Mathematics Flashcards

Jane is creating a unique paint color that calls for one part coloring to every four parts white paint. For a total of 12 gallons of colored paint, how much coloring will Jane require?

Answer: 2 2/5 gallons

The ratio of coloring to white paint is 1:4, meaning there are 1 + 4 = 5 total parts in the mixture. The coloring constitutes 1 part out of these 5 total parts. Therefore, to find the amount of coloring needed for 12 gallons of total paint, you calculate (1/5) * 12 gallons, which equals 12/5 gallons or 2 2/5 gallons.

Students were required to provide an equal approach to express the ratio 8:6 on a test. In the document attached, four of the responses are listed. Which one is the most accurate? Student A: 8/6 Student B: 3/2 Student C: 6:8 Student D: 4/3

Answer: Students A and D

The ratio 8:6 can be expressed as a fraction, 8/6, which is what Student A provided. This fraction can then be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. Simplifying 8/6 yields 4/3, as shown by Student D. Therefore, both 8/6 and 4/3 are accurate and equivalent expressions of the ratio 8:6.

When adding fractions with dissimilar denominators, the common denominator should be the least common multiple of the denominators. When adding the fractions 5/6 and 7/9, what common denominator should you use

Answer: 18

To find the least common denominator for fractions, you need to find the least common multiple (LCM) of their denominators. For the fractions 5/6 and 7/9, the denominators are 6 and 9. The multiples of 6 are 6, 12, 18, 24, etc., and the multiples of 9 are 9, 18, 27, etc. The smallest number that appears in both lists is 18, making it the least common denominator.

The following is a breakdown of a year-end test that includes math, science, and language arts questions: The language arts portion accounts for 30% of the overall score, while the math and science sections each account for 35% of the overall score. What is Marys' overall score if he received an 89 on the math exam, an 85 on the science section, and a 76 on the language arts section? Your answer should be rounded to the nearest whole number.

Answer: 84

To calculate the overall weighted score, multiply each section's score by its corresponding percentage weight and then sum the results. For Math (89 * 0.35 = 31.15), Science (85 * 0.35 = 29.75), and Language Arts (76 * 0.30 = 22.8), the total sum is 31.15 + 29.75 + 22.8 = 83.7. Rounding 83.7 to the nearest whole number gives an overall score of 84.

Choose the response that is the polar opposite of the statement: Prime numbers are usually odd three-digit numbers.

Answer: 129

The statement claims that 'Prime numbers are usually odd three-digit numbers.' To find the polar opposite, we need a number that fits the description of being an odd, three-digit number but is *not* prime, thereby directly contradicting the statement's premise about primality. Among the options, 129 is an odd, three-digit number, but it is divisible by 3 (129 = 3 * 43), meaning it is a composite number, not a prime number. The other options are all prime numbers.

A clothing retailer is offering a deal on boots with a 10% discount and gloves with a 15% discount. A pair of boots typically costs b, and a pair of gloves typically costs g. Which of the following expressions best describes the total cost of one pair of boots and two pairs of gloves during this sale?

Answer: 0.9b + 1.7g

For boots, a 10% discount means the customer pays 90% of the original price, so the cost is 0.9b. For gloves, a 15% discount means the customer pays 85% of the original price, making one pair cost 0.85g. Since the question asks for the cost of one pair of boots and *two* pairs of gloves, the total cost is 0.9b + 2 * (0.85g), which simplifies to 0.9b + 1.7g.

James is about to go on an 840-mile long-distance bicycle adventure. He calculates that he can go 160 miles each day on average. On the day ____ of the trip, he will arrive. Which option indicates the proper fill-in-the-blank number?

Answer: 6th

To determine the day of arrival, divide the total distance of 840 miles by the average daily distance of 160 miles. This calculation yields 840 / 160 = 5.25 days. Since James cannot arrive in a fraction of a day, he will complete the journey sometime during the sixth day, meaning he arrives on the 6th day.

5 less than 3 times a number equals half of it. What number is it?

Answer: x = 2

Let 'x' represent the unknown number. The phrase '5 less than 3 times a number' translates to the expression 3x - 5. The phrase 'equals half of it' translates to x/2. Setting these equal gives the equation 3x - 5 = x/2. Solving for x: multiply by 2 to get 6x - 10 = x, then subtract x from both sides to get 5x - 10 = 0, and finally add 10 and divide by 5 to find x = 2.

Which one(s) demonstrates a correct statement? A) xy(5t⋅2)=5xyt⋅2xy B) ab(2x−3)=2abx−3ab C) 6rt(m+2n)=12mnrt D) 4d(9c÷8c)=36cd÷32dp

Answer: B

Statement B correctly demonstrates the distributive property, where the term `ab` is multiplied by each term inside the parentheses: `ab * 2x` equals `2abx`, and `ab * -3` equals `-3ab`. Therefore, `ab(2x - 3)` correctly expands to `2abx - 3ab`. The other statements contain errors in multiplication, distribution, or simplification.

Sally has a yard sale going on. She earned sales of $15, $21, $12, and $9 in the first four hours. She had hoped for an hourly wage of $15, but with $14.25, she is a little short of her objective. How much sales must she make in the fifth hour to raise her hourly average to $15?

