Question 1

A 100' tape was used to measure a horizontal line found to be 1,500 ft. The tape was then compared with a standard and found to be only 99.97 feet in length. The true length of the measured line is:
A)1,499.00
B)1,499.55 ft
C)1,500.00 ft
D)1,500.45 ft

Accepted Answer

Solution
True length of horizontal line = (measured distance)(steel tape length / standard tape length)
True length = (1,500 ft)(99.97 ft / 100 ft)
True length = 1,499.55 ft

Question 2

Given a triangle with sides a = 20 feet, b = 40 feet, and c = 56, what is the area in square feet? A)71.67 ft ² B)116.00 ft ² C)281.68 ft ² D)None of the above

Accepted Answer

The area of the triangle is 281.68 ft ². Solution Use the formula for the area of a triangle with sides a, b, and c: A = [s(s-a)(s-b)(s-c)]^½ where s = (a + b + c)/2 Where a = 20 ft b = 40 ft c = 56 ft s = (20 ft + 40 ft + 56 ft)/2 = 58 ft A = [58 (58-20)(58 40)(58 56)]^½= 281.68 ft ²

Question 3

Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle. A)105.30 ft ² B)634.3 ft ² C)1,000 ft ² D)1,331.41 ft ²

Accepted Answer

The area of the triangle is 1,331.41 ft ². Solution Use the formula A = 1/2bh Where A = area b = base h = height A = ½ (42.20 ft) (63.10 ft) = 1,331.41 ft ²

Question 4

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12
A)$278.99
B)$268.46
C)$354.22
D)$317.54

Accepted Answer

The mean for the data set above is $268.46. The median or middle number when the numbers are in ascending order ($79.84, $98.12, $111.39, $278.99, $342.16, $466.25, $502.47) is $278.99.

Question 5

What is the median for the following set of numbers? $3.27, $9.42, $6.15, $5.25, $7.62, $4.86, $2.94, $1.16
A)$6.15
B)$4.07
C)$5.45
D)$5.70

Accepted Answer

The median or the middle number when the numbers are in ascending order ($1.16, $2.94, $3.27, $4.86, $5.25, $6.15, $7.62, $9.42) for the set above is $5.70. Whenever there is an even number of entries in a set, putting two numbers in the middle of the ordered entries, those two numbers are averaged to find the median. The mean is about $4.07. There is no mode because each number occurs only one time in the set.

Quiz 1: Mathematics and Statistics

A 100' tape was used to measure a horizontal line found to be 1,500 ft. The tape was then compared with a standard and found to be only 99.97 feet in length. The true length of the measured line is:

Given a triangle with sides a = 20 feet, b = 40 feet, and c = 56, what is the area in square feet?

Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle.

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12

What is the median for the following set of numbers? $3.27, $9.42, $6.15, $5.25, $7.62, $4.86, $2.94, $1.16