Answer:
0.284
Step-by-step explanation:
To carry out this calculation, we begin by describing the sampling distribution of the sample proportion.
The sample size is n = 50 and the population proportion of teachers who made an apparel purchase is 0.56.
Shape: Because np = (50)(0.56) = 28 and n(1 – p) = (50)(0.44) = 22 are both at least 10, the shape of the sampling distribution of the sample proportion is approximately Normal.
Center:
μ
p
^
=
p
=
0
.
5
6
μ
p
^
=p=0.56
Variability: The standard deviation of the sample proportion is approximately
(
0
.
5
6
)
(
0
.
4
4
)
5
0
≈
0
.
0
7
0
2
50
(0.56)(0.44)
≈0.0702.
P(
p
^
p
^
> 0.6) = Normalcdf(lower: 0.6, upper: 1000, mean: 0.56, SD: 0.0702) = 0.284.
P
(
p
^
>
0
.
6
)
=
P
(
z
>
0
.
6
−
0
.
5
6
0
.
0
7
0
2
)
=
P
(
z
>
0
.
5
7
)
=
1
−
0
.
7
1
5
7
=
0
.
2
8
4
3
P(
p
^
>0.6)=P(z>
0.0702
0.6−0.56
)=P(z>0.57)=1−0.7157=0.2843
Answer:
9/16
Step-by-step explanation:
Answer:
f^-1(x) = (x +5)/3
also = 1/3 x + 5/3
Step-by-step explanation:
Just to be clear, the ^-1 has nothing to do with negative exponents. It just unfortunately looks the same as a negative exponent.
Anyway, there's three basic steps. First write y instead of f(x). Then switch the x and y. Then solve for y.
f(x) = 3x - 5
write y in place of f(x).
y = 3x - 5
SWITCH x and y.
x = 3y - 5
SOLVE for y.
-3y + x = -5
-3y = -x - 5
y = (-x - 5)/-3
y = (x + 5)/3
OR
y = (1/3)x + 5/3
f^-1(x) = 1/3 x + 5/3
Step-by-step explanation:
<em>Vamsi is X years old</em>
Vamsi = X
<em>his brother is 3 years elder to him</em>
Brother = X + 3
<em>his uncle is 4 times his age</em>
Uncle = 4X
<em>his aunt is 5 years younger than his uncle</em>
Aunt = Uncle - 5
<em>what will be the age of his uncle 6 years from now</em>
= 4X + 6
<em>what are the ages of vamis brother, uncle and aunt?</em>
Assume Vamis = 15 years
Brother = X + 3 = 15 + 3 = 18
Uncle = 4X = 4 * 15 = 60
Aunt = Uncle - 5 = 60 - 5 = 55
<em>what will be the age of his uncle 6 years from now</em>
Uncle = 4X + 6 = 60 + 6 = 66
Equivalent means they are equal.
14.1x+b = 4.7(3x-3.5)
Solve for b. First subtract 15.1x to both sides.
b = 4.7(3x-3.5) - 14.1x
You can simplify by distributing the 4.7 and combining like terms.
b = 14.1x - 16.45 - 14.1x
The positive and negative 14.1x cancel each other out.
b = -16.45
