• ### Math problem?

Best answer: Compound interest equation is: A = P(1 + r/n)^(tn) Where: A = amount after t years P = principal amount (amount at t = 0) r = annual rate n = number of times compounded per year We are given: P = 3800 A = 9200 r = 0.08 n = 12 Plug in what we know and solve for the unknown "t": A = P(1 + r/n)^(tn) 9200 = 3800(1 +... show more
Best answer: Compound interest equation is: A = P(1 + r/n)^(tn) Where: A = amount after t years P = principal amount (amount at t = 0) r = annual rate n = number of times compounded per year We are given: P = 3800 A = 9200 r = 0.08 n = 12 Plug in what we know and solve for the unknown "t": A = P(1 + r/n)^(tn) 9200 = 3800(1 + 0.08/12)^(t * 12) Any values rounded are done so here, but not in my calculator to reduce chances of errors due to rounding... 9200 = 3800(1 + 0.0066667)^(12t) 9200 = 3800(1.0066667)^(12t) 2.4210526 = (1.0066667)^(12t) Natural log of both sides: ln(2.4210526) = ln[(1.0066667)^(12t)] We can move the exponent out of the log: ln(2.4210526) = 12t ln(1.0066667) Divide both sides by 12 ln(1.0066667): t = ln(2.4210526) / [ 12 ln(1.0066667)] t = 0.8842024 / [ 12(0.0066445)] t = 0.8842024 / 0.0797345 t = 11.08933 Since interest is only added monthly, determine how many months this is past 11 years, then round up to the next month: 11 years 1.07 months So it will take 11 years and 2 months to get over \$9200.
1 answer · Mathematics · 2 days ago
• ### Algebra question?

Best answer: Two consecutive integers. If one is "x", the other is "x + 1" We are told both are negative. The product is 650, so: x(x + 1) = 650 x² + x = 650 x² + x - 650 = 0 (x + 26)(x - 25) = 0 x = 25 and -26 Since we are told that the numbers are negative, we can throw out 25 as the first number, so your two numbers... show more
Best answer: Two consecutive integers. If one is "x", the other is "x + 1" We are told both are negative. The product is 650, so: x(x + 1) = 650 x² + x = 650 x² + x - 650 = 0 (x + 26)(x - 25) = 0 x = 25 and -26 Since we are told that the numbers are negative, we can throw out 25 as the first number, so your two numbers are: -26 and -25
2 answers · Mathematics · 4 days ago
• ### Algebra question?

Best answer: The order of operations that you should have learned 3-4 years ago.
Best answer: The order of operations that you should have learned 3-4 years ago.
1 answer · Mathematics · 4 days ago
• ### Will Spiderman 2000 be included in the PlayStation Classic?

Best answer: Unlikely due to licensing requirements. No one knows anything other than the 5 previously announced games until Sony makes more announcements.
Best answer: Unlikely due to licensing requirements. No one knows anything other than the 5 previously announced games until Sony makes more announcements.
1 answer · PlayStation · 3 days ago
• ### What is directly proportional and inversely proportional?

Best answer: If two values are directly proportional, it means as one goes up, the other does as well. you can use this general form for it using x and y as your variables: y = kx where k is a constant for whatever system you are talking about. Inversely proportional is the opposite. as one goes up, the other goes down. So you can use this... show more
Best answer: If two values are directly proportional, it means as one goes up, the other does as well. you can use this general form for it using x and y as your variables: y = kx where k is a constant for whatever system you are talking about. Inversely proportional is the opposite. as one goes up, the other goes down. So you can use this equation: y = k/x Again, k will be some constant.
1 answer · Mathematics · 4 days ago
• ### Find the value of x .(Sqrt 2x-1)-(sqrt x-4)=2?

