Answer:
n=288
Step-by-step explanation:
Rewrite the equation as
√
n
=
18
√
8
−
8
√
18
.
√
n
=
18
√
8
−
8
√
18
To remove the radical on the left side of the equation, square both sides of the equation.
√n
2
=
(
18
√
8
−
8
√
18
)
2
Simplify each side of the equation.
Use
n
√
a
x
=
a
x
n
to rewrite
√
n as n
1
2
.
(
n
1
2
)
2
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
n
1
2
)
2
.
Multiply the exponents in
(
n
1
2
)
2
.
Apply the power rule and multiply exponents,
(
a
m)n
=
a
m
n
.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Cancel the common factor of 2
Cancel the common factor.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Rewrite the expression.
n
1
=
(
18
√
8
−
8
√
18
)
2
Simplify.
n
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
18
√
8
−
8
√
18
)
2
Simplify each term.
Rewrite
8 as 2
2
⋅
2
.
Factor
4 out of 8
n
=
(
18
√
4
(
2
)
−
8
√
18
)
2
Rewrite
4 as 2
2
n
=
(
18√
2
2
2
−
8
√
18
)
2
Pull terms out from under the radical.
n
=
(
18
(
2
√
2
)
−
8
√
18
)
2
Multiply
2 by 18
n
=
(
36
√
2
−
8
√
18
)
2
Rewrite
18
as
3
2
⋅
2
.
Factor
9
out of
18
.
n
=
(
36
√
2
−
8
√
9
(
2
)
)
2
Rewrite
9
as
3
2
.
n
=
(
36
√
2
−
8
√
3
2
⋅
2
)
2
Pull terms out from under the radical.
n
=
(
36
√
2
−
8
(
3
√
2
)
)
2
Multiply
3
by
−
8
.
n
=
(
36
√
2
−
24
√
2
)
2
Simplify terms.
Subtract
24
√
2
from
36
√
2
.
n
=
(
12
√
2
)
2
Simplify the expression.
Apply the product rule to
12
√
2
.
n
=
12
2
√
2
2
Raise
12
to the power of
2
.
n
=
144
√
2
2
Rewrite
√
2
2
as
2
.
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
n
=
144
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
n
=
144
⋅
2
1
2
⋅
2
Combine
1
2
and
2
.
n
=
144
⋅
2
2
2
Cancel the common factor of
2
.
Cancel the common factor.
n
=
144
⋅
2
2
2
Rewrite the expression.
n
=
144
⋅
2
1
Evaluate the exponent.
n
=
144
⋅
2
Multiply
144
by
2
.
n
=
288
Answer:
Mean is 18
Step-by-step explanation:
We would set up the proportion as X/9=36/X so after we cross multiply we get x^2=324. Then we find the square root of both sides to simplify. ... And the square root of 324 is 18. So the final answer is x=18 or the geometric mean is 18
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;
(the number of times a 4 was rolled)/(total number of rolls)
8/20 = 0.4
0.4*100 = 40%
The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;
P(HT or TH or TT)
The above events are mutually exclusive, thus;
P(HT or TH or TT) = P(HT) + P(TH) + P( TT)
= (22+34+16)/(28+22+34+16)
= 0.72 = 72%
On the other hand, the theoretical probability of obtaining at least one tails,
P(HT or TH or TT) = 3/4
= 75%
This is because there is at least one tail in 3 out of 4 possible outcomes.
Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
To find which cylinder has the greater volume, we need to find out the volume of each one.
As we all know that the formula used to determine the volume of a cylinder is:
V = The base area*the height
<=> V = πh (cubic units)
For example, in my attached photo, we will use this formula to find the volume of each one.
The base area = π = π = 38.46 square in
The height = 8.5 in
=> the volume of Cylinder A
= The base area*the height
= 38.46*8.5
= 326.91 cubic in
The base area = π = π = 22.89 square in
The height = 11 in
=> the volume of Cylinder A
= The base area*the height
= 22.89*11
= 251.79 cubic in
Hence, Cylinder B has the greater volume