the complement, or those who reported improvement, is 1 - 0.62 = 0.38)
- P(improvement | placebo) = 1 - P(no improvement | placebo) = 1 - 0.62 = 0.38
Therefore, we can plug in these values to the formula:
P(placebo and improvement) = 0.2 x 0.38 = 0.076
So P(placebo and improvement) is 0.076, or 7.6%.
P(placebo and improvement) = P(placebo) * P(improvement | placebo)
From the given information, we know that:
- P(placebo) = 1 - P(medication A) = 1 - 0.8 = 0.2
- P(no improvement | placebo) = 0.62 (since 62% reported no improvement, the complement, or those who reported improvement, is 1 - 0.62 = 0.38)
- P(improvement | placebo) = 1 - P(no improvement | placebo) = 1 - 0.62 = 0.38
Therefore, we can plug in these values to the formula:
P(placebo and improvement) = 0.2 x 0.38 = 0.076
So P(placebo and improvement) is 0.076, or 7.6%.
1 answer