A: 1.5
c: 10/3, 3 1/3, 3.3 repeating
b: 20/3, 6 2/3, 6.6 repeating
c: 8/15
d: 1
Answer:
The probability is an Empirical Probability
Step-by-step explanation:
The empirical probability (also know as relative frequency, or experimental probability) is the type of probability that involves the ratio of the number of outcomes in which a certain occurrence or event happens to the total number of trials, not in a theoretical sample space but in an actual experiment.
It uses the number of occurrences of an outcome within a sample set as a basis for determining the probability of that outcome.
Answer:
660 nails
Step-by-step explanation:
Take all of john's nails and multiply by 4.4 because 176/40 is 4.4. Multiply 4.4 by the john's other nails. Add the products together and thats your answer.
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