Best answer: I presume you mean: √(2x - 1) - √(x - 4) = 2 Let's move the second term to the right side, then square both sides: √(2x - 1) = 2 + √(x - 4) 2x - 1 = 4 + 4√(x - 4) + (x - 4) Now simplify and move all terms other than the remaining radical to the other side: 2x - 1 = 4 + 4√(x - 4) + x - 4 2x - 1 = 4√(x - 4) + x x - 1 = 4√(x -... show more
Best answer: I presume you mean: √(2x - 1) - √(x - 4) = 2 Let's move the second term to the right side, then square both sides: √(2x - 1) = 2 + √(x - 4) 2x - 1 = 4 + 4√(x - 4) + (x - 4) Now simplify and move all terms other than the remaining radical to the other side: 2x - 1 = 4 + 4√(x - 4) + x - 4 2x - 1 = 4√(x - 4) + x x - 1 = 4√(x - 4) Now square both sides again: (x - 1)² = 16(x - 4) Simplify to a quadratic: x² - 2x + 1 = 16x - 64 x² - 18x + 65 = 0 This factors: (x - 5)(x - 13) = 0 x = 5 and 13 We have two values for x. Now test them in the original equation to check for extraneous solutions: √(2x - 1) - √(x - 4) = 2 √(2(5) - 1) - √(5 - 4) = 2 and √(2(13) - 1) - √(13 - 4) = 2 √(10 - 1) - √(1) = 2 and √(26 - 1) - √(9) = 2 √(9) - √(1) = 2 and √(25) - √(9) = 2 3 - 1 = 2 and 5 - 3 = 2 2 = 2 and 2 = 2 TRUE and TRUE Both are valid solutions. So the answers are: x = 5 and 13
2 answers · Mathematics · 4 days ago
• ### Find the length of side x. Round to the nearest tenth.?

Best answer: Law of sines says the ratio of the length of a side over the sin of the opposite angle is constant. We have x opposite 45°, so we can set that up: x / sin(45) But our other known length is opposite of an unknown angle, so we need to solve for that first. The sum of three angles in a triangle is always 180, so: 75 + 45 + C = 180 120... show more
Best answer: Law of sines says the ratio of the length of a side over the sin of the opposite angle is constant. We have x opposite 45°, so we can set that up: x / sin(45) But our other known length is opposite of an unknown angle, so we need to solve for that first. The sum of three angles in a triangle is always 180, so: 75 + 45 + C = 180 120 + C = 180 C = 60 So now the other side of the equation is: 9 / sin(60) Set them equal and solve for x: x / sin(45) = 9 / sin(60) x = 9 sin(45) / sin(60) x ≈ 7.3 units
2 answers · Mathematics · 4 days ago
• ### Algebra question?

Best answer: A quadratic would have only one solution if both roots were the same value, or the equation was a perfect square trinomial. So if we say: (x - 1)² = 0 Then expand that: x² - 2x + 1 = 0 Then there is only one root: x = 1
Best answer: A quadratic would have only one solution if both roots were the same value, or the equation was a perfect square trinomial. So if we say: (x - 1)² = 0 Then expand that: x² - 2x + 1 = 0 Then there is only one root: x = 1
4 answers · Mathematics · 4 days ago
• ### How do I calculate population standard deviation?

Best answer: Step 1) Find the mean of the data points. Step 2) For every data point, subtract the mean from it Step 3) Square all results Step 4) Find the mean of the squares Step 5) Get the square root of the previous result
Best answer: Step 1) Find the mean of the data points. Step 2) For every data point, subtract the mean from it Step 3) Square all results Step 4) Find the mean of the squares Step 5) Get the square root of the previous result
1 answer · Mathematics · 2 weeks ago
• ### Amazon sells "Chessmaster - Xbox".?

Best answer: I can't speak for any backward compatibility, but that's a title designed for the original xbox (I call xbox prime so not to be confused with xbox one)
Best answer: I can't speak for any backward compatibility, but that's a title designed for the original xbox (I call xbox prime so not to be confused with xbox one)
2 answers · Xbox · 1 week ago
• ### An open box with a rectangular base is to be constructed from a rectangular piece of cardboard 18 in wide and 22 in long by...?

