<em>Independent variables are variables of a quantity that are not affected by any conditions. </em>
<em>Dependent variables are variables of a quantity that change if conditions relative to that variable changes.</em>
For example, we generally we take x as independent variable by x variable and dependent variable by y variable.
To find the rate of change we get two values of independent variable (x's) and two values of dependent variables (y's) to get two coordinates in form of
(x,1,y1) and (x2,y2).
<h3>And we can find the rate of change by applying slope formula</h3>
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Answer:
Step-by-step explanation:
13p⁵ + 6p - 12p² -(-9p - p² - 13p⁵) = 13p⁵ + 6p - 12p² + 9p + p² + 13p⁵
{Distribute (-1) to the second expression}
= <u>13p⁵ + 13p⁵</u> <u>-12p² + p²</u> <u>+ 6p + 9p</u>
{Combine like terms}
= 26p⁵ - 11p² + 15p
Answer:
20x² - 43xw + 21w²
Step-by-step explanation:
We use FOIL to expand the expression:
F - First
4x(5x) = 20x²
O - Outside
4x(-7w) = -28xw
I - Inside
-3w(5x) = -15xw
L - Last
-3w(-7w) = 21w²
20x² - 28xw - 15xw + 21w²
Combine like terms and add up using correct signs and you should get your answer.
Answer:
the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287
Step-by-step explanation:
When conducting hypothesis tests, the P value tells you the probability of the results happening by random chance. That's why we usually test against a very low alpha level, usually 1% or 5%.
Here P = 28%, so there is a 28% chance that if we take a sample of athletes, about 1 out of 4 times there won't be a significant difference in GPA between males and females.
Let a, b, and c be the times each pump will fill the tank when working alone.
Therefore, in 1 hour;
1/a +1/b = 1/(6/5) = 5/6 ---- (1)
1/a+1/c = 1/(3/2) = 2/3 ---- (2)
1/b+1/c = 1/(2) = 1/2 ---- (3)
From equation (1)
1/a = 5/6-1/b
Substituting for 1/a in eqn (2)
5/6-1/b+1/c = 2/3
-1/b +1/c = -1/6 => 1/c = 1/b - 1/6 --- (4)
Using eqn (4) in eqn (3)
1/b+1/b-1/6 = 1/2
2/b-1/6 = 1/2
2/b =1/2+1/6 = 2/3
1/b = 1/3
Then,
1/c = 1/3 - 1/6 = 1/6
1/a = 5/6 - 1/3 = 1/2
This means, in 1 hour and with all the pumps working together, the tank will be filled to;
1/a+1/b+1/c = 1/2+1/3+1/6 = 1 (filled fully).
Therefore, it will take 1 hour to fill the tank when all pumps are working together.
