Five employees working in the same company give $500, $470, $380, $670 and $400 monthly income tax. What is the mean income tax given by all the employees? (Pre-Algebra)
Option B is the best answer. If we add all these amounts and divide it by 5 we get 484. =500+470+380+670+400/5 A cannot be true as it is obtained after adding all the amounts and dividing by 4. C cannot be true as it is the middle value which is not required. D and E are incorrect because adding all the amounts and dividing them by 5 do not yield these answers.
If ƒ (χ)=4χ-3, then ƒ(-2) =? (Elementary Algebra)
Option D is the best answer. If we put -2 in the equation we get ƒ(-2)=4(-2)2-3=13. A cannot be true as the square of -2 will be a positive 4. Therefore, 16 will have a positive sign and it will operate with -3 to get 13 instead of -16. B cannot be true as putting the value in 4χ2 will result in +16. The resultant expression will be 16-3=13. 13 will have positive sign because the resultant answer will carry the sign of the greatest number. C cannot be true as by substituting the ƒ( χ) with ƒ (-2) we will get 16-3 instead of -16-3. E is incorrect because 16-3=13 not 15
In which of the following options the numbers 6⁄11, 7⁄8 and 1 1⁄4 are arranged in descending order? (Pre-Algebra)
C is the best answer. By simplifying the fraction 1 1⁄4, we get 5⁄4. We can see that among all the three fractions has the numerator greater than the denominator, therefore, it is the biggest fraction. Similarly, the greater is the difference between the numerator and denominator the smaller is the number. 7⁄8 has less difference and 6⁄11has greater difference. So, arranging these fractions in descending order we get this sequence 1 1⁄4 , 7⁄8 , 6⁄11. A cannot be true as it is arranged with respect to numerators only. B cannot be true as it is arranged in ascending order rather than descending one. D is incorrect as it is arranged in ascending order by considering the numerators only. E is incorrect as it is arranged randomly rather than in ascending order.
What is the next term in the geometric sequence 1⁄3, 2⁄3,4⁄3? (Intermediate Algebra)
B is the best choice. Geometric sequence has the common ratio between the two consecutive numbers. If we take the ratio of the consecutive numbers like 2/3 and 1/3 or 4/3 and 2/3, the answer is 2. The formula to find the n term in the geometric sequence is arn-1. Here a is the first term, r is the common ratio and n is the sequence of the number. Putting the values in the formula we get =1⁄3 (2 )4-1 =8/3 A cannot be true because the denominator is not considered. This answer will be true if we have the sequence 1,2,4… C is incorrect because the answer is given by the formula arn which is wrong. is incorrect because it is the value of r. E is incorrect as it is the value of a.
Given f=ab2, f=600, b=10, what is the value of a? (Elementary algebra)
A is the best option. Putting the values in the formula we get f=ab2, we get 600=a(10)2 600=100a 600/100=a 6=a B is incorrect as it can only be true if the expression was f=ab. C is incorrect because it has multiplied the value of f with b. D is incorrect because it is the value of b2. E is the value of f.
In scientific notation, 450,000,000 – 120,000,000 is written as (Pre- Algebra)
B is the best option. To write in scientific notation, first subtract the two numbers. =450,000,000-120,000,000 =330,000,000 Now, write the resultant figure in scientific notation. We know that there are already 7 zeros in the number including 33. Now place the decimal point after the first digit i.e. 3 and count the digits after that. We will write the number 330,000,000 in scientific notation as 3.3 x 108. A is incorrect because there are 8 digits after 3 rather than 9. C is incorrect as the digits after 3 are not six. D is incorrect because the digits after 3 are 8 rather than 7. E cannot be true as the power of 10 is negative which is only possible if the figure is in decimal points.
Which of the following expression is equivalent to 2xy(9x2+18xy+4y2)? (Elementary algebra)
E is the best option. We will multiply each option in the bracket with 2xy. =2xy(9x2+18xy+4y2) The powers of the common variables will be added together and we will get the expression 18x3y+36x2y2+8xy3. A cannot be true because 9x2 will be multiplied by 2xy to get the value 18x3y instead of 18x2y. B cannot be true because the first term 9x2 is multiplied by 2x rather than 2xy. C cannot be true because the second value in the algebraic expression will be multiplied by 2xy to get 36x2y2instead of 36xy2. D is incorrect because 4y2 will be multiplied with 2xy to get 8xy3 instead of 8xy2.
