Answer:
1. The equation is solved by the graphed systems of equations is:
Third option: 7x + 3 = x − 3
2. The solution to the system is:
Fourth option: (3,-1)
3. The graph of the system y = −2x + 3 and 2x + 4y = 8 is:
Third option: Line through point (0, 3) and (1, 1). Line through (0, 2) and (4, 0).
4. The solution to the system is:
Second option: Infinite solutions.
5. Bill will have read the same amount of books as Mandy in:
Fourth option: December
Step-by-step explanation:
Question 1. What equation is solved by the graphed systems of equations?
Two linear equations that intersect at the point (-1, -4)=(x,y)→x=-1, y=-4
a. 7x + 3 = x + 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x+3-x=x+3-x
6x+3=3
Subtracting 3 both sides of the equation:
6x+3-3=3-3
6x=0
Dividing both sides of the equation by 6:
6x/6=0/6
Dividing:
x=0 different to the intersection at x=-1, then this is not the equation.
b. 7x − 3 = x − 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x-3-x=x-3-x
6x-3=-3
Adding 3 both sides of the equation:
6x-3+3=-3+3
6x=0
Dividing both sides of the equation by 6:
6x/6=0/6
Dividing:
x=0 different to the intersection at x=-1, then this is not the equation.
c. 7x + 3 = x − 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x+3-x=x-3-x
6x+3=-3
Subtracting 3 both sides of the equation:
6x+3-3=-3-3
6x=-6
Dividing both sides of the equation by 6:
6x/6=-6/6
Dividing:
x=-1 equal to the intersection at x=-1, then this is the equation.
d. 7x − 3 = x + 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x-3-x=x+3-x
6x-3=3
Adding 3 both sides of the equation:
6x-3+3=3+3
6x=6
Dividing both sides of the equation by 6:
6x/6=6/6
Dividing:
x=1 different to the intersection at x=-1, then this is not the equation.
Question 2 (Multiple Choice Worth 2 points) (06.03) Solve the system 2x + 3y = 3 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
The solution to the system is (3, -1) Fourth option
Please, see the attached graph.
Question 3 (Multiple Choice Worth 2 points) (06.03) What is the graph of the system y = −2x + 3 and 2x + 4y = 8?
Third option: Line through point (0, 3) and (1, 1). Line through (0, 2) and (4, 0).
Please, see the attached graph.
Question 4 (Multiple Choice Worth 2 points) (06.03) Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
Second option: Infinite solutions.
Please, see the attached graph.
Question 5 (Multiple Choice Worth 2 points) (06.03) At the end of April, Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?
Bill
Month Books
May 4
June 8
July 12
August 16
September 20
October 24
November 28
December 32
Books read by Mandy: y=16+2x
Numbers of months since april: x
May: x=1→y=16+2(1)=16+2→y=18 different to 4 (books read by Bill)
June: x=2→y=16+2(2)=16+4→y=20 different to 8 (books read by Bill)
July: x=3→y=16+2(3)=16+6→y=22 different to 12 (books read by Bill)
September: x=5→y=16+2(5)=16+10→y=26 different to 20 (books read by Bill)
October: x=6→y=16+2(6)=16+12→y=28 different to 24 (books read by Bill)
November: x=7→y=16+2(7)=16+14→y=30 different to 28 (books read by Bill)
December: x=8→y=16+2(8)=16+16→y=32 equal to 32 (books read by Bill)
Answer. Fourth option: December
An integer is close to zero if it is "small".
By small, we mean that it is small in absolute value. In fact, for any given distance , there are two integers that are
units away from zero:
and
.
So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.
So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.
Answer:
Step-by-step explanation:
From Bayes' theorem is stated mathematically as the following equation:[2]
{\displaystyle P(A\mid B)={\frac {P(B\mid A)\,P(A)}{P(B)}},}
where A and B are events and P(B) ≠ 0.
P(A) and P(B) are the probabilities of observing A and B without regard to each other.
P(A | B), a conditional probability, is the probability of observing event A given that B is true.
P(B | A) is the probability of observing event B given that A is true.
At this point, go through the attached file before you continue with part B.
Part B)
P(silver) = P(silver from SS)+P(silver from GS)
note P(SS)=P(GG)=P(GS) = 1/3
P(silver from SS) = 1
P(silver from GS) = 1/2
hence
P(Silver from SS) = 1/3
P(Silver from GS) = 1/3 *1/2
P(Silver) = 1/3*1+1/3*1/2
required probability = P(Silver from SS)/P(Silver) = 2/3
