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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 6351. |
At what point do the curves r1 (t) = t, 2 - t, 24 + t2 and r2 (s) = 6 - s, s - 4, s2 intersect? |
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Answer» At what point do the curves r\(_1\) (t) = t, 2 - t, 24 + t² and r\(_2\) (s) = 6 - s, s - 4, s² intersect? Solution: |
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| 6352. |
What is the equation of the line that passes through (-2, -3) and is perpendicular to 2x -3y = 6? |
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Answer» What is the equation of the line that passes through (-2, -3) and is perpendicular to 2x -3y = 6? Solution: |
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| 6353. |
If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1).Find f(5) and f'(5). |
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Answer» If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1). Find f(5) and f'(5). Solution: |
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| 6354. |
Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship? |
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Answer» Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship? Solution: |
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| 6355. |
How do you write an equation in slope-intercept form for a line with points (-3, 1) and (-2, -5)? |
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Answer» How do you write an equation in slope-intercept form for a line with points (-3, 1) and (-2, -5)? Solution: |
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| 6356. |
A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? |
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Answer» A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? Solution: |
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| 6357. |
The value of the expression 12 - 4 × 3 / 2 + 9 is ________. |
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Answer» The value of the expression 12 - 4×3 / 2 + 9 is ________. Solution: |
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| 6358. |
If the tangent line to y = f(x) at (4,3) passes through the point (0,2), Find f(4) and f'(4)? An explanation would also be very helpful. |
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Answer» If the tangent line to y = f(x) at (4,3) passes through the point (0,2), Find f(4) and f'(4)? An explanation would also be very helpful. Solution: |
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| 6359. |
The speed of light is 3.00x108m/s. How fast is this in mph? Use the conversion 1mile = 1610m. |
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Answer» The speed of light is 3.00x108m/s. How fast is this in mph? Use the conversion 1mile = 1610m. Solution: |
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| 6360. |
What is 0.875 as a fraction? |
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Answer» 0.875 as a fraction is expressed as 7/8 A fraction is a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing. |
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| 6361. |
What is the simplified form of 2 over x squared plus x minus 1 over x ? |
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Answer» What is the simplified form of 2 over x squared plus x minus 1 over x ? Solution: |
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| 6362. |
What is 0.25 as a Fraction? |
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Answer» 0.25 as a fraction is written as 1/4. A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator. |
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| 6363. |
What are Independent and Dependent Events in the Probability? |
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Answer» If the occurrence of one event affectsthe probability of another event then it is dependent otherwise independent. Probability defines the likelihood of occurrence of an event. |
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| 6364. |
If sin θ = 5/6, what are the values of cos θ and tan θ? |
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Answer» If sin θ = 5/6, what are the values of cos θ and tan θ? Solution: |
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| 6365. |
Find the product of (4x − 3)(2x² − 7x + 1). |
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Answer» The product of(4x − 3)(2x² − 7x + 1) is 8x³ - 34x² + 25x - 3 The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants. |
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| 6366. |
Solve the following system of equations; 2x + 2y + z = 10, 3x - y + 3z = 10, 2x + 3y - 2z = 6 |
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Answer» Solve the following system of equations; 2x + 2y + z = 10, 3x - y + 3z = 10, 2x + 3y - 2z = 6 Solution: |
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| 6367. |
Find LCM by division method: 48, 72, 80 |
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Answer» The LCM of 48, 72 and 80 using division method is 720. Least Common Multipleis a method to find the smallest common multiple between any two or more numbers |
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| 6368. |
Find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 7π/4? |
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Answer» Find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 7π/4? Solution: |
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| 6369. |
Solve 3x2 + 18x + 15 = 0 by completing the square. |
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Answer» Solve 3x2 + 18x + 15 = 0 by completing the square. Solution: |
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| 6370. |
Use the quadratic formula to solve the equation. -2x2 - 5x + 5 = 0 |
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Answer» Use the quadratic formula to solve the equation. -2x2- 5x + 5 = 0 Solution: |
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| 6371. |
Simplify √24 - 3√45 + 2√20? |
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Answer» Simplify √24 - 3√45 + 2√20? Solution: |
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| 6372. |
Find the value or values of x in the quadratic equation x2 = 6x - 9. |
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Answer» Find the value or values of x in the quadratic equation x2= 6x - 9. Solution: |
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| 6373. |
Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 × 2x |
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Answer» Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 × 2x Solution: |
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| 6374. |
100 pens cost x dollars. How many pens can be purchased for 50 cents, assuming the same rate? |
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Answer» 100 pens cost x dollars. How many pens can be purchased for 50 cents, assuming the same rate? Solution: |
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| 6375. |
What is the integral of sec3(x)? |
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Answer» Answer. The integral of sec3(x) is1/2[(sec xtan x+ ln |sec x+ tan x| ]+ C Integrationis the process of adding or summing up the parts to find the whole. It finds the area under the curve. |
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| 6376. |
