Let p represent the proportion of the population. <span>
Given p=0.60, n=200 we need to calculate
P(^p<0.58).
</span>
According to the rule of thumb, since n*p = 200*0.60
and n*(1-p)= 200*(1-0.60) = 80, both values exceed 5, confirming that n is large enough for the sampling distribution of sample
proportion-^p to comply with the z standard normal distribution. The mean for the sampling distribution will be U^p = p =
0.60, and the standard deviation, δ^p = √[p*(1-p)/n] =
√[0.60*(1-0.60)/200] = √0.0012.
Thus, the probability that the sample proportion
is below 0.58
= P(^p<0.58)
= P{[(^p-U^p)/√[p*(1-p)/n]<[(0.58-0.60)/√0...
= P(z<-0.58)
= P(z<0) - P(-0.58<z<0)
= 0.5 - 0.2190
= 0.281
<span>Thus, the likelihood that the
sample proportion is smaller than 0.58 stands at 0.281 or 28.1%.</span>
Answer: 
Step-by-step explanation:
To determine time "t", we know that:
Where "d" denotes distance, "r" signifies rate, and "t" means time.
Now isolating the time "t":
Initially, we convert miles into feet.
Since 
, thus
Recognizing that:
We substitute these values into to find time in seconds:
Given:
The resulting time in minutes is:
Answer:
The cost difference per mile between the two companies is $0.12.
Step-by-step explanation:
Gabi formulates the equation 
to determine after how many miles, denoted as m, the charges of both companies will be equal.
The first company levies 
for m miles traveled.
The second company's charge for the same m miles is 
.
In these equations, the figures 7.20 and 8.40 signify the initial fees the companies impose.
The values 0.22 and 0.1 represent the respective costs per mile.
As such, the disparity in per-mile charges amounts to 
.
An alternative method to tackle this problem is by calculating the per-mile rate for each company:
1. Cost per mile for the first company
2. Cost per mile for the second company
3. The difference:
The correct response is:
3 inches rise for every foot in length
Explanation:
To derive the rate of change, we need to compute the difference in height and the difference in distance. The rate of change is expressed as rise/run, or
(change in height)/(change in length).
The respective heights at the specified points are 18 inches and 12 inches, resulting in a change of 18-12 = 6 inches.
The corresponding lengths at those points are 6 feet and 4 feet, yielding a change of 6-4 = 2 feet.
This implies our rate of change is (6 inches)/(2 feet), which simplifies to (3 inches)/(1 foot), indicating a rise of 3 inches for each foot of incline on the driveway.
