math

(5/7) x (3/4)

(5/7) x (3/4) = (5x3) / (7x4)= 15/28

factor: 3x^3 + 12x^2 - 6x

a factor common to all terms of a polynomial can be factored out. all three terms in the polynomial 3x^3 + 12x^2 - 6x contain a factor of 3x. Pulling out the common factor yields 3x(x^2 + 4x -2)

(-1) ^57

a negative number raised to an even power yields a positive result. A negative number raised to an odd power yields a negative result. -1 to an even power is 1; -1 to an odd power is -1.

convert 36 km/ hr into m/s if 1 km = 1,000 m and 1 hr = 3,600 s

(36km/hr) x (1000m/1km) x (1 hr/3600s) = 10 m/s

express 5/8 as a decimal

0.625

list all the factors of 18

1, 2, 3, 6, 9 and 18 the factors of integer n are the positive integers that divide into n with no remainder. the multiples of n are the integers that n divides into with no remainder. 3 is a factor of 6, and 18 is a multiple of 6.

put the following in standard scientific notation: 1. 103 2. 123456 3. 103 x 10^2 4. 0.103 x 10^-4 5. (2 x 10^6)(9 x 10^2) 6. 1 x 10^4/2 x 10^7

1. 1.03 x 10^2 2. 1.23456 x 10^5 3. 1.03 x 10^4 4. 1.03 x 10^-5 5. 1.8 x 10^9 6. 5 x 10^-4

express 3/10 as a percentage

1/10 = 0.1 = 10% . 3/10 is 3 times that , so it equals 30%

(4x10^10) / (2x10^-6) =

2 x 10^16

(2x10^-10)(4x10^2) / (4x10^4) =

2x10^-12

(3x10^2) + (3x10^3)=

3.3 x 10^3

(6 x 10^3)^2 =

3.6 x 10^7

express 32% as a fraction in lowest terms

32% means 32/100 which reduces to 8/25

(9x10^6)^(1/2)

3x10^3

(4x10^10) / (2x10^-6) =

7 x 10^-5

7^3 =

7 x7x7 = 343

what is the area of a circle with radius 3

A = pi(r)^2 =pi(3)^2 =9pi

AC = 9, BD = 11, and AD = 15. what is the length of BC A___B___C_______D

A___B___C_____D when points are on a line or line segment and the order is known, you can add or subtract lengths. Since AC=9 and AD =15 CD=AD-AC=15-9=6 now, since BD=11 and CD=6 BC=BD-CD=11-6=5

what is the circumference of a circle with radius 3

C = 2(pi)(r)= 2(pi)(3)= 6(pi)

(3x^2 + 5x +7) - (x^2 + 12) =

Combine like terms (3x^2 -x^2) = 5x + (7-12) = 2x^2 + 5x -5

9-2x(5-3)^2+6/3=

PEMDAS (parentheses first, then exponents, then multiplication/division (left to right), and lastly addition/subtraction (left to right)) 5-3 = 2 2^2 =4 9-2x4+6/3 9-8+2=3

\/16 =

\/n is defined as the non-negative number which squared equals n. there are two numbers when squared equal 16; 4 and -4. by definition, however, \/16 means the non negative square root: 4

what is the greatest prime number less than 37

a prime number is a positive integer that is divisible only by 1 and itself. the smallest prime number, and the only even prime, is 2

which of the following is a multiple of 2 but not a multiple of 4:4 124, 352, 483, 562, 708, 984

an integer is divisible by 2 (even) if the last digit is even. An integer is divisible by 4 if the last two digits make a multiple of 4. the last digit of 562 is 2, which is even, so 562 is a multiple of 2. the last two digits make 62, which is not divisible by 4, so 562 is not divisible by 4.

which of the following is a multiple of 3 but not a multiple of 9? 109, 117, 260, 361, 459, 957, 1001

an integer is divisible by 3 if the sum of its digits is divisible by 3. An integer is divisible by 9 if the sum of its digits is divisible by 9. the sum of the digits in 957 is divisible by 3 butt not by 9.

