Answer:
The solution to the system is 
,
and 
Step-by-step explanation:
Cramer's rule defines the solution of a system of equations in the following way:
, 
and 
where 
, 
and 
are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively. 
is the determinant of the system. Let's see how this rule applies to this system.
The system can be written in matrix form like:
![\left[\begin{array}{ccc}5&-3&1\\0&2&-3\\7&10&0\end{array}\right]\times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}6&11&-13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-3%261%5C%5C0%262%26-3%5C%5C7%2610%260%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%2611%26-13%5Cend%7Barray%7D%5Cright%5D)
Then each of the previous determinants are given by:
Notice how the x-column has been substituted with the answer-column one.
Notice how the y-column has been substituted with the answer-column one.
Then, substituting the values:
If the distance is equal to the counted number of seconds divided by 3, then multiply the distance by 3 to determine the number of counted seconds . . (5 km)(3) = 15 seconds counted between lightning and thunder.
Answer:
Step-by-step explanation:
Enter a problem...
Algebra Examples
Popular Problems Algebra Solve for x 64^(4x)=16^(x+1)
64
4
x
=
16
x
+
1
Create equivalent expressions in the equation that all have equal bases.
4
3
(
4
x
)
=
4
2
(
x
+
1
)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
3
(
4
x
)
=
2
(
x
+
1
)
Solve for
x
.
Tap for fewer steps...
Multiply
4
by
3
.
12
x
=
2
(
x
+
1
)
Simplify
2
(
x
+
1
)
.
Tap for fewer steps...
Apply the distributive property.
12
x
=
2
x
+
2
⋅
1
Multiply
2
by
1
.
12
x
=
2
x
+
2
Move all terms containing
x
to the left side of the equation.
Tap for fewer steps...
Subtract
2
x
from both sides of the equation.
12
x
−
2
x
=
2
Subtract
2
x
from
12
x
.
10
x
=
2
Divide each term by
10
and simplify.
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Divide each term in
10
x
=
2
by
10
.
10
x
10
=
2
10
Cancel the common factor of
10
.
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Cancel the common factor.
10
x
10
=
2
10
Divide
x
by
1
.
x
=
2
10
Cancel the common factor of
2
and
10
.
Tap for fewer steps...
Factor
2
out of
2
.
x
=
2
(
1
)
10
Cancel the common factors.
Tap for fewer steps...
Factor
2
out of
10
.
x
=
2
⋅
1
2
⋅
5
Cancel the common factor.
x
=
2
⋅
1
2
⋅
5
Rewrite the expression.
x
=
1
5
The result can be shown in multiple forms.
Exact Form:
x
=
1
5
Decimal Form:
x
=
0.2
Answer:
the most conservative hypothesis is
<em>H₀</em>: <em>p</em> = 0.18, <em>Hₐ</em>: <em>p</em> > 0.18.
Step-by-step explanation:
The researcher wants to test whether the rate of smoking among adults in Chicago is greater than the national rate of 18% or not.
The hypothesis for this test can be defined as follows:
Null Hypothesis (
): The rate of smoking among adults in Chicago is same as the national rate, i.e. <em>p</em> = 0.18.
Alternate Hypothesis (
): The rate of smoking among adults in Chicago is greater than the national rate, i.e. <em>p</em> > 0.18.
So the most conservative hypothesis is <em>H₀</em>: <em>p</em> = 0.18, <em>Hₐ</em>: <em>p</em> > 0.18.
