Math Flashcards

One third of the candidates for a job were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the job, how many were between 25 and 50?

Answer: 32

First, calculate the number of candidates in the specified age groups. One-third of 84 is (1/3) * 84 = 28 candidates (25 or younger). Two-sevenths of 84 is (2/7) * 84 = 24 candidates (at least 50). The total number of candidates in these two groups is 28 + 24 = 52. To find those between 25 and 50, subtract this sum from the total number of applicants: 84 - 52 = 32 candidates.

Which of the following is a factor of 450 and multiple of 25?

Answer: 75

We need to find a number that is both a factor of 450 and a multiple of 25. Let's check the options. 75 is a multiple of 25 because 25 * 3 = 75. Also, 75 is a factor of 450 because 450 / 75 = 6. Thus, 75 satisfies both conditions.

The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting. Which is the rate at which the plant's height is increasing?

Answer: 3.2 inches per week

The given formula is h - 15 = 3.2t. To find the rate of increase, we can rearrange the formula to solve for h: h = 3.2t + 15. This equation is in the slope-intercept form (y = mx + b), where 'm' represents the rate of change. Therefore, the plant's height is increasing at a rate of 3.2 inches per week.

The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. How high was the initial height of the shrub?

Answer: 15 inches

The initial height of the plant refers to its height at the time of planting, which corresponds to t = 0 weeks. Substitute t = 0 into the given formula: h - 15 = 3.2 * 0. This simplifies to h - 15 = 0, so h = 15. Therefore, the initial height of the shrub was 15 inches.

The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. When was the height 31 inches?

Answer: Some time between 3 and 7 weeks

To find when the height was 31 inches, substitute h = 31 into the formula: 31 - 15 = 3.2t. This simplifies to 16 = 3.2t. Dividing both sides by 3.2 gives t = 16 / 3.2 = 5. Therefore, the height was 31 inches at 5 weeks, which falls between 3 and 7 weeks.

A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday. What is the equation of the axis of symmetry of this graph?

Answer: t = 0

The problem implies a quadratic relationship for temperature T with respect to time t, specifically T = 9 - t². For a parabola of the form y = ax² + bx + c, the axis of symmetry is given by the formula x = -b/(2a). In T = -t² + 9, a = -1 and b = 0, so the axis of symmetry is t = -0/(2*-1) = 0. This means the graph is symmetric about the T-axis (where t=0).

It is necessary to find the times when the temperature is 8o F. Which of the following is the correct equation to do this.

Answer: 9 - t2 = 8

Based on the context of the previous question, the temperature T is given by the equation T = 9 - t². To find the times when the temperature is 8°F, we need to set T equal to 8. This directly leads to the equation 8 = 9 - t², which can be rearranged to 9 - t² = 8.

Which of the following is the equation of the straight line joining the points on the graph corresponding to t = 2 and t = 1?

Answer: T + 3t = 11

First, find the coordinates of the two points on the graph T = 9 - t². When t = 1, T = 9 - 1² = 8, giving point (1, 8). When t = 2, T = 9 - 2² = 5, giving point (2, 5). The slope of the line is (5 - 8) / (2 - 1) = -3. Using the point-slope form T - T₁ = m(t - t₁), with (1, 8) and m = -3, we get T - 8 = -3(t - 1), which simplifies to T - 8 = -3t + 3. Rearranging gives T + 3t = 11.

The formula for the volume V of the sphere = 4(pi)r3 / 3. Which of the following is the closest approximation to the volume when r, the radius, is 11 inches?

Answer: 5573 cubic inches

To approximate the volume, substitute r = 11 inches into the formula V = (4/3)πr³. This gives V = (4/3) * π * (11)³, which is V = (4/3) * π * 1331. Calculating this yields V ≈ (4/3) * 3.14159 * 1331 ≈ 5575.27 cubic inches. The closest approximation among the choices is 5573 cubic inches.

If the radius of the sphere were doubled by what factor would the surface area be enlarged? Note: The formula for the surface area S of the sphere = 4 x (pi) x r2

Answer: 4

The formula for the surface area of a sphere is S = 4πr². If the radius 'r' is doubled, the new radius becomes '2r'. Substituting this into the formula, the new surface area S' = 4π(2r)² = 4π(4r²) = 16πr². Comparing S' to the original S, we see that S' = 4 * (4πr²) = 4S. Therefore, the surface area is enlarged by a factor of 4.

The power of 10 nearest the quantity

Answer: order of magnitude

The power of 10 nearest a quantity is a concept used to express its scale or magnitude. This is precisely the definition of an order of magnitude. It provides a rough estimate of a number's size by rounding it to the nearest power of ten.

The measurement of the outer surface of an object.

Answer: surface area

Surface area is a measurement that quantifies the total area occupied by the exterior surfaces of a three-dimensional object. It is calculated by summing the areas of all the individual faces or curved surfaces that enclose the object. For example, the surface area of a cube is the sum of the areas of its six faces.

A part of a line, with one endpoint, that continues without end in one direction.

Answer: ray

A ray is a fundamental concept in geometry that describes a part of a line. It is characterized by having one definite endpoint and extending infinitely in only one direction. This makes it distinct from a line segment (which has two endpoints) and a line (which extends infinitely in both directions).

In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. c2 = a2 + b2

Answer: Pythagorean theorem

The statement c² = a² + b² describes the Pythagorean theorem. This fundamental theorem applies specifically to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle, denoted as 'c') is equal to the sum of the squares of the lengths of the other two sides (the legs, denoted as 'a' and 'b').

Lines that cross at one point.

Answer: intersecting lines

Lines that cross at one point are fundamentally defined as intersecting lines in geometry. This term describes any two or more lines that share a single common point. Perpendicular lines are a specific type of intersecting lines that cross at a 90-degree angle, but 'intersecting lines' is the broader and most accurate definition for lines crossing at any single point.