alex drove 120 miles at 40 miles per hour and another 120 miles at 60 miles per hour. what was alex's average speed for the whole 240 miles

average A per B = Total A/ Total B average speed = total distance/ total time to find the average speed for 120 miles at 40 mph and 120 miles at 60 mph, don't just average the two speeds. first figure out the total distance and the total time. the total distance is 120+120 = 240 miles. the times are 3 hours for the first leg and 2 hours for the second leg, or 5 hours total. the average speed, then is 240/5 = 48 mph

what is the greatest common factor of 36 and 48

break down both numbers into their prime factorizations and take all the prime factors they have in common. 36 = 2x2x3x3, and 48 = 2x2x2x2x3. what they have in common is two 2's and one 3, so the GCF is 2x2x3=12

how many hours are needed to travel 220 miles at 55 miles per hour

distance = rate x time 220 miles = (55 miles per hour)(x hours) 220 = 55x x = 220/55 =4

in a group of 18 ppl, the ratio of men to women is 1:2 . How many women are there

if the parts add up to the whole, a part-to- part ratio can be turned into 2 part-to-part ratios by putting each number in the original ratio over the sum of the numbers. if the ratio of men to women is 1 to 2, then the men-to-ppl ratio is 1/(1+2) = 1/3 and the women-to-ppl ratio is 2/(1+2) = 2/3 in other words, 2/3 of the 18 ppl are women

if the length of the one side of a triangle is 6 and the length of another side is 4, what is the complete range of possible values for the length of the third side.

if you know the lengths of two sides of a triangle, then yo also know something about the length of the third side: it's greater than the positive difference and less than the sum of the other two sides. Given a side of 4 and a side of 6, the third side must be greater then 6-4 = 2 and less than 6+4 = 10

express 7(1/3) as an improper fraction

multiple the whole number part by the denominator, then add the numerator. the result is the new numerator (over the same denominator). to convert 7(1/3) first multiple 7 by 3, then add 1, to get the new numerator of 22. put that over the same denominator, 3, to get 22/3

(2a)(3a) =

multiply the coefficients and the variables separately. (2a)(3a) = (2*3)(a*a)= 6a^2

which is greater: (3/4) or (5/7)

one way to compare fractions is to re-express them with a common denominator. (3/4) =21/28 and (5/7) = 20/28. 21/28 is greater than 20/28, so 3/4 is greater than 5/7. another way to compare fractions is to convert them both to decimals. (3/4) converts to .75 and (5/7) converts to approximately .714

a box contains 2 white balls, 6 red balls, and 8 green balls. if a ball is chosen at random, what is the probability that the ball is green

probability = # of desired outcomes/ total # of possible outcomes. if 8 of 16 balls are green the probability of choosing a green ball is 8/16 or 1/2

which is larger 2/3 or (2/3)^2

raising a fraction between 0 and 1 to a power yields a number smaller than the original (2/3)^2 = 4/9

what are the x- and y- intercepts for the following functions? (i) y = 2x + 5 (ii) y = (x-4) / (x^2 + 2x -8)

remember, y = 0 at the x -intercept and x= 0 at the y-intercept (i) x-intercept = -(5/2) y-intercept = 5 (ii) x-intercept = 4 y-intercept = (1/2)

what are the sine and cosine values for the following angles 1. 0 degree 2. 90 degree 3. 30 degree 4. 60 degree 5. 45 degree 6. 180 degree

sin cos 1. 0 1 2. 1 0 3. 1/2 \ /(3/2) 4. \/(3/2) 1/2 5.\/(2/2) \/(2/2) 6. 0 -1

what is the slope of the line that contains the points A(2, 3) and B(0,-1)

slope = (change in y) / (change in x) = rise/run the slope of the line that contains the points A(2,3) and B(0,-1) is (-1, -3) / (0,-2) = -4/-2= 2

the average of 10 numbers is 50 . what is the sum of the 10 numbers

sum = (average) x (number of terms) if the average of 10 numbers is 50, then they add up to 10 x 50, or 500

what is the reciprocal of 3/7

switch the numerator and the denominator. the reciprocal of 3/7 is 7/3. the reciprocal of 5 is 1/5. the product of reciprocals is 1.

convert 4 square feet into square inches (1 ft = 12 in)

the key to converting between units with exponents is raising the conversion to the same power as the unit (4ft^2/1) x (12^2 x in^2)/(1^2xft^2) = 576 in^2