Answer: $18

First, calculate the total sales Sally needs to achieve an average of $15 over five hours: $15/hour * 5 hours = $75. Next, sum her sales from the first four hours: $15 + $21 + $12 + $9 = $57. Finally, subtract her current total sales from the desired total sales to find out how much she needs to make in the fifth hour: $75 - $57 = $18.

Tim's socks are strewn around in a drawer. There are four pairs of blue socks, eight pairs of black socks, and four pairs of brown socks. He pulls a blue sock from the drawer at random. What are the chances that the second sock he picks up will be blue as well?

Answer: 1/5

Initially, there are 4 blue socks, 8 black socks, and 4 brown socks, assuming 'pairs' refers to the number of individual socks of that color (e.g., 4 blue socks, not 4 pairs or 8 individual blue socks). This gives a total of 4 + 8 + 4 = 16 socks. After Tim pulls one blue sock, there are 3 blue socks remaining and a total of 15 socks left in the drawer. The probability of picking another blue sock is then the number of remaining blue socks divided by the total remaining socks, which is 3/15, simplifying to 1/5.

Jerry invests in a 24-foot fence to keep his garden safe. He intends to create a rectangle garden. With this amount of fencing, what is the size of the largest rectangular garden Jim can create?

Answer: 36 square feet

The 24-foot fence represents the perimeter of the rectangular garden. For a fixed perimeter, a square encloses the maximum possible area. If the perimeter is 24 feet, then 2 * (length + width) = 24, meaning length + width = 12 feet. For a square, length equals width, so each side would be 6 feet (6 + 6 = 12). The area of this square garden would then be 6 feet * 6 feet = 36 square feet.

A farmer wants to know how much insect damage his corn crop has, so he picks 75 plants at random from different parts of the cornfield and inspects each one for damage. Nine of the 75 plants had been infested with corn borers. He understands that each acre has around 31,000 plants, and he has a 50-acre field to work with. In a 50-acre field, how many afflicted plants would you expect to find?

Answer: 186,000 plants

First, determine the proportion of infested plants from the sample: 9 infested plants out of 75 sampled plants is 9/75, which simplifies to 0.12 or 12%. Next, calculate the total number of plants in the entire 50-acre field by multiplying 50 acres by 31,000 plants per acre, resulting in 1,550,000 total plants. Finally, apply the infestation rate to the total number of plants: 0.12 * 1,550,000 = 186,000 afflicted plants.

Which of the following data sets has a median that is higher than the mean? a) {20,23,24,24,29,34,35} b){12,17,22,28,28,33,34} c) {24,26,29,29,29,34,35} d) {19,21,27,27,30,34,35}

Answer: B

To find the correct dataset, calculate both the mean and the median for each option. The median is the middle value in an ordered dataset. The mean is the sum of all values divided by the count of values. For dataset B, the median is 28, and the mean is approximately 24.86 (174/7). Since 28 is greater than 24.86, dataset B is the one where the median is higher than the mean.

△ABC≅△DEF Is given DE=15 EF=12 DF=9 What is △ABC perimeter ?

Answer: 36

The symbol '≅' indicates that triangle ABC is congruent to triangle DEF. Congruent triangles have identical corresponding sides and angles. Therefore, the side lengths of triangle ABC are the same as those of triangle DEF, which are 15, 12, and 9. To find the perimeter of triangle ABC, simply sum these side lengths: 15 + 12 + 9 = 36.

What is the perfect square of these numbers?

Answer: 169

A perfect square is an integer that can be expressed as the product of an integer multiplied by itself. Among the given options, 169 is a perfect square because it is the result of 13 multiplied by 13 (13 * 13 = 169). The other numbers (65, 150, 80) cannot be expressed as the square of an integer.

Jayson, a student, gets 37 out of 55 on the first test, 47 out of 72 on the second, and 41 out of 64 on the third. Jayson's highest percent score is

Answer: 67%

To find Jayson's highest percentage score, calculate the percentage for each test by dividing the score obtained by the total possible score and multiplying by 100. For the first test, (37/55) * 100% ≈ 67.27%. For the second, (47/72) * 100% ≈ 65.28%. For the third, (41/64) * 100% ≈ 64.06%. Comparing these, 67.27% is the highest, which rounds to 67%.

Which of the following would be considered an improper fraction?

Answer: 7/2

An improper fraction is defined as a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In the option 7/2, the numerator (7) is greater than the denominator (2), making it an improper fraction. The other options are either proper fractions or a mixed number.

Which of the following is the same as the 4:12 ratio?

Answer: 1/3

A ratio like 4:12 can be expressed as a fraction, 4/12. To find an equivalent and simplified form, divide both parts of the ratio (or numerator and denominator of the fraction) by their greatest common divisor. In this case, both 4 and 12 are divisible by 4, so 4 ÷ 4 = 1 and 12 ÷ 4 = 3, resulting in the simplified ratio or fraction of 1/3.

What percentage of 150 is 32 percent?

Answer: 48

To find '32 percent of 150,' first convert the percentage to a decimal by dividing it by 100, which gives 0.32. Then, multiply this decimal by the number 150. So, 0.32 * 150 equals 48.