8446 + Interview Questions in Applied Maths Page 108 InterviewSolution

5351.	A bag contains 6 red marbles, 4 blue marbles, 7 green marbles, and 3 yellow marbles. a marble is drawn from the bag and is not replaced. Then a second marble is drawn. What is the probability that both marbles were green?
Answer» A bag contains 6 red marbles, 4 blue marbles, 7 green marbles, and 3 yellow marbles. a marble is drawn from the bag and is not replaced. Then a second marble is drawn. What is the probability that both marbles were green? Solution:

Discussion

5352.	Isthe empty set a subset of the empty set?
Answer» Yes. The empty set is a subset of the empty set A set is defined as a collection of objects. Each object inside a set is called an 'Element'.

Discussion

5353.	Find the value of the expression 2x3 + 3y2 - 17 when x = 3 and y = 4.
Answer» Find the value of the expression 2x³ + 3y² - 17 when x = 3 and y = 4. Solution:

Discussion

5354.	What is an irrational number in math?
Answer» Irrational numbers are a set of real numbers that cannot be expressed in the form of fractions or ratios. Ex: π, √2, e,√5. Theirrational numbers cannot be expressed as a simple fraction in the form of p/q where p and q are real numbers and q is not equal to 0.

Discussion

5355.	How do you write two hundred million as numbers?
Answer» Two hundred million is written as 200,000,000. Million is a place value that is used in the International Number System.

Discussion

5356.	Given the function f(x) = 0.5\|x - 4\| - 3, for what values of x is f(x) = 7?
Answer» Given the function f(x) = 0.5\|x - 4\| - 3, for what values of x is f(x) = 7? Solution:

Discussion

5357.	Factor completely 5x2 - 40. 5(x + 8)(x - 8),5(x2 - 8),5(x + 8)(x - 5),Prime
Answer» Factor completely 5x²- 40. Solution:

Discussion

5358.	Over what interval is the graph of f(x) = -(x + 8))2 - 1 decreasing?
Answer» Over what interval is the graph of f(x) = -(x + 8⁾²- 1 decreasing? Solution:

Discussion

5359.	Choose one of the factors of 1331x3 - 8y3. 4, 11x - 2y, 121x2 + 44xy + 4y2, 121x2 - 22xy + 4y2
Answer» Choose one of the factors of 1331x³ - 8y³. Solution:

Discussion

5360.	Divide 33 photos into two groups so the ratio is 4:7.
Answer» Divide 33 photos into two groups so the ratio is 4:7. Solution:

Discussion

5361.	How Many Zeros in a Trillion?
Answer» There are 12 zeros in a trillion. A trillion is 1,000,000,000,000, or it can be represented as10 to the 12th power, or one million million.

Discussion

5362.	A triangle has side lengths of 3cm, 4cm, and, 6cm. Is it a right triangle explain?
Answer» No,a triangle havingside lengths 3cm, 4cm, and, 6cm is not a right triangle. We will be using the concept ofPythagoras theoremand check whether it isa right-angled triangle or not.

Discussion

5363.	What time is 12 am in military time?
Answer» What time is 12 am in military time? Solution:

Discussion

5364.	Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t9/2); t = 1
Answer» Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t^9/2); t = 1 Solution:

Discussion

5365.	Atriangle is classified as an equilateral triangle when it has
Answer» Atriangle is classified as an equilateral triangle when it has all its sides equal. A triangle is a 2-dimensional figure formed by three non-collinear points.

Discussion

5366.	Solve for x: 4x2 - 4a2x + (a4 - b4) = 0
Answer» Solve for x: 4x²- 4a²x + (a⁴- b⁴) = 0 Solution:

Discussion

5367.	If Anton can carry 3 boxes per trip, how many trips will it take him to move 51 boxes? 17, 27, 30, 37
Answer» If Anton can carry 3 boxes per trip, how many trips will it take him to move 51 boxes? 17, 27, 30, 37 Solution:

Discussion

5368.	(1) 10 (2) 100 (3) 1000 (4) 1
Answer» The A.M. of the first ten odd numbers is 10, that is option(1). The arithmetic mean is nothing but an average of the values in the data set.

Discussion

5369.	Choose the correct option. The A.M. of the first ten odd numbers is
Answer» The A.M. of the first ten odd numbers is 10, that is option(1). The arithmetic mean is nothing but an average of the values in the data set.