How to find the highest mean and highest standard deviation on a graph

the mean is represented at the peak of a normal curve. the highest mean is at the greatest value where the peak lies on the curve the curve that deviates the most from the mean has the highest standard deviation. that curve is the widest curve

what is the median of 12, 15, 23, 40, and 40

the median is the middle value. the median of 12, 15, 23, 40, and 40 is 23 because its the middle value: two numbers are smaller and two numbers are bigger. if there's an even number of values, the median is halfway between the two middle values. the median of 12, 15, 23, and 40 is 19 because its halfway between the two middle values 15 and 23

f is the midpoint of EH and G is the midpoint of FH. If EH = 32, what is the length of FG E______F__G__H

the midpoint of a segment divides it into two halves of equal length. since EH =32 and F is the midpoint of EH, FH = 32/2 = 16. Then, since G is the midpoint of FH, FG = 16/2 = 8

what is the mode of 12, 15, 23, 40, and 40

the mode is the number that appears the most often. 40 is the mode. if two numbers appear equally often, the are both modes.

(\/6)/(\/3) =

the product of square roots is equal to the square root of the product: \/3 x \/5 = (\/3x5_) = . the quotient of square roots is equal to the square of the quotient: (\/6)/ (\/3) = (\/6 / 3) = \/2

what is the remainder when 487 is divided by 5

the remainder is the number left over after division. 487 is 2 more than 485 is a multiple of 5, so when 487 is divided by 5, the remainder will be 2.

what is the positive difference between the sum of 4 and 5 and the product of 4 and 5

the sum is the result of addition. the difference is the result of subtraction. the product is the result of multiplication. the sum of 4 and 5 is 9. the product of 4 and 5 is 20. the positive difference between 9 and 20 is 11

if a bag contains 3 white balls, 6 green balls, 8 red balls, and 13 blue balls, what is the probability of drawing a white ball, replacing it, and drawing a blue ball

the word "and" is key to the question. it indicates that we will multiple the probability of drawing a white ball by the probability of drawing a blue ball P(white) x P(blue) = (3/30) x (13/30) = (39/900) = ( 13/300)

if a bag contains 3 white balls, 6 green balls, 8 red balls, and 13 blue balls, what is the probability of drawing a green or red ball

the word "or" is key to the question. it indicates that we will add the probability of drawing a green ball to the probability of drawing a red ball. P(green) + P(red) = 6/30 + 8/30= 14/30= 7/15

(2/15) + (3/10)

to add or subtract fractions, first find a common denominator, then add or subtract the numerators: (2/15) + (3/10) = 4/30 + 9/30 = 4+9/30= 13/30

2a + 3a =

to combine like terms, keep the variable part unchanged while adding or subtracting the coefficients. 2a + 3a= (2+3)a = 5a

How many integers are there from 13 through 31, inclusive

to count consecutive integers, subtract the smallest from the largest and add 1. to count the integers from 13 through 31, subtract: 31-1=18. then add 1:18+1=1

the average of 4 numbers is 7. if 3 of the numbers are 3, 5, and 8, what is the fourth number

to find a missing number when you're given the average, use the sum. if the average of 4 numbers is 7, then the sum of those 4 numbers is 4 x , or 27. three of the numbers (3,5, and 8) add up to 16 of that 28, which leaves 12 for the fourth number

what is the average (arithmetic mean) of 12, 15, 23, 40 and 40

to find the average of a set of numbers, add them up and divide by the number of numbers average = (sum of the terms/number of terms) to find the average of the 5 numbers 12, 15, 23, 40 and 40 first add them up: 12+15+23+40+40 = 130. then divide the sum by 5: 130 / 5 = 26

what is the average of all the integers from 13 through 77, inclusive

to find the average of evenly spaced numbers, just average the smallest and the largest. the average of all the integers from 13 through 77 is the smae as the average of 13 and 77. (13+77)/(2) = 90/2= 45

what is the distance between P(1,1) and Q(7,9)

to find the distance between points, use the Pythagorean theorem or special right triangles. the difference between the x's is one leg and the difference between the y's is the other leg. here one leg is 7-1 = 6 and the other leg is 9-1 = 8. this triangle is 2 times the 3-4-5 right triangle. the distance between the points is the hypotenuse, which is 2 times 5, or 10

what is the least common multiple of 12 and 15

to find the least common multiple, check out the multiples of the larger number until you find one that's also a multiple of the smaller. taking the multiples of 15: 15 is not divisible by 12; 30's not is 45. but the next multiple of 15, 60, is divisible by 12, so its the LCM.

