Mathematics Grade Flashcards

Which of the following always represents an odd integer?

Answer: The product of two odd integers

Let's examine each option: The sum of three even integers is always even (e.g., 2+4+6=12). The sum of two odd integers is always even (e.g., 3+5=8). The product of two odd integers is always odd (e.g., 3*5=15). The product of two consecutive integers is always even (one must be even, e.g., 2*3=6). The sum of three consecutive integers can be odd or even (e.g., 1+2+3=6, 2+3+4=9). Thus, only the product of two odd integers always results in an odd integer.

How many 200-milliliter portions of juice can be poured from a 2-liter pitcher?

Answer: 10

First, convert the pitcher's volume from liters to milliliters. Since 1 liter equals 1000 milliliters, a 2-liter pitcher holds 2 * 1000 = 2000 milliliters. To find out how many 200-milliliter portions can be poured, divide the total volume by the size of each portion: 2000 ml / 200 ml = 10 portions.

Take the temperature in degrees Fahrenheit, subtract 32 from it, and multiply the result by to get the temperature in degrees Celsius. How many degrees Celsius, to the nearest degree, does a furnace have to be at to reach 393 degrees Fahrenheit?

Answer: 201

The problem provides the formula for converting Fahrenheit to Celsius: C = (F - 32) * (5/9). Substitute the given Fahrenheit temperature (393) into the formula: C = (393 - 32) * (5/9). This simplifies to C = (361) * (5/9) = 1805 / 9, which is approximately 200.55. Rounded to the nearest degree, the temperature is 201 degrees Celsius.

Mario's math book weighs 5 pounds, her science book weighs 6, her history book weighs 4, and her English book weighs 3. How many various arrangements of one or more books can Li cram into her bag without the books' combined weight exceeding 12 pounds?

Answer: 11

We need to list all combinations of books whose total weight does not exceed 12 pounds. Individual books (5, 6, 4, 3 lbs) are 4 combinations. Two-book combinations (5+6=11, 5+4=9, 5+3=8, 6+4=10, 6+3=9, 4+3=7) are 6 combinations. For three-book combinations, only Math+History+English (5+4+3=12) fits. All four books exceed 12 lbs. Summing these up, 4 + 6 + 1 = 11 various arrangements.

The rate of ascent for an airplane is 66.8 feet per minute. It descends twice as quickly as it ascends. How many feet will the airplane descend in 30 minutes, presuming a constant rate of descent?

Answer: 4008

First, determine the airplane's descent rate. It descends twice as quickly as it ascends, so its descent rate is 66.8 feet per minute * 2 = 133.6 feet per minute. To find the total distance the airplane will descend in 30 minutes, multiply the descent rate by the time: 133.6 feet/minute * 30 minutes = 4008 feet.

How does increasing the value of x by 2 in the equation y = 4 x affect the value of y?

Answer: It is 8 more than the original amount.

The equation is y = 4x. If x is increased by 2, the new value of x becomes (x + 2). Substituting this into the equation gives y_new = 4 * (x + 2). Distributing the 4, we get y_new = 4x + 8. Since the original y was 4x, the new y is 8 more than the original amount.

1 + 3=41 + 3 + 5 = 91+3 + 5 + 7 = 161 + 3 + 5+7 + 9 = 25 . How many consecutive odd integers must add up to 144 in order for the sum to be 144, as suggested by the pattern in the four examples above?

Answer: 12

The pattern shows that the sum of the first 'n' consecutive odd integers is equal to n squared (n^2). For example, 1+3+5 (3 odd integers) equals 9, which is 3^2. To find how many consecutive odd integers sum to 144, we need to find the number 'n' such that n^2 = 144. Taking the square root of 144 gives n = 12, meaning 12 consecutive odd integers are required.

The characteristics of a particular 4-sided figure are as follows. There is only one set of opposite sides that are parallel and one set of opposite sides that are the same length. The lengths of the parallel sides are not equal. Which of the following statements about the sides with equal lengths must be accurate?

