Math Flashcards

The volume of a cube is 64 cubic feet. What is the cube's surface area?

Answer: 96 square feet

First, find the side length of the cube. Since the volume of a cube is side³, and the volume is 64 cubic feet, the side length is the cube root of 64, which is 4 feet. A cube has 6 identical square faces. The area of one face is side², so 4² = 16 square feet. The total surface area is 6 times the area of one face, resulting in 6 * 16 = 96 square feet.

What does A equal if F = M x A?

Answer: F/M

The given equation F = M x A represents Newton's second law of motion. To solve for 'A' (acceleration), you need to isolate it on one side of the equation. This is achieved by dividing both sides of the equation by 'M' (mass). Therefore, A = F/M.

3,451 out of 7,562 college students have participated in an intramural sports program. What percentage of students have participated in intramural sports?

Answer: 45.6%

To calculate the percentage of students who participated, divide the number of participating students by the total number of students, then multiply by 100. So, (3,451 / 7,562) * 100. This calculation yields approximately 45.636%. Rounded to one decimal place, the percentage is 45.6%.

The result of dividing 40 by.08 is

Answer: 500

To divide 40 by 0.08, it's helpful to eliminate the decimal in the divisor. Multiply both the numerator (40) and the denominator (0.08) by 100. This transforms the problem into 4000 divided by 8. Performing this division, 4000 / 8 equals 500.

With four shirts and five ties, how many different combinations of shirts and ties are possible?

Answer: 20

To find the total number of different combinations, you multiply the number of options available for each independent choice. In this scenario, there are 4 choices for shirts and 5 choices for ties. Therefore, 4 shirts * 5 ties = 20 different combinations are possible.

How much does ¾ pound of rice cost if a pound of rice costs $4.20?

Answer: $3.15

To find the cost of ¾ pound of rice, multiply the cost per pound ($4.20) by the fraction ¾. This calculation is $4.20 * (3/4). You can perform this as ($4.20 * 3) / 4, which equals $12.60 / 4. The final cost is $3.15.

If 0.05z equals 1, then z equals

Answer: 20

To solve for 'z' in the equation 0.05z = 1, you need to isolate 'z'. This is done by dividing both sides of the equation by 0.05. So, z = 1 / 0.05. Dividing 1 by 0.05 is equivalent to dividing 1 by (5/100), which simplifies to 1 * (100/5) = 20.

What does 4(x-y) + 7 equal if x = y?

Answer: 7

Given that x = y, substitute 'x' for 'y' in the expression 4(x-y) + 7. This simplifies the term (x-y) to (x-x), which equals 0. Therefore, the expression becomes 4(0) + 7. Since 4 multiplied by 0 is 0, the entire expression simplifies to 0 + 7, which equals 7.

The length of a shipping container is 327 feet, and the width is 15.3 feet. What is the volume of the container (rounded to the next whole number) if the height is 12.6 feet?

Answer: 63,039 cubic feet

The volume of a rectangular container is calculated by multiplying its length, width, and height. So, Volume = 327 feet * 15.3 feet * 12.6 feet. This calculation yields 63,038.94 cubic feet. When rounded to the nearest whole number, the volume is 63,039 cubic feet.

What is the value of 4 cubed?

Answer: 64

The term '4 cubed' means 4 raised to the power of 3, or 4³. This involves multiplying 4 by itself three times. So, 4 * 4 * 4. First, 4 * 4 equals 16. Then, 16 * 4 equals 64.

Which of the numbers below is NOT a prime number?

Answer: 93

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. To determine which number is not prime, check for divisibility by other numbers. 93 is divisible by 3 (since the sum of its digits, 9+3=12, is divisible by 3), as 93 = 3 * 31. Since 93 has factors other than 1 and itself, it is not a prime number.

Canmore has a temperature of -1°C. What is the temperature in degrees Fahrenheit using the formula F° = C°x (9/5) + 32?

Answer: 30.2

To convert -1°C to Fahrenheit, substitute -1 into the given formula F° = C° * (9/5) + 32. This becomes F° = (-1) * (9/5) + 32. Calculating (-1) * (9/5) gives -1.8. Adding 32 to -1.8 results in 30.2°F.

What percentage of the office workforce is present if 1/3 of the staff is on vacation and 1/4 of those who are not on vacation are sick?

Answer: 1/2

If 1/3 of the staff is on vacation, then 1 - 1/3 = 2/3 of the staff are not on vacation. Of those not on vacation, 1/4 are sick, meaning (1/4) * (2/3) = 1/6 of the total staff are sick. The total staff not present is 1/3 (vacation) + 1/6 (sick) = 2/6 + 1/6 = 3/6 = 1/2. Therefore, if 1/2 of the staff is not present, then 1 - 1/2 = 1/2 of the staff is present.

If x + y + 15 equals 30, and x + y equals z, then 40 - z equals

Answer: 25

First, use the equation x + y + 15 = 30 to find the value of (x + y). Subtracting 15 from both sides gives x + y = 15. Since x + y is equal to z, we know that z = 15. Finally, substitute z = 15 into the expression 40 - z, which results in 40 - 15 = 25.

Which of the options below completes the equation: (9 x 2) + (4 x 3) = (_____)

Answer: (10 x 3)

First, calculate the value of the left side of the equation: (9 x 2) + (4 x 3) = 18 + 12 = 30. Now, evaluate each option to find which one also equals 30. Option A, (10 x 3), equals 30, which correctly completes the equation.

A woman has a budget of Z dollars. How much money does she have left after she spends $500?

Answer: Z - 500

When money is spent, it is deducted from the initial amount. If the woman begins with a budget of Z dollars and spends $500, the amount of money she has left is the initial budget minus the amount spent. Therefore, the expression representing her remaining money is Z - 500.

Three baseball cards, three football cards, and six hockey cards make up a stack of sports cards. What is the chance that one of the cards chosen at random is a hockey card?

Answer: 1/2

First, calculate the total number of cards in the stack: 3 baseball + 3 football + 6 hockey = 12 cards. The number of hockey cards, which is the favorable outcome, is 6. The probability of choosing a hockey card is the number of hockey cards divided by the total number of cards, which is 6/12. This fraction simplifies to 1/2.

What is the median of the data set including -3x, -6x, x, -9x, and 5x if x > 0?

Answer: -3x

To find the median, first arrange the data set in ascending order. Since x > 0, the ordered set is -9x, -6x, -3x, x, 5x. The median is the middle value in an ordered data set. With five values, the third value in the ordered list is the median, which is -3x.

There are 4 Chocolate Rolls, 3 Lollipops, 5 Toblerone, and 6 Starbursts in a bag of candy. What's the chance you'll get a lollipop if you pick one piece of candy at random?

Answer: 1/6

First, calculate the total number of candy pieces in the bag: 4 Chocolate Rolls + 3 Lollipops + 5 Toblerone + 6 Starbursts = 18 pieces. The number of lollipops is 3. The probability of picking a lollipop is the number of lollipops divided by the total number of candy pieces, which is 3/18. This fraction simplifies to 1/6.

The card set for a game consists of seven red cards and twenty-one green cards. What is the chance that one of these cards will be red if a player chooses one at random?

Answer: 1/4

First, determine the total number of cards in the set: 7 red cards + 21 green cards = 28 cards. The number of red cards, which is the favorable outcome, is 7. The probability of choosing a red card is the number of red cards divided by the total number of cards, which is 7/28. This fraction simplifies to 1/4.