Best answer: Starting with a piece of cardboard that is 18" by 22", we have a starting length and width. If we cut out x" by x" squares from the corners, the length and widths each gets reduced by 2x (since there is a left and right side and a top and bottom side), so the new lengths and widths become: (18 - 2x) and (22 -... show more
Best answer: Starting with a piece of cardboard that is 18" by 22", we have a starting length and width. If we cut out x" by x" squares from the corners, the length and widths each gets reduced by 2x (since there is a left and right side and a top and bottom side), so the new lengths and widths become: (18 - 2x) and (22 - 2x) with the height of the box being x The volume in terms of x is then: V(x) = lwh V(x) = (18 - 2x)(22 - 2x)x Simplify and put into standard form: V(x) = (396 - 36x - 44x + 4x²)x V(x) = (396 - 80x + 4x²)x V(x) = (4x² - 80x + 396)x V(x) = 4x³ - 80x² + 396x That's your function for volume in terms of x. For the domain of x, it cannot be zero otherwise you don't have a box. it can't be half of the smallest dimension since you will no longer have length. so the domain is: 0 < x < 9 So you can graph the function in this domain using whatever method you know of. To find the maximum volume, we can solve for the zero of the first derivative and throw out any value of x that is outside of this domain: V(x) = 4x³ - 80x² + 396x V'(x) = 12x² - 160x + 396 0 = 12x² - 160x + 396 Divide both sides by 2: 0 = 6x² - 80x + 198 Using quadratic equation: x = [ -b ± √(b² - 4ac)] / (2a) x = [ -(-80) ± √((-80)² - 4(6)(198))] / (2 * 6) x = [ 80 ± √(6400 - 4752)] / 12 x = [ 80 ± √(1648)] / 12 x = [ 80 ± √(16 * 103)] / 12 x = [ 80 ± 4√(103)] / 12 factor out a 4 and cancel out: x = [ 20 ± √(103)] / 3 Using 10.15 as an approximation for √103, we get: x = (20 + 10.15) / 3 and (20 - 10.15) / 3 x = 30.15 / 3 and 9.85 / 3 x = 10.05 and 3.283 We said that x had to be less than 9, so we can throw out the one answer, leaving this as the only value: x = (20 - √103) / 3 inches
4 answers · Mathematics · 1 week ago
• ### Can you explain this division? 613 divided by 71?

Best answer: You eventually will when you find out that there are 0 71's in 6 and 0 71's in 61. So the next step is to see how many 71's in 613. If you can see it without having to use the zero placeholders, go ahead. Just note that if you end up with a remainder larger than your divisor, you missed a step.
Best answer: You eventually will when you find out that there are 0 71's in 6 and 0 71's in 61. So the next step is to see how many 71's in 613. If you can see it without having to use the zero placeholders, go ahead. Just note that if you end up with a remainder larger than your divisor, you missed a step.
4 answers · Mathematics · 4 months ago
• ### What's the growth factor here?

Best answer: I think your first row's Growth/Decay rate as a % is wrong. If the factor is 2.47, it's an increase of 147% (basically, subtract 1, then multiply by 100. This pattern is followed in the second row, 3.43 compared to 243%, is to subtract 3.43 by 1 and then multiply by 100. So to get from the rate as a % to the factor, we reverse... show more
Best answer: I think your first row's Growth/Decay rate as a % is wrong. If the factor is 2.47, it's an increase of 147% (basically, subtract 1, then multiply by 100. This pattern is followed in the second row, 3.43 compared to 243%, is to subtract 3.43 by 1 and then multiply by 100. So to get from the rate as a % to the factor, we reverse the steps: Start with rate as a percent, divide by 100, then add 1. So starting with: 34.94% divide by 100 to get: 0.3494 Then add 1: 1.3494 If this is to be rounded to 2DP, you'd have: 1.35
1 answer · Mathematics · 1 week ago
• ### Trigonometry help?

Best answer: You are given a right triangle with a known angle, known hypotenuse, and an unknown adjacent length. You can use cosine to solve for the unknown length: cos() = adj/hyp cos(55) = x / 72 0.573576 = x / 72 x = 41.2975 So rounded to the nearest whole, the answer is: 41 in.
Best answer: You are given a right triangle with a known angle, known hypotenuse, and an unknown adjacent length. You can use cosine to solve for the unknown length: cos() = adj/hyp cos(55) = x / 72 0.573576 = x / 72 x = 41.2975 So rounded to the nearest whole, the answer is: 41 in.
1 answer · Mathematics · 2 weeks ago
• ### Calc question?

