We have a "rectangular" double loop, meaning that both loops go to completion.
So there are 3*4=12 executions of t:=t+ij.
Assuming two operatiions per execution of the innermost loop, (i.e. ignoring the implied additions in increment of subscripts), we have 12*2=24 operations in all.
Here the number of operations (+ or *) is exactly known (=24).
Big-O estimates are used for cases with a varying scale of operations, governed by a variable (usually n) to indicate the sensitivity of the number of operations relative to a change in the size of n.
Here we do not have a scale, nor n is defined. The number of operations is constant and known at 24. So a variable is required to find the big-O estimate.
Answer:
A. 15, 20, and 25
Step-by-step explanation:
Note that 3-4-5 is a pythagorean triple via following:

Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.
Answer:
a) P(x<5)=0.
b) E(X)=15.
c) P(8<x<13)=0.3.
d) P=0.216.
e) P=1.
Step-by-step explanation:
We have the function:

a) We calculate the probability that you need less than 5 minutes to get up:

Therefore, the probability is P(x<5)=0.
b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.
E(X)=15.
c) We calculate the probability that you will need between 8 and 13 minutes:
![P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3](https://tex.z-dn.net/?f=P%288%5Cleq%20x%5Cleq%2013%29%3DP%2810%5Cleqx%5Cleq%2013%29%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D%5Cint_%7B10%7D%5E%7B13%7D%20f%28x%29%5C%2C%20dx%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D%5Cint_%7B10%7D%5E%7B13%7D%20%5Cfrac%7B1%7D%7B10%7D%20%5C%2C%20dx%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D%5Cfrac%7B1%7D%7B10%7D%20%5Ccdot%20%5Bx%5D_%7B10%7D%5E%7B13%7D%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D%5Cfrac%7B1%7D%7B10%7D%20%5Ccdot%20%2813-10%29%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D%5Cfrac%7B3%7D%7B10%7D%5C%5C%5C%5CP%288%5Cleq%20x%5Cleq%2013%29%3D0.3)
Therefore, the probability is P(8<x<13)=0.3.
d) We calculate the probability that you will be late to each of the 9:30am classes next week:
![P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6](https://tex.z-dn.net/?f=P%28x%3E14%29%3D%5Cint_%7B14%7D%5E%7B20%7D%20f%28x%29%5C%2C%20dx%5C%5C%5C%5CP%28x%3E14%29%3D%5Cint_%7B14%7D%5E%7B20%7D%20%5Cfrac%7B1%7D%7B10%7D%20%5C%2C%20dx%5C%5C%5C%5CP%28x%3E14%29%3D%5Cfrac%7B1%7D%7B10%7D%20%5Bx%5D_%7B14%7D%5E%7B20%7D%5C%5C%5C%5CP%28x%3E14%29%3D%5Cfrac%7B6%7D%7B10%7D%5C%5C%5C%5CP%28x%3E14%29%3D0.6)
You have 9:30am classes three times a week. So, we get:

Therefore, the probability is P=0.216.
e) We calculate the probability that you are late to at least one 9am class next week:
![P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1](https://tex.z-dn.net/?f=P%28x%3E9.5%29%3D%5Cint_%7B10%7D%5E%7B20%7D%20f%28x%29%5C%2C%20dx%5C%5C%5C%5CP%28x%3E9.5%29%3D%5Cint_%7B10%7D%5E%7B20%7D%20%5Cfrac%7B1%7D%7B10%7D%20%5C%2C%20dx%5C%5C%5C%5CP%28x%3E9.5%29%3D%5Cfrac%7B1%7D%7B10%7D%20%5Bx%5D_%7B10%7D%5E%7B20%7D%5C%5C%5C%5CP%28x%3E9.5%29%3D1)
Therefore, the probability is P=1.
Answer:
g(x) = (-1/25)x + (203/25)
Step-by-step explanation:
The general equation for a line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
We know that perpendicular lines have opposite-signed, reciprocal slopes of the original line. Therefore, if the slope of f(x) is m = 25, the slope of g(x) must be m = (-1/25).
To find the y-intercept, we can use the newfound slope and the values from the given point to isolate "b".
g(x) = mx + b <----- General equation
g(x) = (-1/25)x + b <----- Plug (-1/25) in "m"
8 = (-1/25)(3) + b <----- Plug in "x" and "y" from point
8 = (-3/25) + b <----- Multiply (1/25) and 3
200/25 = (-3/25) + b <----- Covert 8 to a fraction
203/25 = b <----- Add (3/25) to both sides
Now that we know both the values of the slope and y-intercept, we can construct the equation of g(x).
g(x) = (-1/25)x + (203/25)
The standard form is:

Degree = 5, leading coefficient=4
The 5th degree polynomial is:
Quintic function
it is a trinomial
<u>What is standard form of a polynomial?</u>
When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.
So, standard form is:

To find the degree of the polynomial, add up the exponents of each term and select the highest sum ( if there are more than 1 variable in single term) or highest power of variable
Degree = 5
In a polynomial, the leading term is the term with the highest power of x.
So, leading coefficient=4
The 5th degree polynomial is:
Quintic function
It has 3 terms. so, it is a trinomial
To learn more about the standard form of a polynomial from the given link
brainly.com/question/26552651
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