Answer
Construction Model Stats
User
Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
ChatGPT
To find the mean, we add up all the values and divide by the number of values:
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
User
The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.
ChatGPT
We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:
tan(18 degrees) = h / d
Solving for h, we get:
h = d * tan(18 degrees)
Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:
h = 510 feet * tan(18 degrees)
h ≈ 157.3 feet
Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.
User
The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.
Which of the following is the best approximation for its perimeter?
(1) 68 inches
(3) 84 inches
(2) 75 inches
(4) 180 inches
ChatGPT
To find the perimeter of a regular polygon with n sides, we can use the formula:
Perimeter = n * s
where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.
In a regular polygon with n sides, the interior angle at each vertex is given by:
Interior angle = (n - 2) * 180 degrees / n
In a 15-sided polygon, the interior angle at each vertex is:
(15 - 2) * 180 degrees / 15 = 156 degrees
If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:
sin(78 degrees) = 12 / (1/2 * s)
s = 2 * 12 / sin(78 degrees)
s ≈ 2.17 inches
Finally, we can find the perimeter of the polygon:
Perimeter = 15 * s
Perimeter ≈ 32.55 inches
Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.
Answer:
To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.
Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:
$69,500 / 26 = $2,673.08
Her total deductions from her most recent paycheck were:
$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85
So her net pay was:
$2,673.08 - $812.85 = $1,860.23
To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:
($1,860.23 / $2,673.08) x 100 ≈ 69.59%
Therefore, the closest option is (3) 69.59%.