Answer:
y = 5/6x - 5.167
Or
y = 5/6x - 31/6
Step-by-step explanation:
The equation of a line
y = mx + c
Step 1: find the slope
m = y2 - y1 / x2 - x1
Given points
( 0 , -7) ( 5 , -1)
x1 = 0
y1 = -7
x2 = 5
y2 = -1
Insert the values into the equation
m = -1 - (-7) / 5 - 0
m = -1 + 7 / 5
m = 6/5
y = 6/5x + c
Step 2: sub any of the two points given into the equation
y = 5/6x + c
( 5 , -1)
x = 5
y = -1
-1 = 5/6(5) + c
-1 = 5*5/6 + c
-1 = 25/6 + c.
c = -1 - 25/6
LCM = 6
c = -6 - 25 / 6
c = -31/6
c = -5.167
Step 3: sub c into the equation
y = 5/6x + c
y = 5/6x - 31/6
Or
y = 5/6x - 5.167
The equation of the line is
y = 5/6x - 5.167
The inequality would be 3.1h + 2.3b ≥100
Step-by-step explanation:
Earning of Tammy for each hour of work= $3.1
Total hours she worked= h
Earning for picking each bushel of apple= $2.3
Total bushel she picks= b
Her goal = minimum of $100
Hence total earning from working= earning from each hour* no of hours worked
Total earning= 3.1h
Similarly, total earning from picking up apple bushels= earning from picking one bushel*no of bushels picked
Total earning= 2.3b
According to question total earning must be greater than $100
Hence, 3.1h + 2.3b ≥100
Answer:
Q(t) = Q_o*e^(-0.000120968*t)
Step-by-step explanation:
Given:
- The ODE of the life of Carbon-14:
Q' = -r*Q
- The initial conditions Q(0) = Q_o
- Carbon isotope reaches its half life in t = 5730 yrs
Find:
The expression for Q(t).
Solution:
- Assuming Q(t) satisfies:
Q' = -r*Q
- Separate variables:
dQ / Q = -r .dt
- Integrate both sides:
Ln(Q) = -r*t + C
- Make the relation for Q:
Q = C*e^(-r*t)
- Using initial conditions given:
Q(0) = Q_o
Q_o = C*e^(-r*0)
C = Q_o
- The relation is:
Q(t) = Q_o*e^(-r*t)
- We are also given that the half life of carbon is t = 5730 years:
Q_o / 2 = Q_o*e^(-5730*r)
-Ln(0.5) = 5730*r
r = -Ln(0.5)/5730
r = 0.000120968
- Hence, our expression for Q(t) would be:
Q(t) = Q_o*e^(-0.000120968*t)
The answer is yes but its could be false or 6:00
Answer:
a) 
b) 
c) 
Step-by-step explanation:
For this case we have a total of 1254 people. 672 are women and 582 are female.
We know that 124 women wnat on to graduate school.
And 198 male want on to graduate school
We can define the following events:
F = The alumnus selected is female
M= The alumnus selected is male
A= Female and attend graduate school
And we can find the probabilities required using the empirical definition of probability like this:
Part a
Part b
Part c
For this case we find the probability for the event A: The student selected is female and did attend graduate school
And using the complement rule we find P(A') representing the probability that the female selected did not attend graduate school like this:
