Answer:
Step-by-step explanation:
we know that
The number of kWh of energy that the model house generate per year is given by the sum of kWh of energy generates by the windmills multiplied by the number of windmills, plus the kWh of energy generates by the solar panels multiplied by the number of solar panels.
so
For 10 year
Multiply the expression above by 10
Apply distributive property
First, note that Then
Consider all options:
A.
By the definition,
Now
Option A is true.
B.
By the definition,
Then
Option B is false.
3.
By the definition,
Now
Option C is false.
D.
By the definition,
As you can see and option D is not true.
E.
By the definition,
Then
This option is false.
Answer:
s = 21.33*π in
Step-by-step explanation:
Given:
- The complete data is given in the figure (attached):
Solution:
- The bugs lands on the end of the wiper blade furthest to the pivot. The arc length (s) swept by a wiper in one cycle i.e θ = 120° would be given by:
s = 2*r*θ
- Where, r: The distance between the bug and the pivot = 16 in
θ : Angle swept in radians
- The distance travelled by the bug is s:
s = 2*(16)*( 120 / 180 ) * π
s = 21.33*π in
Answer:
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Step-by-step explanation:
We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of Americans who decide to not go to college = 48%
n = sample of American adults = 331
p = population proportion of Americans who decide to not go to
college because they cannot afford it
<em>Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.</em>
<em />
<u>So, 90% confidence interval for the population proportion, p is ;</u>
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < < 1.645) = 0.90
P( <
<
) = 0.90
P( < p <
) = 0.90
<u>90% confidence interval for p</u> = [ ,
]
= [ ,
]
= [0.4348, 0.5252]
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.
3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.
So, the margin of error =
= 54.79
n =
n = 3001.88 ≈ 3002
Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.