Write an equation to model each problem. Solve the equation.
1 answer:
Answer:
1) The equation of the temperature in function of the time is
T(t) = 12 - 2t, with t in hours
The temperature is -4F after 8 hours, so, at P.M.
2) 6.75 = 7.50r
Her rate of deductions is 10% a day.
Step-by-step explanation:
1) This problem can be modeled by a first order equation
T(t) = T(0) + rt
In which T(0) is the temperature at instant zero and r is the rate of growth(r>0) or decline(r<0).
Since at 12 noon, the temperature outside is 12F, T(0) = 12. The temperature drops at the steady rate of 2F an hour, so r = -2.
The equation of the temperature in function of the time is
T(t) = 12 - 2t, with t in hours
The temperature is -4F when
-4 = 12 - 2t
2t = 16
t = 8h
The temperature is -4F after 8 hours, so, at P.M.
2) This problem can be modeled by the following first order equation
P = rP(0).
Where P is her pay, r is the rate of the initial money that Zelly takes home and P(0) is her initial pay.
In hour problem, we have that P = $6.75 and P(0) = $7.50.
So
6.75 = 7.50r
r = 0.9 means that Zelly keeps 90% of her pay. It means that her rate of deductions is 10% a day.
You might be interested in
Answer:
a) 0.1587
b) 0.0475
c) 0.7938
Step-by-step explanation:
Let's start defining our random variable.
X : ''Thickness (in mm) of ancient prehistoric Native American pot shards discovered in a Hopi village''
X is modeled as a normal random variable.
X ~ N(μ,σ)
Where μ is the mean and σ is the standard deviation.
To calculate all the probabilities, we are going to normalize the random variable X.
We are going to call to the standard normal distribution ''Z''.
[(X - μ) / σ] ≅ Z
We normalize by subtracting the mean to X and then dividing by standard deviation.
We can find the values of probabilities for Z in a standard normal distribution table.
We are going to call Φ(A) to the normal standard cumulative distribution evaluated in a value ''A''
a)
Φ(-1) = 0.1587
b)
1 - Φ(1.666) = 1 - 0.9525 = 0.0475
c)
Φ(1.666) - Φ(-1) = 0.9525 - 0.1587 = 0.7938