If a quadratic-time algorithm requires 3 minutes to process 100 data values on a particular computer, approximately how long would it take for the algorithm to process 10,000 data values?

The answer is 30 minutes

Step-by-step explanation:

First, let us calculate the number of data value processed in 1 minute:

3min > 100 data processed

1min>x data processed.

Cross multiple: 3min* x = 1min*100data

Make x the subject: x= 100/3data.

We now have the data value processed in 1 minute, so we can go ahead and calculate the time required to process 1000 data value as follows:

1min >100/3 data

x min >1000 data

Cross multiply: 100/3 x = 1*1000

(100/3)x=1000.

Now make x the subject:

x= 1000/(100/3)

x=1000*3/100

x=10*3

x=30 min.

Hence we need 30 minutes to process 1000 data values.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

b

step-by-step explanation:

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