what number is 25% more than 40

to increase a number by a percent, add the percent to 100% convert to a decimal, and multiple. to increase 40 by 25% , add 25% to 100%, convert 125% to 1.25, and multiple by 40. 1.25 x 40 = 50

(x + 3)(x+4)

to multiply binomials, use FOIL. to multiple (x +3) by (x+4), first multiple the First terms: x * x = x^2. next the Outer terms: x * 4 = 4x. Then the Inner terms: 3* x = 3x. And finally the Last terms: 3 * 4 =12. Then add and combine like terms: x^2 + 4x + 3x +12 = x^2 + 7x +12

(x^3) x (x^4)

to multiply powers, add the exponents: x^(3+4) = x^7 to divide powers, subtract the exponents (y^13) /(y^8) = y^(13-8) = y^5

(x^3)^4

to raise a power to an exponent, multiply the exponents (x^3)^4 = x^ (3x4) = x^12

if 3x-10y = -5x + 6y, what is the value of x in terms of y

to solve an equation for one varialbe in terms of another means to isolate the one varialbe on one side of the equation, leaving an expression cotaining the other variable on the other side of the equation. to solve the equation 3x-10y = -5x+6y in terms of y, isolate x: 3x-10y = -5x + 6y 3x + 5x = 6y + 10y 8x = 16y x = 2y

if 5x -12 = -2x+9, what is the value of x

to solve an equation, do whatever is necessary to both sides to isolate the variable. to solve the equation 5x-12= -2x+9, first get all the x's on one side by addding 2x to both sides: 7x-12=9 then add 12 to both sides: 7x=21 then divide both sides by 7 to get: x = 3

what is the complete range of values of x for which 35x+7<-3 and -2x + 7 > 1

to solve an inequality, do whatever is necessary to both sides to isolate the variable. Just remember that when you multiply or divide both sides by a negative number, you must reverse the sign. to solve -5x + 7 < -3, subtract 7 from both sides to get: -5x < -10. now divide both sides by -5, remembering to reverse the sign: x > 2. to solve -2x + 7> 1, subtract 7 from both sides to get: -2x>-6. now divide both sides by -2 (reversing the sign) to get: x<3

(\/4/9) =

to take the square root of a fraction, take the square roots of the numerator and denominator separately (\/4/9) = (\/4) / (\/9) = 2/3

express 2/3 as a percentage

when converting, remember that 1/3 = .333... = 33(1/3)%. 2/3 is twice that , so it equals 66(2/3)%

express 75% as a fraction in lowest term

when converting, remember that 1/4 = .25 = 25% 75% is 3 times that , so it equals 3/4

Express 2/5 as a decimal

when converting, remember that 1/5 = .2 = 20% . 2/5 is twice that much, so it equals 0.4

express 37(1/2) % as a fraction in lowest terms

when converting, remember that 1/8 = .125 = 12(1/2)%. 37(1/2)% is 3 times that, so it equals 3/8

if 4x + 3y = 8 and x + y = 3, what is the value of x

you can solve for two variables only if you have two distinct equations. combine the equations in such a way that one of the variables cancels out. to solve the two equations 4x +3y = 8 and x + y = 3, multiple both sides of the second equation by -3 to get: -3x - 3y = -9. now add the two equations, the 3y and the -3y cancel out, leaving: x = -1

(7.5x10^-5) -(5x10^-6) =

7 x 10 ^-5

(1/2)/(3/5) =

to divide fractions, invert the second one and multiply: (1/2)/(5/3) =(1x5/2x3) =5/6

a basket contains 12 apples and 20 oranges. what is the ratio of oranges to apples

to find a ratio, put the number associated with the word "of" on top and the quantity associated with the word "to" on the bottom and reduce. the ratio of 20 oranges to 12 apples is 20/12, which reduces to 5/3