Discussion

5370.	What is 0.2 as a Fraction?
Answer» 0.2 as a fraction is 1/5. Fractions represent a part of the whole.

Discussion

5371.	Two sides of a triangle measure 5inand 12in. Which could be the length of the third side?
Answer» Two sides of a triangle measure 5inand 12in. Which could be the length of the third side? Solution:

Discussion

5372.	A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?
Answer» A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly? Solution:

Discussion

5373.	Which function below is the inverse of f(x) = x2 - 25? x squared over 25 ±square root of the quantity x plus 25 ±5 times the square root of x 1 over quantity x squared minus 25
Answer» Which function below is the inverse of f(x) = x²- 25? Solution:

Discussion

5374.	What is the next two letters in the sequence: a - e - f - h - i - k - l - m - …
Answer» What is the next two letters in the sequence: a - e - f - h - i - k - l - m - … Solution:

Discussion

5375.	Let f be the function defined by f(x) = x3+ x. If g(x) = f-1(x) and g(2) = 1. What is the value of g'(2)?
Answer» Let f be the function defined by f(x) =x³+ x. If g(x) = f^-1(x) and g(2) = 1. What is the value of g'(2)? Solution:

Discussion

5376.	Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5
Answer» Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5 Solution:

Discussion

5377.	Let f(x) = 2x + 2. Solve f-1(x) when x = 4
Answer» Let f(x) = 2x + 2. Solve f^-1(x) when x = 4 Solution:

Discussion

5378.	Given the function f(x) = 4(x + 3) - 5, solve for the inverse function when x = 3.
Answer» Given the function f(x) = 4(x + 3)-5, solve for the inverse function when x = 3. Solution:

Discussion

5379.	Prove that sin6A + cos6A =1 - 3sin2A cos2A
Answer» Making both the sides equal in the given solution, proves the desired expression. Make use of the trigonometric identity as well as the cubic formula to answer this question.

Discussion

5380.	If \|u\| = 6,\|v\| = 11 , and u · v = 1, find \|u + v\|?
Answer» If \|u\| = 6,\|v\| = 11 , and u · v = 1, find \|u + v\|? Solution:

Discussion

5381.	Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}
Answer» Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)} Solution:

Discussion

5382.	What is 100 km/h in mph?
Answer» 100 km/h is equal to 62.14 mph We can convert kilometer per hour (km/h) into miles per hour (mph) using the conversion factor for metric units.

Discussion

5383.	How to express 2to the power of 31?
Answer» 2to the power of 31can be expressed as 2³¹= 2× 2× 2× … 31 times=214748e49. Powers orexponentsaredefined as the total number of times we use the number ina multiplication.For example, 7to the power of 3 means 7is multiplied 3 times.

Discussion

5384.	How to multiply square roots?
Answer» To multiply square roots, we multiply the whole number part and the square root parts separately. Square is a number obtained when a number is raised to the power of two. The square roots are the inverse of squares. They are obtained by raising a number to the power of 1/2.

Discussion

5385.	How many roots do the following equations have? -12x2- 25x + 5 + x3= 0
Answer» How many roots do the following equations have? -12x²- 25x + 5 + x³= 0 Solution:

Discussion

5386.	2x - y - 4 = 0 and3x + y - 9 = 0,what is the solution set of the given system?
Answer» 2x - y - 4 = 0 and3x + y - 9 = 0,what is the solution set of the given system? Solution:

Discussion

5387.	Consider the quadratic function f(x) = -2x2 + 5x - 4. The leading coefficient of the function is
Answer» Consider the quadratic function f(x) = -2x²+ 5x - 4. The leading coefficient of the function is Solution:

Discussion

5388.	Find the exact value of the trigonometric function at the given real number. sin(4π/3), sec(7π/3), cot(-2π/3)
Answer» Find the exact value of the trigonometric function at the given real number. sin(4π/3), sec(7π/3), cot(-2π/3) Solution:

Discussion

5389.	In the center of town there is a square park with side length 30 ft. If a person walks from one corner of the park to the opposite corner, how far does the person walk? Round to the nearest foot.
Answer» In the center of town there is a square park with side length 30 ft. If a person walks from one corner of the park to the opposite corner, how far does the person walk? Round to the nearest foot. Solution:

Discussion

5390.	How do you integrate cot2(x)dx?
Answer» ∫ cot²(x)dx = -cot x-x+C . We will use the identity cosec²x=1 +cot²xto integratecot²(x)dx.

Discussion

5391.	How to express 7to the power of 4?
Answer» 7to the power of 4can be expressed as 7⁴= 7× 7× 7× 7 = 2401 Powers orexponentsaredefined as the total number of times we use the number ina multiplication.For example, 9to the power of 3 means 9is multiplied 3 times.

Discussion

5392.	Give the statement of Pythagoras Theorem
Answer» Pythagoras theorem states thatin a right-angled triangle the square of the hypotenuse is equal to the sum of the square of the other two sides. Pythagoras of Samos is a greek mathematician who stated the relationship between the sides of a right-angled triangle. It was named after him as as ‘Pythagoreantheorem’

Discussion

5393.	If (9/7)3× (49/81)(2x-6)= (7/9)9, What is the value of x?
Answer» If (9/7)³× (49/81)^(2x-6)= (7/9)⁹then value of x is 6 To provethis equation true we will use exponential power identity.

