Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of hours of dog walking. Taylor charges $15 for the first hour and $10 for each additional hour. Therefore:
Let g(x) represent how much Taylor charges. Hence:
g(x) = 15 for 0 ≤ x ≤ 1
g(x) = 15 + 10(x - 1) = 15 + 10x - 10 = 10x + 5 for x > 1
g(x) can be represented by the piecewise function:
Lucy charges f(x) is modeled by the piecewise function:
Therefore the charge for walking a dog for 2.5 hours by either Taylor or Lucy is:
For Taylor; f(2.5) = 10(2.5) + 5 = $30
For Lucy; g(2.5) = 10(2.5) = $25
Therefore Taylor charges more by walking a dog for 2.5 hours. Taylors charge is $5 more than Lucy charge ($30 - $25).
Answer:
0.087 = 8.7% probability that this person made a day visit.
0.652 = 65.2% probability that this person made a one-night visit.
0.261 = 26.1% probability that this person made a two-night visit.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Made a purchase.
Probability of making a purchase:
10% of 20%(day visit)
30% of 50%(one night)
20% of 30%(two night).
So
How likely is it that this person made a day visit?
Here event B is a day visit.
10% of 20% is the percentage of purchases and day visit. So
So
0.087 = 8.7% probability that this person made a day visit.
A one-night visit?
Event B is a one night visit.
The percentage of both(one night visit and purchase) is 30% of 50%. So
So
0.652 = 65.2% probability that this person made a one-night visit.
A two-night visit?
Event B is a two night visit.
The percentage of both(two night visit and purchase) is 20% of 30%. So
Then
0.261 = 26.1% probability that this person made a two-night visit.
Answer:
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion (if no previous estimate use 0.5) and M is the desired margin of error.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of .
The margin of error is of:
95% confidence level
So , z is the value of Z that has a p-value of , so .
Needed sample size:
The needed sample size is n. We have that:
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion (if no previous estimate use 0.5) and M is the desired margin of error.
Answer:
15.74% of the player's serves were between 115 mph and 145 mph
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
What percentage of the player's serves were between 115 mph and 145 mph
This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.
X = 145
has a pvalue of 0.9987
X = 115
has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
15.74% of the player's serves were between 115 mph and 145 mph
A total of 27% of the player's serves at the U.S. Open Tennis Championship were between 115mph and 145mph. This was found using the Empirical Rule which applies to a normal distribution of serve speeds.
This problem is a classic example of the use of the Empirical Rule in statistics. The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normal distribution, which is a bell-shaped curve (mound-shaped and symmetric) as mentioned in the problem. This rule states that approximately 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Given that the mean serve speed is 100 mph and the standard deviation is 15 mph, serves of 115 mph are one standard deviation above the mean and serves of 145 mph are three standard deviations above the mean. Therefore, we are looking for the percentage of serves between these two values. According to the Empirical Rule, this would be 95% (coverage for up to 2 standard deviations) minus 68% (coverage for up to 1 standard deviation), which equals 27%. So, 27% of the player's serves were between 115 mph and 145 mph.
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3,7,11,15,19
Answer:
Arithmetic Sequence:
d=4
Step-by-step explanation:
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 4 o the previous term in the sequence gives the next term. In other words, aₙ=a₁+d(n-1)
Answer: The required equation of the ellipse in standard form is
Step-by-step explanation: We are given to find the equation of an ellipse in standard form with the vertical major axis of length 10 units and minor axis of length 8 units.
Since the major axis is vertical, so it will lie on the Y-axis. Let the standard form of the ellipse be given by
where the length of major axis is 2a units and length of minor axis is 2b units.
According to the given information, we have
and
Substituting the values of a and b in equation (i), we get
Thus, the required equation of the ellipse in standard form is
Answer: 5/33
Step-by-step explanation: There are 12 fruits and 5 are oranges.
If you draw an orange, then there are 11 fruits and 4 oranges. (5/12)x(4/11)=20/132 or 5/33 in simplest form.