Answer:
p = 5/7
Step-by-step explanation:
The given function is:
for -4 ≦ x < 1
for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
The point where g(x) starts during the second interval is:
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p = 
Thus the value of p for which g(x) will be continuous is .
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
Substituting the point identified in part (a) i.e. x=1, we get:
This value agrees with the answer found in previous part.
Answer:
44x + 54
Step-by-step explanation:
The nth term of an arithmetic sequence is given by :
Tn = a + (n - 1)d
d = common difference = T2 - T1
d = T2 - T1
a = first term = - x + 9
d = 4x + 14 - (-x + 9)
d = 4x + 14 + x - 9
d = 5x + 5
The 10th term:
T(10) = (-x + 9) + (10 - 1)*(5x + 5)
T(10) = - x + 9 + 9(5x + 5)
T(10) = - x + 9 + 45x + 45
T(10) = 44x + 54
Hence, the 10th term is 44x + 54
1
a= 6/12 or one half.
b= 1/2 , one half.
step by step:
multiply the top numbers by eachothers
do the same with the bottom.
Answer:
The players expectation is -0.1052
Step-by-step explanation:
Consider the Roulette numbers to from 1-36, also the two green zeroes 0 and 00,
Thus, there are 38 places on which the ball can land.
On first 36 numbers, 12 of them are divisible by 3. Also there are 26 numbers which are not divisible by 3.
The probability of a wager winning is: 12/38 or 6/19
Now the probability of a wager to loss is: 26/38 or 13/19
So for a 6/19 chance of winning $4 and a 13/19 chance of losing $2.
Therefore, the expected outcome is:
4 × 6/19 + -2 × 13/19 = 1.2632 - 1.3684 = -0.1052
The expected value comes up with a negative sign. Hence, he will lose money.
The players expectation is -0.1052
Bender fine we those. W td