Best answer: For a, you are given the equations, so just substitute and solve: (920 + 2x - 0.02x² + 0.00007x³) / 100 (920 + 2 * 100 - 0.02 * 100² + 0.00007 * 100³) / 100 (920 + 200 - 0.02 * 10000 + 0.00007 * 1000000) / 100 (1120 - 200 + 70) / 100 990 / 100 \$9.90 per toy average when 100 are produced. ----------------- Find the marginal cost, so... show more
Best answer: For a, you are given the equations, so just substitute and solve: (920 + 2x - 0.02x² + 0.00007x³) / 100 (920 + 2 * 100 - 0.02 * 100² + 0.00007 * 100³) / 100 (920 + 200 - 0.02 * 10000 + 0.00007 * 1000000) / 100 (1120 - 200 + 70) / 100 990 / 100 \$9.90 per toy average when 100 are produced. ----------------- Find the marginal cost, so C'(100). So first, find C'(x) (the first derivative): C(x) = 920 + 2x - 0.02x² + 0.00007x³ C'(x) = 2 - 0.04x + 0.00021x² C'(100) = 2 - 0.04(100) + 0.00021(100)² C'(100) = 2 - 4 + 0.00021(10000) C'(100) = 2 - 4 + 2.1 C'(100) = 0.1 The marginal cost when 100 toys are produced is 10 cents. For part c, You are asked to solve for C(101) - C(100), which should be close to C'(100): C(101) - C(100) [920 + 2(101) - 0.02(101)² + 0.00007(101)³] - [920 + 2(100) - 0.02(100)² + 0.00007(100)³] [920 + 202 - 0.02(10201) + 0.00007(1030301)] - [920 + 200 - 0.02(10000) + 0.00007(1000000)] (920 + 202 - 204.02 + 72.12107) - (920 + 200 - 200 + 70) 990.10107 - 990 0.10107 Rounded to the nearest penny, a 10 cent difference.
1 answer · Mathematics · 2 weeks ago
• ### State the range of values of 𝑥 for which the quadratic inequality 𝑥2 −6𝑥 ≥ 0.?

Best answer: x² - 6x ≥ 0 If we factor out the x, we get: x(x - 6) ≥ 0 So values that are equal to zero are in the solution set. This gives us 0 and 6. We are also looking for values that are greater than zero (aka: positive), so let's look at the ranges around our two values: if x > 6 we have positive times positive, which is positive,... show more
Best answer: x² - 6x ≥ 0 If we factor out the x, we get: x(x - 6) ≥ 0 So values that are equal to zero are in the solution set. This gives us 0 and 6. We are also looking for values that are greater than zero (aka: positive), so let's look at the ranges around our two values: if x > 6 we have positive times positive, which is positive, in our solution set. if 0 < x < 6 we have positive times negative, which is negative, not in our solution set. if x < 0 we have negative times negative, which is positive, in our solution set. So including the zeros, your answer is: x ≤ 0 and x ≥ 6
2 answers · Mathematics · 2 weeks ago
• ### By doing rational zeros, I find out the roots of 3x^3+17x^2+21x-9 are 1/3 and -3.?

