Answer:
Graph number 1
Step-by-step explanation:
According to the equation the y-intercept is 2. The only graph with the y-intercept of (0,2) is the first graph. So, graph number 1 represents the function.
Answer:If you would like to know what will the approximate population be after 3 years, you can calculate this using the following steps:
an initial population ... 298 quail
an annual rate ... 8%
an exponential function to model the quail population:
f = 298(1+8%)^t = 298(1+8/100)^t
f ... quail population
t ... time (years)
t = 3 years
f = 298(1+8/100)^t = 298(1.08)^3 = 375.4 quail
375.4 quail after 3 years.
Since the opposite operation of addition is subtraction you subtract. So you add 14 both sides and now z is by itself. finally just add 2 and 14 which is 16
Answer:-10
Step-by-step explanation: The slope-intercept form is
y
=
m
x
+
b
y
=
m
x
+
b
, where
m
m
is the slope and
b
b
is the y-intercept.
y
=
m
x
+
b
y
=
m
x
+
b
Find the values of
m
m
and
b
b
using the form
y
=
m
x
+
b
y
=
m
x
+
b
.
m
=
−
6
m
=
-
6
b
=
−
10
b
=
-
10
The slope of the line is the value of
m
m
, and the y-intercept is the value of
b
b
.
Slope:
−
6
-
6
y-intercept:
−
10
Answer:
(a) ¬(p→¬q)
(b) ¬p→q
(c) ¬((p→q)→¬(q→p))
Step-by-step explanation
taking into account the truth table for the conditional connective:
<u>p | q | p→q </u>
T | T | T
T | F | F
F | T | T
F | F | T
(a) and (b) can be seen from truth tables:
for (a) <u>p∧q</u>:
<u>p | q | ¬q | p→¬q | ¬(p→¬q) | p∧q</u>
T | T | F | F | T | T
T | F | T | T | F | F
F | T | F | T | F | F
F | F | T | T | F | F
As they have the same truth table, they are equivalent.
In a similar manner, for (b) p∨q:
<u>p | q | ¬p | ¬p→q | p∨q</u>
T | T | F | T | T
T | F | F | T | T
F | T | T | T | T
F | F | T | F | F
again, the truth tables are the same.
For (c)p↔q, we have to remember that p ↔ q can be written as (p→q)∧(q→p). By replacing p with (p→q) and q with (q→p) in the answer for part (a) we can change the ∧ connector to an equivalent using ¬ and →. Doing this we get ¬((p→q)→¬(q→p))
