A = 4,
we denote one side of the rectangle with
a
, and the other with
b
we can write, that:
a
⋅
b
=
16
so we can write, that
b
=
16
a
Now we can write perimeter
P
as a function of
a
P
=
2
⋅
(
a
+
16
a
)
We are looking for the smallest perimeter, so we have to calculate derivative:
P
(
a
)
=
2
a
+
32
a
P
'
(
a
)
=
2
+
(
−
32
a
2
)
P
'
(
a
)
=
2
−
32
a
2
=
2
a
2
−
32
a
2
The extreme values can only be found in points where
P
'
(
a
)
=
0
P
'
(
a
)
=
0
⇔
2
a
2
−
32
=
0
2
a
2
−
32
=
0
x
a
2
−
16
=
0
×
x
.
.
a
2
=
16
×
×
x
a
=
−
4
or
a
=
4
Since, length is a scalar quantity, therefore, it cannot be negative,
When
a
=
4
,
b
=
16
4
b
=
4
Answer:
A
Step-by-step explanation:
The two angles given are vertical angles because they are opposite of each other
Using it's concept, the range of the given exponential function is:
C. 0 < y ≤ 46638.
<h3>What is the range of a function?</h3>
The range of a function is the set that contains all possible output values for the function.
In this problem, the function is:
y = 46,638(0.78)^x.
It is an exponential function with initial value 46,638 and rate of change 0.78. Exponential functions that are not shifted down, such as this one, are never negative nor zero, hence the range also has the restriction y > 0, and is given by:
C. 0 < y ≤ 46638.
More can be learned about the range of a function at brainly.com/question/28388172
#SPJ1
Jane = x years
Tom = x+8
*5 Years Ago
Jane= x-5
Tom= (x+8)-5=>x+3---------------------------
x+3=3(x-5)<span>x+3=3x-15
3x-x=18
2x=18
x=9
Jane = 9 years
Tome = 9+8 = 17 years</span>
Given Information:
Population proportion = p = 0.55
Sample size 1 = n₁ = 30
Sample size 2 = n₂ = 100
Sample size 3 = n₃ = 1000
Required Information:
Standard error = σ = ?
Answer:
Step-by-step explanation:
The standard error for sample proportions from a population is given by
Where p is the population proportion and n is the sample size.
For sample size n₁ = 30
For sample size n₂ = 100
For sample size n₃ = 1000
As you can notice, the standard error decreases as the sample size increases.
Therefore, the greater the sample size lesser will be the standard error.