What is the equation of a line that passes through the points (3, 6) and (8, 4)? |
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Answer» What is the equation of a line that passes through the points (3, 6) and (8, 4)? Solution: |
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| 6377. |
The sequence (an) is defined by a0 = 1 and a (n+1)= 2an +2 for n = 0,1,2.... what is the value of a3? |
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Answer» The sequence (an) is defined by a0 = 1 and a (n+1) = 2an +2 for n=0,1,2.... what is the value of a3? Solution: |
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| 6378. |
Classify the expression 7x3+ 2x2- 9x + 1 as a monomial, binomial, trinomial, or polynomial. |
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Answer» Classify the expression 7x3+ 2x2- 9x + 1 as a monomial, binomial, trinomial, or polynomial. Solution: |
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| 6379. |
Solve the following system of equations; 4x + 7y - 2z = 0, 3x - 5y + 3z = 9, 3x + 6y - z = 1 |
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Answer» Solve the following system of equations; 4x + 7y - 2z = 0, 3x - 5y + 3z = 9, 3x + 6y - z = 1 Solution: |
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| 6380. |
A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon? |
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Answer» A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon? Solution: |
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| 6381. |
Describe the law of Identities. |
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Answer» Various laws of identities are given below. The Law of identities helps in simplifying complex problems into a simpler ones. |
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| 6382. |
Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 15/8 , x in quadrant II |
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Answer» Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 15/8 , x in quadrant II Solution: |
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| 6383. |
Solve log4(y − 9) + log4(4) = log4(64). |
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Answer» For log4(y − 9) + log4(4) = log4(64),the value of y = 25. We will use the properties of the logarithm to solve the equation. |
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| 6384. |
What is the simple interest of a loan for $1,000 with 5 percent interest after 3 years? |
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Answer» What is the simple interest of a loan for $1,000 with 5 percent interest after 3 years? Solution: |
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| 6385. |
Find cot θ of csc θ = sqrt 5/2 and tan θ |
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Answer» Find cot θ of csc θ = sqrt 5/2 and tan θ Solution: |
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| 6386. |
If a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)? |
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Answer» If a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)? Solution: |
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| 6387. |
Find all solutions to the equation in the interval [0, 2π). cos x = sin 2x |
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Answer» Find all solutions to the equation in the interval [0, 2π). cos x = sin 2x Solution: |
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| 6388. |
Find the area of a regular hexagon with the given measurement. 4-inch side A = sq. in. |
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Answer» Find the area of a regular hexagon with the given measurement. 4-inch side A = sq. in. Solution: |
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| 6389. |
Solve 2cos2x + cosx - 1 = 0 for x over the interval [0, 2π). |
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Answer» Solve 2cos2x + cosx - 1 = 0 for x over the interval [0, 2π). Solution: |
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| 6390. |
Each unit on the map represents 5 miles. What is the actual distance from ocean front to seaside? |
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Answer» Each unit on the map represents 5 miles. What is the actual distance from ocean front to seaside?
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| 6391. |
How to find out what percentage a number is of another number? |
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Answer» Write the given numbers in terms of a fraction and multiply it by 100. Percentage is a number or ratio which is expressed in terms of 100. |
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| 6392. |
A data value is considered _______ if its z-score is less than minus−2 or greater than 2. |
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Answer» A data value is considered _______ if its z-score is less than minus−2 or greater than 2. Solution: |
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| 6393. |
Solve the system algebraically. 5x + 2y = 10 and3x + 2y = 6 |
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Answer» Solve the system algebraically. 5x + 2y = 10 and3x + 2y = 6 Solution: |
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| 6394. |
How to find the diameter of a circle with the radius? |
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Answer» Diameter = 2× Radius The diameter of a circle is twice its radius. |
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| 6395. |
What is the average velocity (in kilometers per hour) of a cart that travels 100 km in 5 hours? |
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Answer» The average velocity of the cart is 20 km/hr We will use the concept of velocity, displacement, and time in order to find the average velocity. |
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| 6396. |
How are the semicircle and the diameter of a circle related? |
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Answer» A diameter divides the circle into two semi-circles. A semicircle is half of a circle and thediameterof a circle is a straight line joining a point from one end of the circle to a point on the other end of the circle, passing through the center. |
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| 6397. |
Find the general solution of the given differential equation. dy/dx + y = e7x |
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Answer» Find the general solution of the given differential equation. dy/dx + y = e7x Solution: |
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| 6398. |
Solve the triangle. A = 45°, b = 34, c = 27 |
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Answer» Solve the triangle. A = 45°, b = 34, c = 27 Solution: |
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| 6399. |
If f(x) + x2[f(x)]3= 10 and f(1) = 2. Find f'(1). |
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Answer» If f(x) + x2[f(x)]3= 10 and f(1) = 2, thenf'(1) = -16/13 We will be using the concept of differentiation to solve this. |
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| 6400. |
What is the common difference between successive terms in the sequence? 9, 2.5, -4, -10.5, -17, … |
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Answer» What is the common difference between successive terms in the sequence? 9, 2.5, -4, -10.5, -17, … Solution: |
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