Answer:
rate of change = 3
Step-by-step explanation:
to find the rate of change
(0,-4) (1,-1)
= = 3
Answer:
the equation D ) would cause a consistent-independent system.
Step-by-step explanation:
A ) 5 x + y = 7 /*( -2 )
10 x + 2 y = 14
--------------------
- 10 x - 2 y = - 14
10 x + 2 y = 14
------------------------
0 x = 0 ( Dependent system )
B ) 5 x + y = 7 / * 3
- 15 x - 3 y = - 6
--------------------------
15 x + 3 y = 21
- 15 x - 3 y = - 6
-------------------------
0 x = 15 ( Inconsistent system )
C ) 5 x + y = 7
5 x + y = - 7 / * ( - 1 )
---------------------------
5 x + y = 7
- 5 x - y = 7
------------------
0 x = 14 ( Inconsistent system )
D ) 5 x + y = 7 / * ( - 2 )
6 x + 2 y = 7
------------------
- 10 x - 2 y = - 14
6 x + 2 y = 7
-----------------------
- 4 x = - 7; x = 7/4; y = - 7/4
Simplify 1/3(6x - 15) to 6x - 15/3
6x - 15/3 = 1/2(10x - 4)
Factor out the common term; 3
3(2x - 5)/3 = 1/2(10x - 4)
Cancel out 3
2x - 5 = 1/2(10x - 4)
Simplify 1/2(10x - 4) to 10x - 4/2
2x - 5 = 10x - 4/2
Factor out the common term; 2
2x - 5 = 2(5x - 2)/2
Cancel out 2
2x - 5 = 5x - 2
Subtract 2x from both sides
-5 = 5x - 2 - 2x
Simplify 5x - 2 - 2x to 3x - 2
-5 = 3x - 2
Add 2 to both sides
-5 + 2 = 3x
Simplify -5 + 2 to -3
-3 = 3x
Divide both sides by 3
- 1 = x
Switch sides
<u>x = -1</u>
Answer:
Fast ball challenge
Step-by-step explanation:
Given
Slow Ball Challenge
Fast Ball Challenge
Required
Which should he choose?
To do this, we simply calculate the expected earnings of both.
Considering the slow ball challenge
First, we calculate the binomial probability that he hits all 7 pitches
Where
--- pitches
--- all hits
--- probability of hit
So, we have:
Using a calculator:
--- This is the probability that he wins
i.e.
The probability that he lose is:
---- Complement rule
The expected value is then calculated as:
Using a calculator, we have:
Considering the fast ball challenge
First, we calculate the binomial probability that he hits all 3 pitches
Where
--- pitches
--- all hits
--- probability of hit
So, we have:
Using a calculator:
--- This is the probability that he wins
i.e.
The probability that he lose is:
---- Complement rule
The expected value is then calculated as:
Using a calculator, we have:
So, we have:
-- Slow ball
--- Fast ball
<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>
Answer:
The set of all points on a plane equidistant to a given point
Step-by-step explanation:
"following"?