Answer: They are not parallel.

The description fits an isosceles trapezoid, which has exactly one pair of parallel sides and one pair of non-parallel sides that are equal in length. Since the figure has 'only one set of opposite sides that are parallel,' the sides with equal lengths cannot be parallel. If they were parallel, the figure would have two sets of parallel sides, making it a parallelogram, which contradicts the given condition.

A company had 90 employees the previous year. The number of employees increased this year by 10%. This year, how many people work for the company?

Answer: 99

To find the increase in employees, calculate 10% of the original 90 employees. 10% of 90 is 0.10 * 90 = 9 employees. Then, add this increase to the original number of employees: 90 + 9 = 99 employees. Therefore, the company now has 99 people working for it.

The perimeter of a rectangular playground is 390 feet. The playground has a width of 75 feet. How long does it last?

Answer: 120 Feet

The perimeter of a rectangle is calculated using the formula P = 2 * (length + width). We are given the perimeter (P = 390 feet) and the width (75 feet). Substitute these values into the formula: 390 = 2 * (length + 75). Divide both sides by 2 to get 195 = length + 75. Finally, subtract 75 from 195 to find the length: length = 195 - 75 = 120 feet.

The points with the coordinates (2, 1) and are the endpoints of a line segment (8, 9). What are the coordinates of this line segment's midpoint?

Answer: (5, 5)

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is found using the formula ((x1 + x2)/2, (y1 + y2)/2). For the given points (2, 1) and (8, 9), the x-coordinate of the midpoint is (2 + 8)/2 = 10/2 = 5. The y-coordinate is (1 + 9)/2 = 10/2 = 5. Thus, the midpoint coordinates are (5, 5).

A restaurant served dinner to Ms. Helen and her three friends. $67 was the total. Moreover, they left a $13 tip. They left a tip that was roughly what % of the total bill.

Answer: 20%

To calculate the percentage tip, divide the tip amount by the total bill amount and multiply by 100. In this case, the tip is $13 and the total bill is $67. So, ($13 / $67) * 100. This calculation results in approximately 19.40%, which, when rounded to the nearest whole percentage, is 20%.

A specific kind of measuring tool can measure length with an accuracy of 0.05 centimeters. When this instrument reads 3.7 centimeters, it means that the length is at least that much longer?

Answer: 3.65 centimeters

An accuracy of 0.05 centimeters means the actual length could be 0.05 cm more or less than the reading. If the instrument reads 3.7 cm, the actual length falls within the range of 3.7 - 0.05 cm and 3.7 + 0.05 cm. This means the length is between 3.65 cm and 3.75 cm. Therefore, the length is at least 3.65 centimeters.

The Titanic cruise ship measured 882 feet in length. Which of the following lengths is closest?

Answer: Fifty car lengths

To find the closest length, we need to estimate the length of the objects mentioned. A typical car is about 15-18 feet long; using an average of 17 feet, fifty car lengths would be 50 * 17 = 850 feet. This is very close to the Titanic's length of 882 feet. Other options like school buses, skateboards, moving vans, or bicycles would result in significantly different total lengths.

Which of the following comes closest to a 15 percent tip on a $24.99 restaurant bill?

Answer: $3.75

To estimate a 15% tip on $24.99, it's easiest to round $24.99 to $25. First, calculate 10% of $25, which is $2.50. Then, calculate 5% of $25, which is half of 10%, or $1.25. Adding these two amounts together ($2.50 + $1.25) gives a total tip of $3.75, which is the closest option.

Cheng is preparing treat bags for her sister's birthday celebration. She distributes 65 candies evenly among 15 bags, ensuring that each bag contains as many candies as possible. How many pieces does she still have?

Answer: 5

To find out how many candies Cheng still has, we need to perform division with a remainder. Divide the total number of candies (65) by the number of bags (15). 65 divided by 15 is 4 with a remainder, because 15 * 4 = 60. Subtracting 60 from 65 leaves a remainder of 5. Therefore, Cheng still has 5 pieces of candy.