Answer:
19.44 hours, about 19 hours 26 minutes
Step-by-step explanation:
The exponential equation that describes your caffeine level can be written as ...
c(t) = 120·(1 -0.12)^t . . . . where t is in hours and c(t) is in mg
We want to find t for c(t) = 10, so ...
10 = 120(0.88^t)
10/120 = 0.88^t . . . . . . . divide by 120
log(1/12) = t·log(0.88) . . . take logarithms
t = log(1/12)/log(0.88) ≈ 19.4386
It will take about 19.44 hours, or 19 hours 26 minutes, for the caffeine level in your system to decrease to 10 mg.
Answer:
54
Step-by-step explanation:
Parentheses (14 + 42 - 6) = 50:
⇒ 50/10 + 7²
Exponents 7² = 49:
⇒ 50/10 + 49
Multiplication/division 50/10 = 5:
⇒ 5 + 49
Addition/subtraction: 5 + 49 = 54
⇒ 54
Answer: 312 students purchased a ticket
Step-by-step explanation:
Let x represent the number of raffle tickets sold to parents.
Let y represent the number of raffle tickets sold to students.
The school sold 371 tickets. This means that
x + y = 371
x = 371 - y
The parent tickets cost $6 each and the student tickets cost $1.50 each and the school raised a total of $822. This means that
6x + 1.5y = 822 - - - - - - - -1
Substituting x = 371 - y into equation 1, it becomes
6(371 - y) + 1.5y = 822
2226 - 6y + 1.5y = 822
- 6y + 1.5y = 822 - 2226
- 4.5y = - 1404
y = -1404/-4.5
y = 312
x = 371 - y
x = 371 - 312
x = 59
They rented 18 altogether, it says it in the problem. to find the total bill however
18 x 225
(amount of cabins) x (price each)
18x225
4,050$
Answer:
the height of the rectangular prism is 2cm
Step-by-step explanation:
the question says
volume of a rectangular prism equals 80cm³
the length of the rectangular prism is equals to 20cm
the width of the rectangular prism equals to 2cm
the height of the rectangular prism is unknown ?
solution
to find the height we will use the fomular of finding the volume of a prism
volume of a rectangular prism = length × width × height
80 = 20 × 2 × h
80 = 40h
divide both sides by 40
80/40 = 40h/40
2 = h
h = 2cm
therefore the height of the rectangular prism is 2cm