Discussion

5394.	If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)?
Answer» If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)? Solution:

Discussion

5395.	How to express 3to the power of 7?
Answer» 3to the power of 7can be expressed as 3⁷= 3× 3× 3× 3× 3× 3× 3= 2,187. Powers orexponentsaredefined as the total number of times we use the number ina multiplication.For example, 6to the power of5means 6is multiplied 5times.

Discussion

5396.	Express 33/2in radical form.
Answer» 3^3/2in radical form is√3³= √27 An expression that uses a root, such as asquare root, cube rootisknown as a radical notation.

Discussion

5397.	If x - 12y = -210 and x - 6y = 90, then x =
Answer» If x - 12y = -210 and x - 6y = 90, then x = Solution:

Discussion

5398.	Write the quadratic function f(x) = 3x2 - 6x + 9 in vertex form.
Answer» Write the quadratic function f(x) = 3x² - 6x + 9 in vertex form. Solution:

Discussion

5399.	The Hardy-Weinberg principle is written as the equation p2 + 2pq + q2 = 1. What does p represent?
Answer» The Hardy-Weinberg principle is written as the equation p² + 2pq + q² = 1. What does p represent? Solution:

Discussion

5400.	A hemispherical tank is filled with water and has a diameter of 20 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
Answer» A hemispherical tank is filled with water and has a diameter of 20 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound? Solution:

Discussion

Explore topic-wise InterviewSolutions in .

A bag contains 6 red marbles, 4 blue marbles, 7 green marbles, and 3 yellow marbles. a marble is drawn from the bag and is not replaced. Then a second marble is drawn. What is the probability that both marbles were green?

Isthe empty set a subset of the empty set?

Find the value of the expression 2x3 + 3y2 - 17 when x = 3 and y = 4.

What is an irrational number in math?

How do you write two hundred million as numbers?

Given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?

Factor completely 5x2 - 40. 5(x + 8)(x - 8),5(x2 - 8),5(x + 8)(x - 5),Prime

Over what interval is the graph of f(x) = -(x + 8))2 - 1 decreasing?

Choose one of the factors of 1331x3 - 8y3. 4, 11x - 2y, 121x2 + 44xy + 4y2, 121x2 - 22xy + 4y2

Divide 33 photos into two groups so the ratio is 4:7.

How Many Zeros in a Trillion?

A triangle has side lengths of 3cm, 4cm, and, 6cm. Is it a right triangle explain?

What time is 12 am in military time?

Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t9/2); t = 1

Atriangle is classified as an equilateral triangle when it has

Solve for x: 4x2 - 4a2x + (a4 - b4) = 0

If Anton can carry 3 boxes per trip, how many trips will it take him to move 51 boxes? 17, 27, 30, 37

(1) 10 (2) 100 (3) 1000 (4) 1

Choose the correct option. The A.M. of the first ten odd numbers is

What is 0.2 as a Fraction?

Two sides of a triangle measure 5inand 12in. Which could be the length of the third side?

A multiple-choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?

Which function below is the inverse of f(x) = x2 - 25? x squared over 25 ±square root of the quantity x plus 25 ±5 times the square root of x 1 over quantity x squared minus 25

What is the next two letters in the sequence: a - e - f - h - i - k - l - m - …

Let f be the function defined by f(x) = x3+ x. If g(x) = f-1(x) and g(2) = 1. What is the value of g'(2)?

Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5

Let f(x) = 2x + 2. Solve f-1(x) when x = 4

Given the function f(x) = 4(x + 3) - 5, solve for the inverse function when x = 3.

Prove that sin6A + cos6A =1 - 3sin2A cos2A

If |u| = 6,|v| = 11 , and u · v = 1, find |u + v|?

Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}

What is 100 km/h in mph?

How to express 2to the power of 31?

How to multiply square roots?

How many roots do the following equations have? -12x2- 25x + 5 + x3= 0

2x - y - 4 = 0 and3x + y - 9 = 0,what is the solution set of the given system?

Consider the quadratic function f(x) = -2x2 + 5x - 4. The leading coefficient of the function is

Find the exact value of the trigonometric function at the given real number. sin(4π/3), sec(7π/3), cot(-2π/3)

In the center of town there is a square park with side length 30 ft. If a person walks from one corner of the park to the opposite corner, how far does the person walk? Round to the nearest foot.

How do you integrate cot2(x)dx?

How to express 7to the power of 4?

Give the statement of Pythagoras Theorem

If (9/7)3× (49/81)(2x-6)= (7/9)9, What is the value of x?

If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)?

How to express 3to the power of 7?

Express 33/2in radical form.

If x - 12y = -210 and x - 6y = 90, then x =

Write the quadratic function f(x) = 3x2 - 6x + 9 in vertex form.

The Hardy-Weinberg principle is written as the equation p2 + 2pq + q2 = 1. What does p represent?

A hemispherical tank is filled with water and has a diameter of 20 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?