Answer:
D.
Combination; number of ways = 10
Step-by-step explanation:
Permutation is when order matters
Combinations is when order doesn't matter.
Since there are two identical gift cards, it doesn't matter who gets the first gift card and who gets the second gift card, so this is a combination
There are 5 people choose 2
n!
--------
r!(n − r)!
where n is the number of items and r is how many we choose
5! 5*4*3*2*1
-------- = ------------------ = 10
2! (5-2)! 2*1 ( 3*2*1)
D.
Combination; number of ways = 10
Answer:
cos^(-1)(12/13) = 22.62°
Step-by-step explanation:
Inverse trig functions are used to find angles. I was taught SOH CAH TOA: sine = opposite/hypotenuse, cosine = adjacent / hypotenuse, tan = opposite / adjacent.
Here, we have an adjacent side length and the hypotenuse. So we use inverse cosine.
Answer:
8( 3x+2y) ( 9x^2 -6xy +4y^2)
Step-by-step explanation:
216x^3 + 64y^3
Factor out the greatest common factor of 8
8( 27x^3 +8y^3)
Rewriting
8 ( (3x)^3 + (2y)^2))
Recognizing this as the difference of cubes)
a^3 + b^3 = (a+b) (a^2-ab+b^2)
8 ( (3x)^3 + (2y)^2)) = 8( 3x+2y) ( 9x^2 -(3x)(2y) +4y^2)
=8( 3x+2y) ( 9x^2 -6xy +4y^2)
Answer:
The dependent variable depends on the independent variable.
Step-by-step explanation:
- The variable whose values are deliberately changed by the researcher in order to obtain the desired outcome is called independent variable...
- The values of the independent variable can be changed as per requirement, by the researcher...
- Manipulation can be done in the values of independent variable, but the researcher observes the value of a dependent variable during an experiment.
- An independent variable is a presumed cause whereas dependent variable is a measured effect.
- In a simple linear regression, ‘y’ denotes dependent variable while ‘x’ denotes independent variable, which means y depends on x
Answer:
d) 
Step-by-step explanation:
b) 
This expression is not equivalent, as the original expression, 
, has 9 multiplied to 
instead of y. You can interchange values like this when it comes to addition, but not multiplication.
c) 
This expression is also not equivalent. After opening up the parentheses, it would again result in y being multiplied to .
d)
This expression is equivalent, as 9 and are still being multiplied together and y is added to the product. We can actually rearrange this to look like the original expression:
I hope this helps!
