Practice Interim Assessment 1

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Questions and Answers

What is the correct property to use for the second step in the proof of the equation $5t - 2 = 13$?

Addition Property of Equality

Multiplication Property of Equality

Subtraction Property of Equality (correct)

Division Property of Equality

Which property is used in the fourth step of the proof for the equation $5t - 2 = 13$?

Multiplication Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Division Property of Equality (correct)

What is the relative frequency of juniors preferring yellow as the common room color?

0.25

0.15

0.18 (correct)

0.33

Based on the two-way relative frequency table, is there an association between seniors and their preference for the color white?

There is an association because seniors are more likely to choose white. Signup and view all the answers

In the preferred vegetable survey, which day showed a higher preference for corn?

Monday Signup and view all the answers

What is the total relative frequency for carrots according to the preferred vegetable survey?

0.32 Signup and view all the answers

How do the total relative frequencies of the days compare in the vegetable survey?

Monday has a higher total than Tuesday. Signup and view all the answers

What is the relative frequency of surveyed students who prefer gray as the common room color?

0.27 Signup and view all the answers

What is the length in yards of segment QR if point Q is the midpoint of PR and PR = 21.75 yards?

10.875 yards Signup and view all the answers

What is the measure of angle CBD if ray BC bisects ∠ABD and m∠ABD = 78°?

39 degrees Signup and view all the answers

What is the measure of angle RTU if RTG and GTU are adjacent angles with m∠RTG = 5.8° and m∠GTU = 113.6°?

119.4 degrees Signup and view all the answers

What is the best estimate of the area of the city if each unit equals 5 miles and the grid covers approximately 38 units?

190 square miles Signup and view all the answers

What is the maximum number of students that can attend a dance if the gym is 30 yards by 20 yards and the maximum capacity is 2 students per square yard?

1,200 students Signup and view all the answers

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

If the measures of ∠ABC and ∠DBC are equal, then ray BC bisects ∠ABD. Signup and view all the answers

If the lengths of KL and ST are represented by the expressions 8x - 17 and -2x + 18 respectively, for what value of x are the segments congruent?

3 Signup and view all the answers

If m∠CBD = 90°, what is the measure of angle ABC if angles ABC and CBD form a linear pair?

180 degrees Signup and view all the answers

Which statement is correct regarding the preferences of shoppers on Monday and Tuesday?

Monday shoppers prefer peas more than Tuesday shoppers prefer corn. Signup and view all the answers

What can be said about the standard deviations for the time spent looking at the two sculptures?

Sculpture H has a greater standard deviation than Sculpture G. Signup and view all the answers

Based on the data collected for leaf collection day, which statement is likely true?

Street S has a smaller median number of bags than Street T. Signup and view all the answers

What is the mean of the following data set: 6, 8, 16, 4, 17, 26, 8, 5, 5, 5?

11.2 Signup and view all the answers

Which of the following statements must be true regarding the dot plots for data sets A and B?

The median of data set A is equal to the median of data set B. Signup and view all the answers

Which statement accurately describes the interquartile range for the bags put out for leaf collection?

Both streets have the same interquartile range. Signup and view all the answers

In a scenario where one street puts out considerably more bags than the other, which statement could be true?

Street T could have a higher standard deviation than Street S, indicating more variability. Signup and view all the answers

How do the shopping preferences differ between Monday and Tuesday shoppers for vegetables?

Monday shoppers show a broader preference for a variety of vegetables. Signup and view all the answers

Study Notes

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.

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