Given:
Cost to build a bookshelf = $20
Cost to build a table = $45
Amount available to spend = $600
Let x = number of bookshelves built.
Let y = number of tables built.
The total number of bookshelves and tables = 18.
Therefore
x + y = 18.
That is,
y = 18 - x (1)
The total amount available to build x bookshelves and y tables = $600. Therefore
20x + 45y = 600
That is (dividing through by 5),
4x + 9y = 120 (2)
Substitute (1) into (2).
4x + 9(18 - x) = 120
4x + 162 - 9x = 120
-5x = -42
x = 8.4
From (1),obtain
y = 18 - 8.4 = 9.6
Because we cannot have fractional bookshelves and tables, we shall test values of x=8, 9 and y=9,10 for profit
Note: The profit is $60 per bookshelf and $100 per table.
If x = 8, then y = 18-8 = 10.
The profit = 8*60 + 10*100 = $1480
If x = 9, then y = 18-9 = 9.
The profit = 9*60 + 9*100 = $1440
The choice of 8 bookshelves and 10 tables is more profitable.
Answer: 8 bookshelves and 10 tables.
Answer:
a) P(t>3)=0.30
b) P(t>10|t>9)=0.67
Step-by-step explanation:
We have a repair time modeled as an exponentially random variable, with mean 1/0.4=2.5 hours.
The parameter λ of the exponential distribution is the inverse of the mean, so its λ=0.4 h^-1.
The probabity that a repair time exceeds k hours can be written as:
(a) the probability that a repair time exceeds 3 hours?
(b) the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours?
The exponential distribution has a memoryless property, in which the probabilities of future events are not dependant of past events.
In this case, the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours is equal to the probability that a repair takes at least (10-9)=1 hour.
Answer:
I don't know
Step-by-step explanation:
because I don't see the pattern
Answer:
log_4(256)=4
log_4(1/1024)=-5
log_4(16)=2
log_4(1/256)=-4
Step-by-step explanation:
We want to write a number, x, such that
Log_4(y)=x.
In exponential form that is 4^x=y.
So first number is x=4.
4^4=256 which means log_4(256) is 4 as a logarithm with base 4.
The second number is x=-5.
4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.
The third number is x=2.
4^2=16 so log_4(16) is 2 as a logarithm with base 4.
The fourth number is x=-4.
Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).
