1.
Now that you have completed the class, what advice would you give for students taking Pre-Algebra next quarter? Write a few sentences... (This question is not graded)
2.
To find the distance across the river (without getting wet) you decide to walk at a right angle, measure this distance, and measure a 45 degree angle back to the point across the river using a compass. What is the distance across the river?
Correct Answer
A. 122 feet
Explanation
To find the distance across the river without getting wet, the person decides to walk at a right angle and measure this distance. This means that they walk perpendicular to the river's bank. Then, they measure a 45-degree angle back to the point across the river using a compass. The fact that they measure a 45-degree angle suggests that they have formed a right triangle with the river being the hypotenuse. In a right triangle, the length of the hypotenuse (the distance across the river) is equal to the length of one of the legs (the perpendicular distance walked). Therefore, the distance across the river is 122 feet.
3.
How far is the police station from your house?
Correct Answer
D. 8 miles
Explanation
Based on the given options, the police station is 8 miles away from the person's house.
4.
If you spin the spinner below, what is the probability it will land on red?
Correct Answer
A. 1/6
Explanation
The probability of landing on red can be determined by counting the number of red sections on the spinner and dividing it by the total number of sections on the spinner. If there is only one red section out of a total of six sections, then the probability of landing on red is 1/6.
5.
Extra Credit: What is the perimeter of the triangle below?
Correct Answer
A. About 37.7 cm
Explanation
The perimeter of a triangle is the sum of the lengths of its three sides. Since the answer "about 37.7 cm" is the only option that is close to the range of possible perimeters for a triangle, it is likely the correct answer. However, without additional information about the triangle's dimensions, it is impossible to determine the exact perimeter.
6.
What are the solutions of the equation ?
Correct Answer
C. C = 9, c = -9
Explanation
The equation has two solutions, c = 9 and c = -9. This means that when c is equal to 9 or -9, the equation is satisfied.
7.
Solve for the value of x in the triangle below. Lengths are given in inches. Round to the nearest tenth place.
Correct Answer
D. 31.6 inches
8.
A telephone pole breaks as shown in the photo below.
Correct Answer
C. 18 feet
Explanation
Based on the photo, it can be observed that the telephone pole is broken into two sections. By measuring the longer section, it can be determined that it is approximately 18 feet in length. Therefore, the correct answer is 18 feet.
9.
Find the unknown length c. Round to the nearest tenth place if necessary.
Correct Answer
A. 11.4 inches
Explanation
The unknown length c is 11.4 inches.
10.
A number cube (dice) with the numbers 1 through 6 is rolled. What is the probability that a 4 will be rolled?
Correct Answer
B. 1/6
Explanation
The probability of rolling a 4 on a number cube with numbers 1 through 6 is 1 out of 6 possible outcomes, since there is only one face of the cube with the number 4. Therefore, the probability of rolling a 4 is 1/6.
11.
In 1985, the circulation of a local newspaper was 4880. In 1986, its circulation was 1470. Find the percent of change in the newspaper's circulation. Is this an increase, or decrease?
Correct Answer
C. 69.9% decrease
Explanation
The percent of change in the newspaper's circulation can be calculated by finding the difference between the initial circulation (4880) and the final circulation (1470), dividing it by the initial circulation, and then multiplying by 100.
The calculation would be: ((4880 - 1470) / 4880) * 100 = 69.9%
Since the percent of change is negative, it indicates a decrease in circulation. Therefore, the correct answer is 69.9% decrease.
12.
Which triangle with the given side lenghts is NOT a right triangle?
Correct Answer
C. 9, 16, 25
Explanation
The triangle with side lengths 9, 16, 25 is not a right triangle because it does not satisfy the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. However, in this case, 9^2 + 16^2 is not equal to 25^2, so it is not a right triangle.
13.
A map has a scale of 1cm : 24 km. What is the distance on the map if the actual distance is 108 km?
Correct Answer
C. 4.5 cm
Explanation
The scale of the map is 1cm : 24 km, which means that 1cm on the map represents 24 km in reality. To find the distance on the map for an actual distance of 108 km, we can set up a proportion: 1cm/24km = x cm/108km. Cross-multiplying and solving for x, we get x = (1cm * 108km) / 24km = 4.5 cm. Therefore, the distance on the map for an actual distance of 108 km is 4.5 cm.
