Answer:
Use y + x = 3 and solve for either x or y.
Step-by-step explanation:
Substitution is a method to solve a system of equations by substituting an expression from one equation into the other.
To begin, first solve one equation by isolating for one variable. Choose the equation which will have the least number of steps to do so.
y + x = 3 can be solve for x or y by subtracting the other variable. Since this only requires one step use this equation. Either variable can be used.
Answer:
Step-by-step explanation:
given that
A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.
Each box of cereal is supposed to contain 13 ounces of cereal.
A random sample of 31 boxes is tested.
The average weight is 12.58 ounces and the standard deviation is 0.25 ounces.
Sample mean = 12.58
Sample std deviation = 0.25
Sample size = 31
Sample std error = 
confidence interval can be calculated using t critical value because population sd is not known.
df = 30
t critical for two tailed = 1.697
Margin of error = 
conidence interval = 
Since this does not contain 13 oz. we reject the claim that each box contains exactly 13 oz.
Answer:
Explanation:
First, we must determine the circumference of the paddle wheel.
The formula for the circumference of a circle is:
c
=
2
π
r
Where
r
is the radius of the circle.
However, we know
d
=
2
r
where
d
is the diameter of the circle.
Therefore:
c
=
2
r
π
=
d
π
Substituting
12
ft
for
d
gives a circumference of:
c
=
12
π
ft
The time it takes to complete 1 revolution can be found using the formula:
t
=
d
s
Where:
t
is the time it takes: what we are solving for in this problem.
d
is the distance traveled: we calculated this as
12
π
ft
s
is the speed traveled: from the problem we know this is
7.2
ft
sec
Substituting and calculating
t
gives:
t
=
12
π
ft
7.2
ft
sec
t
=
12
π
ft
sec
7.2
ft
t
=
12
π
ft
sec
7.2
ft
t
=
12
π
sec
7.2
t
=
1
.
¯
6
π
sec
Two find how long it would take for 100 revolutions we can multiply this time by
100
100
×
1
.
¯
6
π
sec
⇒
166
.
¯
6
π
sec
If a number is required for the answer we can use 3.14 as an estimate for
π
giving:
166
.
¯
6
π
sec
⇒
166
.
¯
6
×
3.14
sec
⇒
523
sec
Step-by-step explanation:
, you have
