Answer:
There are 10 counters in the bag and you want the 4
As their is only one for the probability is
1/10
There are now 9 counters left in the bag.
You only want the even ones , which are 2 6 8 and 10 ( four has been taken out)
There are only four even counters in the bag of nine counters so the probability is
4/9
As you want both of these to occur, you need to multiply them
1/10 x 4/9 = 49/90
Step-by-step explanation:
P(A)= 4+5+6= 15/2= 75%
P(B)= 6+4=10 5/10= 50%
P(C)= 5+4=9 6/9= 66.6%
Answer:
Part c: Contained within the explanation
Part b: gcd(1200,560)=80
Part a: q=-6 r=1
Step-by-step explanation:
I will start with c and work my way up:
Part c:
Proof:
We want to shoe that bL=a+c for some integer L given:
bM=a for some integer M and bK=c for some integer K.
If a=bM and c=bK,
then a+c=bM+bK.
a+c=bM+bK
a+c=b(M+K) by factoring using distributive property
Now we have what we wanted to prove since integers are closed under addition. M+K is an integer since M and K are integers.
So L=M+K in bL=a+c.
We have shown b|(a+c) given b|a and b|c.
//
Part b:
We are going to use Euclidean's Algorithm.
Start with bigger number and see how much smaller number goes into it:
1200=2(560)+80
560=80(7)
This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.
Part a:
Find q and r such that:
-65=q(11)+r
We want to find q and r such that they satisfy the division algorithm.
r is suppose to be a positive integer less than 11.
So q=-6 gives:
-65=(-6)(11)+r
-65=-66+r
So r=1 since r=-65+66.
So q=-6 while r=1.
Answer: The discount is $30, making the sale price $270.
Step-by-step explanation: Take your initial value times the percent of your discount to find the discount amount: in this case, it is 300 * .10 = 30. Then you can subtract that value from your initial value, 300-30=270 to get the sale price.
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 2, 3)
m = 
= 
= - 
, thus
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3) , then
3 = 
+ c ⇒ c = 3 - = 
y = - x + ← in slope- intercept form
Multiply through by 3 to clear the fractions
3y = - 2x + 5 ( add 2x to both sides )
2x + 3y = 5 ( subtract 5 from both sides )
2x + 3y - 5 = 0 ← in general form
