1500 customers hold a VISA card; 500 hold an American Express card; and, 75 hold a VISA and an American Express. What is the pro
1 answer:
Answer:
There is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.
Step-by-step explanation:
Number of customers having a Visa card = 1,500
Number of customers having an American Express card = 500
Number of customers having Visa and American Express card = 75
Total number of customers = 1,500 + 500 = 2,000
We are asked to find the probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.
This problem is related to conditional probability which is given by
For the given problem it becomes
The probability P(VISA and AE) is given by
P(VISA and AE) = 75/2000
P(VISA and AE) = 0.0375
The probability P(AE) is given by
P(AE) = 500/2000
P(AE) = 0.25
Finally,
Therefore, there is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.
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4a is the lactus rectum
a is the distance from the focus to the vertex
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Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
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y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
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The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1