Answer:
b=4
Step-by-step explanation:
So, we have the function . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
Now, cross multiply.
Solve for b. Factor using the numbers -4 and -2.
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
a) 3(-2) + 4(3) = -6 + 12 = 6
b) 2(-2) -3(3) +5 = -4 -9 + 5 = -8
c) 4(-2) -(3) = -8 -3 = -11
d) -(-2) -2(3) = 4 -6 = -2
e) (1/2)(-2) +(3) = -1 +3 = 2
f) (2/3)(3) -(1/2)(-2) = 2 + 1 = 3
ANSWER
"If x=7, then x - 2 = 5"
EXPLANATION
Let
be a propositional statement.
The converse of this statement is
In other words, the converse of the statement,
"If p then q" is "If q, then p"
The given given conditional statement is
"If x - 2 = 5, then x = 7"
Therefore the converse is
"If x=7, then x - 2 = 5"
Answers:
a) 0.0625
b) 0.9375
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Work Shown:
The probability of landing on heads is 1/2 = 0.5 since both sides are equally likely to land on. Getting 4 heads in a row is (1/2)^4 = (0.5)^4 = 0.0625
The event of getting at least one tail is the complement of getting all four heads. This is because you either get all four heads or you get at least one tail. One or the other must happen. We subtract the result we got from 1 to get 1-0.0625 = 0.9375
You can think of it like this
P(getting all four heads) + P(getting at least one tail) = 1
The phrasing "at least one tail" means "one tail or more".