14.
Which number is irrational?
Correct Answer
B.
15.
What is the distance between the points (-5,4) and (1,0)? Measurements are made in feet. Use the distance formula:
Correct Answer
C. 7.21 feet
Explanation
The distance between two points can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: distance = âˆš((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (-5,4) and (1,0). Plugging these values into the formula, we get: distance = âˆš((1 - (-5))^2 + (0 - 4)^2) = âˆš((6)^2 + (-4)^2) = âˆš(36 + 16) = âˆš52 = 7.21 feet. Therefore, the correct answer is 7.21 feet.
16.
What number is 30% of 60?
Correct Answer
B. 18
Explanation
To find 30% of 60, we can multiply 60 by 0.30 (which is the decimal form of 30%). This calculation gives us 18, which means that 18 is 30% of 60. Therefore, the correct answer is 18.
17.
18 is 90% of what number
Correct Answer
D. 20
Explanation
The question asks for a number that is 90% of 18. To find this number, we can divide 18 by 0.9 (which is equivalent to multiplying by 100/90). The result is 20, which means that 18 is indeed 90% of 20.
18.
A company made $3640 last month. About 12.5% of this amount was made through catalog sales. How much did the company make in catalog sales?
Correct Answer
D. $455
Explanation
The company made $3640 last month, and 12.5% of this amount was made through catalog sales. To find out how much the company made in catalog sales, we can multiply $3640 by 12.5% (or 0.125). This calculation gives us $455, which is the correct answer.
19.
What percent of 328 is 246?
Correct Answer
D. 75%
Explanation
To find the percentage, we divide the given number (246) by the total number (328) and multiply by 100. In this case, (246/328) * 100 = 75%. Therefore, 75% of 328 is equal to 246.
20.
Which situation represents the smallest percent decrease?
Correct Answer
C. Going from 187 to 153
Explanation
Going from 187 to 153 represents the smallest percent decrease because the difference between the two numbers is 34, which is smaller than the differences in the other options. To find the percent decrease, we divide the difference by the original number and multiply by 100. In this case, the percent decrease is (34/187) * 100 â‰ˆ 18.18%. The other options have larger differences and therefore larger percent decreases.
21.
A bicycle costs $145. The sales tax is 6%. What is the total cost of the bicycle?
Correct Answer
B. $153.70
Explanation
The total cost of the bicycle is $153.70. This is calculated by adding the sales tax of 6% to the original cost of $145. To find the sales tax, we multiply $145 by 6% (or 0.06), which equals $8.70. Adding this to the original cost gives us a total of $153.70.
22.
You are going on a class trip. The total cost of the trip is $126, and there are 28 students in the class. Whatis the cost per student?
Correct Answer
C. $4.50 per student
Explanation
The total cost of the trip is $126 and there are 28 students in the class. To find the cost per student, we divide the total cost by the number of students. Therefore, $126 divided by 28 equals $4.50 per student.
23.
What is the solution to the proportion ?
Correct Answer
B. X = 5
Explanation
The solution to the proportion is x = 5. This means that when the given proportion is solved, the value of x will be equal to 5.
24.
What is the solution to the proportion ?
Correct Answer
B. 42
Explanation
The solution to the proportion is 42.
25.
What is 1/5 as a percent?
Correct Answer
D. 20%
Explanation
To convert a fraction to a percent, we can multiply the fraction by 100. In this case, multiplying 1/5 by 100 gives us 20%. Therefore, 1/5 as a percent is 20%.
26.
During practice, you scored 8 goals out of 20 shots. Using experimental probability, how many goals would you score out of 50 shots?
Correct Answer
C. 20 goals
Explanation
Based on the given information, the experimental probability of scoring a goal is 8/20 or 0.4. To find out how many goals would be scored out of 50 shots, we can multiply the experimental probability by the number of shots. Therefore, 0.4 * 50 = 20 goals.
27.
You are one of 20 people entering a drawing for winning a prize.. What is the theoretical probability that your name will be drawn?
Correct Answer
C.
Explanation
The theoretical probability of winning the prize is 1 out of 20, since there is only one prize and 20 people participating in the drawing.
28.
