Math Flashcards

2.45 + 0.54 + 0.07 =

Answer: 3.06

To add decimals, align the numbers vertically by their decimal points. Then, add the digits in each column, starting from the rightmost digit, and carry over to the next column as needed. Performing this operation for 2.45 + 0.54 + 0.07 yields a sum of 3.06.

Which of the following represents the smallest value?

Answer: 0.000799

To determine the smallest value among decimals, compare the digits from left to right, starting with the largest place value. The number 0.000799 has zeros in the tenths, hundredths, and thousandths places, indicating it is significantly smaller than the other options which have non-zero digits in higher place values.

5.36 - 0.78 =

Answer: 4.58

To subtract decimals, align the numbers vertically by their decimal points. Subtract the digits in each column, starting from the rightmost digit, borrowing from the left if a digit in the top number is smaller than the corresponding digit in the bottom number. Performing this calculation for 5.36 - 0.78 results in 4.58.

Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?

Answer: 27

To find the new production, first calculate 18% of 23 dolls: 0.18 * 23 = 4.14 dolls. Since you cannot produce a fraction of a doll, round this to the nearest whole number, which is 4 dolls. Adding this increase to the original production gives 23 + 4 = 27 dolls per month.

Two cars are side by side. One is 3.9 meters long. The other is 6% shorter. How long is the second car?

Answer: 3.7 meters

First, calculate 6% of the first car's length: 0.06 * 3.9 meters = 0.234 meters. Then, subtract this amount from the first car's length to find the length of the second car: 3.9 - 0.234 = 3.666 meters. Rounding to one decimal place, the second car is approximately 3.7 meters long.

A rectangle's width is 23 cm and its length is 9cm. What is its area?

Answer: 207 cm2

The area of a rectangle is calculated by multiplying its length by its width. Given a width of 23 cm and a length of 9 cm, the area is simply 23 cm * 9 cm. This multiplication yields a total area of 207 cm^2.

Sam's new porch is 50 square feet in size and rectangular. What is the perimeter of the porch if the length of the porch is two times the width?

Answer: 30 feet

Let the width of the porch be 'w' and the length be '2w'. The area is length * width, so 2w * w = 2w^2 = 50 square feet. Solving for w, we get w^2 = 25, which means w = 5 feet. The length is then 2 * 5 = 10 feet. The perimeter is 2 * (length + width) = 2 * (10 + 5) = 2 * 15 = 30 feet.

Solve for x as follows: 3(x+1) = 5(x−2)+7

Answer: 3

First, distribute the numbers on both sides of the equation: 3x + 3 = 5x - 10 + 7. Simplify the right side to get 3x + 3 = 5x - 3. Next, subtract 3x from both sides, resulting in 3 = 2x - 3. Finally, add 3 to both sides (6 = 2x) and divide by 2, which gives x = 3.

What is the chance of choosing a man from a group of four males and eight females?

Answer: 1⁄3

The total number of people in the group is the sum of males and females: 4 males + 8 females = 12 people. The number of favorable outcomes (choosing a man) is 4. The probability is calculated as the number of favorable outcomes divided by the total number of outcomes, which is 4/12, simplifying to 1/3.

If 3t - 7 = 5t, then 6t=

Answer: -21

First, solve the equation 3t - 7 = 5t for 't'. Subtract 3t from both sides to get -7 = 2t, then divide by 2 to find t = -7/2. Now, substitute this value of 't' into the expression 6t: 6 * (-7/2) = -42/2, which simplifies to -21.

The variables x and y are directly proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Answer: 6

When variables x and y are directly proportional, their relationship is expressed as y = kx, where k is the constant of proportionality. Using the given values (y=2 when x=3), we find k = 2/3. To find y when x=9, substitute k and x into the equation: y = (2/3) * 9 = 18/3 = 6.

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered?

Answer: 10

Let 's' be the number of sandwiches and 'p' be the number of soups. We have two equations: s + p = 18 (total people) and 7.75s + 4.50p = 113.50 (total cost). From the first equation, p = 18 - s. Substitute this into the second equation: 7.75s + 4.50(18 - s) = 113.50. This simplifies to 7.75s + 81 - 4.50s = 113.50, which further simplifies to 3.25s = 32.50. Dividing by 3.25 gives s = 10 sandwiches.

(3x^2 y^3 )^3 =

Answer: 27 x^6 y^9

To raise a product to a power, you must raise each factor within the product to that power. Therefore, (3x^2 y^3)^3 becomes 3^3 * (x^2)^3 * (y^3)^3. This simplifies to 27 * x^(2*3) * y^(3*3), resulting in 27x^6y^9.

There are 3x-2 trees planted in each row of a rectangular parcel of land. If there are total of 24x-16 trees planted in the parcel , how many rows of trees are there in the parcel?

Answer: 8

To find the number of rows, divide the total number of trees by the number of trees in each row. The total number of trees is 24x - 16, and the number of trees per row is 3x - 2. Factoring out 8 from the total trees gives 8(3x - 2). Thus, (24x - 16) / (3x - 2) simplifies to 8(3x - 2) / (3x - 2), which equals 8.

A ball was kicked into the air from a balcony 20 ft above the ground , and the ball's height above the ground, in feet, t seconds after the ball was kicked was h(t) = 20 - 16t^2 + 32t. What was the maximum height, in feet, of the ball above the ground after it was kicked?

Answer: 36

The height function h(t) = -16t^2 + 32t + 20 is a quadratic equation representing a downward-opening parabola, meaning its maximum value occurs at the vertex. The t-coordinate of the vertex is found using t = -b / (2a), where a = -16 and b = 32. This gives t = -32 / (2 * -16) = 1 second. Substituting t=1 back into the height function yields h(1) = 20 - 16(1)^2 + 32(1) = 20 - 16 + 32 = 36 feet, which is the maximum height.