195=67+(200-67)e^(-10k)
195=67+133e^(-10k)
128=133e^(-10k)
128/133=e^(-10k)
ln(128/133)=-10k
k=-ln(128/133)/10
T(t)=67+133e^(tln(128/133)/10), if T(t)=180
180=67+133e^(tln(128/133)/10)
113=133e^(tln(128/133)/10)
113/133=e^(tln(128/133)/10)
ln(113/133)=tln(128/133)/10
10ln(113/133)=tln(128/133)
t=10ln(113/133)/ln(128/133)
t≈42.5 minutes...
t≈40 minutes (to nearest 5 minutes? :P)
Answer:
It is a simple interest account
Step-by-step explanation:
As we might see from the given earnings, the amount of money he earned each year is the same as in the previous year. This means that the amount of money is growing linearly instead of exponentialy. This is characteristic to a simple interest account, which is found by using the formula:
I=Prt
where I = interest earned.
P = principal
r = Interest rate
t = time in years,
if we use this formula to calculate the amount of money earned after t years, we can see it will be the same as the values reported:
I=$300(0.02/year)(1year)=$6
I=$300(0.02/year)(2years)=$12
I=$300(0.02/year)(3years)=$18
So this simple interest account.
<h3>Answer:</h3>
x = -2
<h3>Explanation:</h3>
The line represents the output value (y) for a given input value (x). Where the lines cross, the output values are equal. These lines cross at x=-2.
We are given the functions:
<span>S (p) = 40 + 0.008 p^3 --->
1</span>
<span>D (p) = 200 – 0.16 p^2 --->
2</span>
T o find for the price in which the price of supply equals
demand, all we have to do is to equate the two equations, equation 1 and 2, and
calculate for the value of p, therefore:
S (p) = D (p)
40 + 0.008 p^3 = 200 – 0.16 p^2
0.008 p^3 + 0.16 p^2 = 160
p^3 + 20 p^2 = 20,000
p^3 + 20 p^2 – 20,000 = 0
Calculating for the roots using the calculator gives us:
p = 21.86, -20.93±21.84i
Since price cannot be imaginary therefore:
p = 21.86
Answer:
Answer:
Option B is correct.
Miguel should study for the Science quiz as he will do worse in that quiz by guessing.
Step-by-step explanation:
Miguel has to take two quizzes
1) 4 true or false questions on History with a 0.5 chance of acing the quiz
Expected number of correct questions = np
n = number of questions
p = probability of acing the test
Expected number of correct questions = 4 × 0.5 = 2
2) 3 multiple choice questions on Science with a 0.2 chance of acing the quiz.
Expected number of correct questions = 0.2 × 3 = 0.6
It is evident that guessing would yield a worse result in the Science quiz with less than 1 question expected to be correct than history, where he is still expected to get 2 questions correctly by guessing.