To get promoted to grade 6, students must pass English, math and science exam. Past record shows that 85% students pass the English exam and 60% of the students who pass the English exam also pass the science and math exams. Out of 100 students, how many will be promoted to grade 6? (Pre-algebra)
A is the best option. It is given that 85% out of 100 students pass the English test. It means that converting this percentage into number of students we get =85/100 x 100 =85 students Now, out of these 85 students 60% pass science and math exams too. So, here we will convert 60% into number of students like this 60/100 χ 85=51 students B is incorrect because it gives the number of students who pass the English test only. C is incorrect because it directly calculates number of students who pass the science and math exam from the total number of students’ D is incorrect because we get the number 51 after solving the question in two steps rather than 15. E is incorrect because after solving the question in two steps we get the resultant number 51 rather than 40.
The product of two complex numbers (4i+5) and (-4i+5) is (Intermediate algebra)
B is the best option. We will multiply the complex numbers just like we multiply two algebraic expressions. =(4i+5) (-4i+5) =4i(-4i+5) + 5(-4i+5) =-16i2+20i-20i+25 =-16i2+25 We know that i=√-1. Putting the value of i in the expression, we get =16+25 =41 A is incorrect because -16i2 will be equal to 16 rather than -16. C is incorrect because after multiplying the numbers we get the expression -16i2+20i-20i+25 instead of -16i2+20i+25. D is incorrect because after multiplying the complex numbers, we do not get-16i2+20i+20i+25. E is incorrect because 16i2 has the positive sign, while actually it contains the negative sign after simplifying the multiplication.
What fraction exactly lies halfway between 4⁄5 and 5⁄6? ( Pre-algebra)
E is the best option. To find the equation which exactly lies half way between the two fractions we will use the formula: = 1⁄2 (a+b) = 1⁄2 (4⁄5 + 5⁄6) = 1⁄2 (24+ 25⁄30) = 1⁄2 (49⁄30) = 49⁄60 A is incorrect because it just gives the next number by adding 1 to the numerator and denominator respectively. B is incorrect because it is the value of a+b rather than 1/2 (a+b). C is incorrect because gives the reciprocal of the actual answer. D is incorrect because it is calculated by subtracting 1 from the lowest value.
A rectangle who has the length of 7 centimeters, has the perimeter of 26 centimeters. What is area of the rectangle in centimeter square? ( Plane geometry)
C is the best option. The perimeter of the rectangle has the formula 2(l+w) 2(l + w) = 26 2((7+w) =26 7+w=13 w=6 The area of the rectangle is lw. Multiplying length 7 by width 6 we get 42. A is incorrect as it is two times the given perimeter of the rectangle. B is incorrect because it is the value of l+w. D is incorrect because 6 is the value of width. E is incorrect because after substituting values of length and width in the formula we get 42 not 12.
If x: y=3:8 and y: z=2:5, then what is the ratio of x: z? (Pre-algebra)
B is the best option. x: y=3/8 and y: z=2/5 x/y x y/z= 3/8 x 2/5 =6/40 A is incorrect because we cannot take the value of x and z from the ratios as it is to find x: z. C is incorrect because it has taken the value of z and x from the ratios x:y and y:z. D is incorrect because it is the reciprocal of the simplified form of x:y. E is incorrect because we get the value 6:40 instead of 3:2 after simplifying the ratios.
What is the difference between median and mean of the set {3,5,7,10,11,15}? ( Pre-algebra)
D is the best option. The mean of the set is calculated as: 3+5+7+10+11+15/6=8.5 Since, this is the set of even numbers, therefore, the median is calculated by adding the middle two numbers and then dividing them by 2. =10 + 7⁄2 =17/2 =8.5 By taking the difference between mean and the median we get 0. A is incorrect because it has added the mean and the median instead of subtracting it. B is incorrect because it is the value of mean and the median. C is incorrect because by subtracting mean and the median we get 0 instead of 2. E is incorrect because it is the difference of middle two numbers.
The grade distribution of 300 college students is shown below. ( Pre-Algebra) If one student is randomly selected from the college, then what is the probability that that the student has either got A or B grade?
E is the best option. To find the probability, we will do the following procedure. =Number of students who got A grade + Number of students who got B grade / Total number of students =180+ 80⁄300 =260⁄300 A cannot be true as it reflects the probability that the selected student has got A grade only. B cannot be true as it reflects that the selected student has got B grade only. C is incorrect as it divides total number of students with the sum of students who got A and B grades respectively. D is incorrect because it divides total number of students with the number of students who achieved A grade.
In the figure, below a line intersects two lines WX and YZ. What is true about the figure below? (Plane geometry)
C is the best option. When a line intersects a single line, then it forms to angles. Sum of two angles formed after intersection is equal to 180°. <C and <D are formed when the line intersects WX. These two angles are equal to 180°. A cannot be true <C and <D must be equal to 180°. B is incorrect <E and <H should be of the same measure. D is incorrect because <G and <H should be equal to 180° rather than 360°. E is incorrect as <E and <F should be equal to 180°.
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