<h3>
Answer: 5/9</h3>
As an approximate decimal, this is 0.5556 which converts to 55.56%
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Explanation:
Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.
We then select a house at random. Someone tells us (or we have some kind of prior knowledge) that whichever house is selected, they have an answering machine. We can ignore the 10 households that don't have an answering machine. Out of those 90 households, 50 have both features. So 50/90 = 5/9 is the probability of getting a household with both features.
The answer would be 1/2 or 50% if we didn't have the prior knowledge of the household having an answering machine. But with this prior knowledge, the conditions change and so does the probability.
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You could also compute 0.50/0.90 to get the same answer.
Answer:
D. Car B was 10 miles east of car A
Step-by-step explanation:
→ Work out how many miles car A travelled
130
→ Work out how many miles car B travelled in 2 hrs
120
→ Find the difference
Car A is bigger by 10 miles
Angles:
2 acute angles and 2 obtuse angles
Sides:
2 pairs pf parallel sides
The one is a vertical translation of the parent function to the left of one
making it -1.
The average value of f over the region D is 243/4
To answer the question, we need to know what the average value of a function is
<h3>What is the average value of a function?</h3>
The average value of a function f(x) over an interval [a,b] is given by
Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).
x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9
So, ![\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bb%20-%20a%7D%20%5Cint%5Climits%5Eb_a%20%7Bf%28x%2Cy%29%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B1%7D%7B1%20-%200%7D%20%5Cint%5Climits%5E1_0%20%5Cint%5Climits%5E9_0%20%7B3xy%7D%20%5C%2C%20dxdy%20%5C%5C%3D%20%5Cfrac%7B3%7D%7B1%7D%20%5Cint%5Climits%5E1_0%20%7Bx%7D%20%5C%2Cdx%5Cint%5Climits%5E9_0%20%7By%7D%20%5C%2Cdy%5C%5C%20%3D%20%20%5Cfrac%7B3%7D%7B1%7D%20%5B%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%20%5D%5E%7B1%7D_%7B0%7D%5B%5Cfrac%7By%5E%7B2%7D%20%7D%7B2%7D%20%5D%5E%7B9%7D_%7B0%7D%20%20%5C%5C%3D%203%5B%5Cfrac%7B1%5E%7B2%7D%20%7D%7B2%7D%20-%20%5Cfrac%7B0%5E%7B2%7D%7D%7B2%7D%20%5D%20%5B%5Cfrac%7B9%5E%7B2%7D%20%7D%7B2%7D%20-%20%5Cfrac%7B0%5E%7B2%7D%7D%7B2%7D%20%5D%20%5C%5C%3D%203%5B%5Cfrac%7B1%7D%7B2%7D%20-%200%20%5D%5B%5Cfrac%7B81%7D%7B2%7D%20-%200%20%5D%5C%5C%3D%20%20%5Cfrac%7B81%7D%7B2%7D%20X3%20X%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%3D%20%20%5Cfrac%7B243%7D%7B4%7D)
So, the average value of f over the region D is 243/4
Learn more about average value of a function here:
brainly.com/question/15870615
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