Answer:
C=14
Step-by-step explanation:
To find the minimum value, graph each of the inequalities. After graphing each inequality, test a point and shade the region that satisfies the inequality. Once all inequalities have been shaded, find the region where they all overlap. The region will be bounded by intersection points. Test each of these points into C=x+3y. The least value for C is the minimum.
(14,0) (0,17.5) (3.08,3.64)
C=14+3(0) C=0+3(17.5) C=3.08 + 3(3.64)
C=14 C=52.5 C=14
Answer:
x = 12
y = 13
Step-by-step explanation:
Let's assume the two numbers as x and y.
The sum of the two numbers is 25
So,
The product of the two numbers is 156
- xy = 156
- x(25 - x) = 156
- 25x - x² = 156
- x² - 25x + 156 = 0
- x² - 13x - 12x - 156 = 0
- (x - 12) • (x - 13) = 0
- x - 13 = 0
- x = 13
- x - 12 = 0
- x = 12
Hence, the two numbers are 13 and 12.
Answer:
287 miles
Step-by-step explanation:
The base fee was $17.99 and an additional 76 cents ($0.76) for every mile.
We can represent the amount he will pay for rent with the equation below:
C = 17.99 + 0.76m
where m = number of miles driven
Jim paid $236.11, therefore:
236.11 = 17.99 + 0.76m
0.76m = 236.11 - 17.99
0.76m =218.12
m = 218.12 / 0.76 = 287 miles
Jim drove 287 miles.
The expected length of code for one encoded symbol is

where
is the probability of picking the letter
, and
is the length of code needed to encode
.
is given to us, and we have

so that we expect a contribution of

bits to the code per encoded letter. For a string of length
, we would then expect
.
By definition of variance, we have
![\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BL%5D%3DE%5Cleft%5B%28L-E%5BL%5D%29%5E2%5Cright%5D%3DE%5BL%5E2%5D-E%5BL%5D%5E2)
For a string consisting of one letter, we have

so that the variance for the length such a string is

"squared" bits per encoded letter. For a string of length
, we would get
.
Answer:
The correct option is (c).
Step-by-step explanation:
The given number is -0.904.
We need to represent the number in scientific notation.
Any number can be written in scientific notation as follows :

Where
a is a real number and b is an integer
We can write it as follows :

Hence, the correct option is (c).