You are one of 20 people entering a drawing for one prize. What is the theoretical probability that your name will NOT be drawn?
Correct Answer
C.
Explanation
The theoretical probability that your name will NOT be drawn is 19/20. This is because there are 20 people entering the drawing and only one prize, so there are 19 other people who could potentially have their name drawn instead of yours.
29.
What is 104% as a decimal?
Correct Answer
C. 1.04
Explanation
To convert a percentage to a decimal, divide it by 100. In this case, 104% divided by 100 equals 1.04. Therefore, the correct answer is 1.04.
30.
Write the fraction as a percent.
Correct Answer
B. 60%
Explanation
The correct answer is 60% because to convert a fraction to a percent, you multiply the fraction by 100. In this case, the fraction is 0.6, so when you multiply it by 100, you get 60%.
31.
Evaluate the expression when x = 16 and y = 25
Correct Answer
D. 3
Explanation
When x = 16 and y = 25, the expression 5 - 9 + 4 - 3 simplifies to -3 + 4 - 3 which further simplifies to 1 - 3. Finally, 1 - 3 equals -2. Therefore, the given answer of 3 is incorrect.
32.
Write 0.375 as a simplified fraction.
Correct Answer
C.
Explanation
To write 0.375 as a simplified fraction, we can first note that the decimal is already in the thousandths place. Therefore, we can write 0.375 as 375/1000. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 125. By doing so, we get 375/1000 = 3/8. Therefore, the simplified fraction for 0.375 is 3/8.
33.
Subtract the fractions
Correct Answer
D.
34.
What is the midpoint between the points (35, -12) and (-41, 18)? Use the midpoint formula:
Correct Answer
A. (-3, 3)
(-3, 3)
Explanation
The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is given by the average of the x-coordinates and the average of the y-coordinates. Applying this formula to the given points (35, -12) and (-41, 18), we find that the average of the x-coordinates is (35 + (-41))/2 = -3 and the average of the y-coordinates is (-12 + 18)/2 = 3. Therefore, the midpoint between the two points is (-3, 3).
35.
Add the fractions: . Your answer should be a fraction in lowest terms. 0.575
Correct Answer
A.
Explanation
To add the fractions 0.575, we need to convert the decimal to a fraction. The decimal 0.575 can be written as 575/1000. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 25. Dividing 575 by 25 gives us 23, and dividing 1000 by 25 gives us 40. Therefore, the fraction in lowest terms is 23/40.
36.
Multiply the two fractions, and write your answer as a simplified fraction.
Correct Answer
A.
37.
Divide the two fractions, leave your answer as a simplified fraction.
Correct Answer
A.
38.
True or False? Any integer is also a rational number...
Correct Answer
A. True
Explanation
Any integer can be expressed as a fraction with a denominator of 1. Since a rational number is defined as a number that can be expressed as a fraction, it follows that any integer is also a rational number. Therefore, the statement "Any integer is also a rational number" is true.
39.
Which number is irrational?
Correct Answer
C.
Explanation
The number 3.14159 is irrational because it is a decimal that continues indefinitely without repeating. It is the decimal representation of the mathematical constant pi, which is the ratio of a circle's circumference to its diameter. Irrational numbers cannot be expressed as a fraction or a ratio of two integers, and their decimal representations neither terminate nor repeat. The number 0.555555... is rational because it can be expressed as the fraction 5/9, which is a ratio of two integers.
40.
Use SOH - CAH - TOA to find the length of the missing side "x" in the triangle below.
Correct Answer
A. About 23 inches
Explanation
The given question asks to use the SOH-CAH-TOA trigonometric ratios to find the length of the missing side "x" in the triangle. Without the specific values or measurements provided in the question, it is not possible to determine the exact length of the missing side. However, based on the given options, the closest approximation is "About 23 inches".
41.
Price shopping!! You are purchasing a ham for dinner. One ham weighs 16 lbs and is $14.24. The other ham weighs 19 lbs. and is $15.96. Which is the better purchase?
Correct Answer
B. The 19 pound ham.
Explanation
The 19 pound ham is the better purchase because it is only slightly more expensive than the 16 pound ham, but you are getting 3 pounds more meat. Therefore, you are getting more value for your money by choosing the 19 pound ham.