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How many liters of a 7 percent solution of salt should be added to a 19 percent solution in order to obtain 456 liters of a 15 percent solution?
This is an algebra problem. There will be 2 equations and 2 unknowns. Let x = amount of 7% solution, and y = amount of 19% solution. .07x + .19y = .15*456. x + y = 456; or x = 456-y which will substitute into the first equation. .07(456-y) +.19y = .15*456. 31.92-.07y+.19y = 68.4. .12y = 36.48. y = 304L (amount of 19% solution to add). x = 456-y. x = 456 - 304. x = 152L (amount of 7% solution to add).
What is 4.414 x 109 in standard form?
4.414*109 = 4,414,000,000
What two numbers multiply together to equal -15 and add together to equal -7?
x + y = -7xy = -15y = -x - 7x(-x - 7) = -15-x^2 - 7x = -15 multiplying both sides by -1x^2 + 7x = 15 complete the square;(x^2 + 7x + 49/4) = 15 + 49/4(x + 7/2)^2 = 109/4(x + 7/2) = (plus & minus)square root of 109/41. x = -7/2 + (square root of 109)/22. x = -7/2 - (square root of 109)/2y = -x - 7y = -[-7/2 + (square root of 109)/2] - 7 = 7/2 - (square root of 109)/2 - 71. y = -7/2 - (square root of 109)/2 ory = -x - 7y = -[-7/2 - (square root of 109)/2] - 7 = 7/2 + (square root of 109)/2 - 72. y = -7/2 + (square root of 109)/2 Check it:
What is the annual interest rate if 1600 is invested for 6 years and 456 in interest is earned?
Use the formula I = P x R x TWhere I=interestP=principal investmentR=interest rateT=time in yearsIn this case, we want to know R, so re-arrange the formula to get:R = I / (P x T)=456/ (1600x6)=456/9600=0.0475=4.75%
What are the basic rules of exponents?
In order to add or subtract numbers with exponents, the exponents must be the same. In order to multiply numbers with exponents, you complete the multiplication and add the exponents. In order to divide numbers with exponents, you complete the division, and subtract the bottom exponent from the top exponent. Examples: Addition: 4.6 x 107 + 2.5 x 109 = 0.046 x 109 + 2.5 x 109 = 2.546 x 109 Subtraction: 6.7 x 108 - 2.1 x 105 = 6.7 x 108 - 0.0021 x 108 = 6.66979 x 108 Multiplication: 5.3 x 102 x 8.4 x 106 = 44.52 x 102+6 = 44.52 x 108 = 4.452 x 109 Division: 6.2 x 1012/3.1 x 106 = 2.0 x 1012-6 = 2.0 x 106
