Practice Interim Assessment 1

Midpoint

• Point Q is the midpoint of segment PR, meaning it divides the segment into two equal halves.
• PR = 21.75 yards, therefore QR = 21.75 / 2 = 10.875 yards.

Angle Bisectors

• Ray BC bisects angle ABD, dividing it into two congruent angles.
• If angle ABD measures 78 degrees, then angle CBD measures 78 / 2 = 39 degrees.

Adjacent Angles

• Angles RTG and GTU are adjacent because they share a common side and vertex.
• The sum of adjacent angles equals the measure of the larger angle.
• Angle RTU is the sum of angles RTG and GTU, making it 5.8 + 113.6 = 119.4 degrees.

Area Estimation

• The city is approximately a rectangle with a length of 7 units and a width of 5 units, making an approximate area of 35 square units.
• Each unit represents 5 miles, so the estimated area is 35 square units * 25 square miles/square unit = 875 square miles.

City Population Changes

• The city's current population is 875 square miles * 11,172 people/square mile = 9,796,600 people.
• In ten years, the city is expected to have 875 square miles * 9,500 people/square mile = 8,312,500 people.
• The expected population decrease is 9,796,600 - 8,312,500 = 1,484,100 fewer people.

Maximum Capacity

• The maximum capacity of the gym is 2 students per square yard.
• The area of the gym is 30 * 20 = 600 square yards.
• The maximum number of students is 600 square yards * 2 students/square yard = 1200 students.

Converse Statement

• The converse of the conditional statement "If ray BC bisects ∠𝐴𝐵𝐷, then the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are equal," is: "If the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are equal, then ray BC bisects ∠𝐴𝐵𝐷."

Congruent Segments

• Segments KL and ST are congruent when they have the same length.
• Therefore, 8x - 17 = -2x + 18.
• Combining like terms, we get 10x = 35, so x = 3.5.

Segment Length

• Point P lies on segment QR, dividing it into two parts.
• If QP = 4x + 5 feet and PR = x + 2 feet, and QR = QP + PR, then QR = 5x + 7 feet.
• To find x, we use the given QP = 17 feet, so 4x+5 = 17 feet.
• Solving for x: 4x = 12 feet, x = 3 feet.
• Therefore, QR = 5(3) + 7 = 22 feet.

Linear Pair

• Angles ABC and CBD are a linear pair because they are adjacent, and their non-common sides form a straight line.
• The sum of a linear pair equals 180 degrees.
• If angle CBD measures 90 degrees then angle ABC measures 180 - 90 = 90 degrees.

Vertical Angles

• Angles UYF and FY'T are vertical angles because they are formed by the intersection of two lines and share a common vertex.
• Vertical angles are congruent (have equal measures).
• If angle UYF measures 42 degrees, then angle FY'T also measures 42 degrees.

Angle Measurement

• The sum of the angles around a point equals 360 degrees.
• The total measure of angles x, y, and z is 360 degrees.
• If x = 65 degrees and y = 75 degrees, then z = 360 - 65 - 75 = 220 degrees degrees.

Proof

• The given equation is 5t - 2 = 13.
• To isolate the variable "t," we need to use the addition property of equality by adding 2 to both sides of the equation.
• This results in 5t = 15.
• Finally, to solve for "t," we can utilize the division property of equality by dividing both sides of the equation by 5.
• This gives us t = 3.

Relative Frequency

• The relative frequency of surveyed students who prefer yellow as the common room color given that they are juniors is 0.18.
• This is found by dividing the joint relative frequency of juniors who prefer yellow (0.18) by the marginal relative frequency of juniors (0.48).
• 0.18 / 0.48 = 0.375.

Association

• There is an association between seniors and a preferred common room color of white.
• Seniors are more likely to choose white than the overall survey population is likely to choose white (0.33 compared to 0.48).

Probability

• The probability of a person who shops on Monday preferring peas is 0.16.
• The probability of a person who shops on Tuesday preferring corn is 0.17.
• Therefore, it is more likely that a person who shops on Tuesday prefers corn than a person who shops on Monday prefers peas.

Standard Deviation

• The standard deviation for sculpture G is greater than the standard deviation for sculpture H.
• This can be determined because the distribution of sculpture G is more spread out than the distribution of sculpture H.

Data Set Analysis

• The data set for Street S has a smaller median number of bags than Street T. This is because the center of the data set is located more to the left for Street S than for Street T.
• Street S and Street T have the same interquartile range for the number of bags put out for leaf collection. This means that the spread of the middle 50% of the data is the same for both streets.

Mean

• The mean of a set of data is calculated by summing all of the values and then dividing by the number of values. The sum of the given data set is 107.
• Therefore, the mean is 107 / 10 = 10.7.

Dot Plots

• The standard deviation of data set A is greater than the standard deviation of data set B.
• This is because the data in data set A is more spread out than the data in data set B. However, the median is the same for both data sets because the distribution is symmetrical.