Best answer: Let's start with this expression equal to 0 to make a function, since you are trying to solve for the zeroes: 3x³ + 17x² + 21x - 9 = 0 The Rational Root Therorm states that any rational roots will be a factor of the constant term (-9) over a factor of the high-degree coefficient (3), so your possible options are: ±1, ±3, ±9, ±1/3... show more
Best answer: Let's start with this expression equal to 0 to make a function, since you are trying to solve for the zeroes: 3x³ + 17x² + 21x - 9 = 0 The Rational Root Therorm states that any rational roots will be a factor of the constant term (-9) over a factor of the high-degree coefficient (3), so your possible options are: ±1, ±3, ±9, ±1/3 (±3/3 and ±9/3 create duplicates of ±1 and ±3, so we don't have to include them again). So we have 8 possible options. It's possible that none of them are roots, or up to 3 of them could be. It's time to brute force check the 8 values since we know that two of them should be, and they are in the list of possible rational roots, I'll test them: 3x³ + 17x² + 21x - 9 3(1/3)³ + 17(1/3)² + 21(1/3) - 9 and 3(-3)³ + 17(-3)² + 21(-3) - 9 3(1/27) + 17(1/9) + 21/3 - 9 and 3(-27) + 17(9) - 63 - 9 3/27 + 17/9 + 21/3 - 9 and -81 + 153 - 63 - 9 1/9 + 17/9 + 63/9 - 81/9 and 0 0/9 and 0 0 and 0 So both of them are roots. Which leaves one left to find. We can turn each root into a factor, then multiply both factors together to get a quadratic which will also be a factor, then divide that from the original polynomial to get a linear expression remaining, which will tell us what the final root is: Known roots are: x = -3 and x = 1/3 So the factors are: (x + 3)(3x - 1) Multiply them together: 3x² - x + 9x - 3 3x² + 8x - 3 Now divide that by the original expression: . . . . . . . . . __x_+_3_____________ 3x² + 8x - 3 ) 3x³ + 17x² + 21x - 9 . . . . . . . . . . 3x³ + 8x² - 3x . . . . . . . . ---------------------------- . . . . . . . . . . . . . . . . 9x² + 24x - 9 . . . . . . . . . . . . . . . . 9x² + 24x - 9 . . . . . . . . . . . . . . . ------------------------ . . . . . . . . . . . . . . . . . . . . . . . . . 0 So the third root is also -3. The fully factored form of your original equation is: (3x - 1)(x + 3)² = 0 And your roots are: x = -3 and 1/3
3 answers · Mathematics · 2 weeks ago
• ### When i download a game from playstation now can i play it even after my subscription ends?

Best answer: No. It requires continual membership to the program to continue playing it.
Best answer: No. It requires continual membership to the program to continue playing it.
2 answers · PlayStation · 2 weeks ago
• ### What is the order of operations?

Best answer: Perform any operations within parenthesis first (and if there are nested parenthesis, work from the inside set outward. Then resolve any exponents (square roots can count as both an exponent and parenthesis if a longer expression is under the radical) Then handle any multiplication and division at the same step, in order from left to... show more
Best answer: Perform any operations within parenthesis first (and if there are nested parenthesis, work from the inside set outward. Then resolve any exponents (square roots can count as both an exponent and parenthesis if a longer expression is under the radical) Then handle any multiplication and division at the same step, in order from left to right Then any addition and subtraction at the same step, in order from left to right.
2 answers · Mathematics · 2 weeks ago
• ### Rational Equations word problems?

Best answer: Let x = number of people on the tour. We know the cost is \$1200, so the average cost per person is the expression: 1200 / x If we add 4 more people, at the same total cost, the average is reduced by \$15. So the average cost per person if you add 4 more people is: 1200 / (x + 4) And that is \$15 less than the original: 1200 / x -... show more
Best answer: Let x = number of people on the tour. We know the cost is \$1200, so the average cost per person is the expression: 1200 / x If we add 4 more people, at the same total cost, the average is reduced by \$15. So the average cost per person if you add 4 more people is: 1200 / (x + 4) And that is \$15 less than the original: 1200 / x - 15 Set them equal and solve for x: 1200 / (x + 4) = 1200 / x - 15 Let's start with dividing both sides by 15 to simplify the equation a little: 80 / (x + 4) = 80 / x - 1 Now multiply both sides the LCD, which is x(x + 4): 80x = 80(x + 4) - x(x + 4) Simplify this to a quadratic and solve: 80x = 80x + 320 - x² - 4x 0 = 320 - x² - 4x 0 = -x² - 4x + 320 I don't like having a leading coefficient that is negative, so I'll multiply both halves by -1, then I'll solve this by completing the square, so I'll add 320 to both sides: 0 = x² + 4x - 320 320 = x² + 4x Adding 4 to both sides, then we can factor the right side: 324 = x² + 4x + 4 324 = (x + 2)² Square root of both sides: ±18 = x + 2 Subtracting 2 from both sides: x = -20 and 16 We can't have a negative number of people paying a negative amount, so throw that out, leaving: 16 people initially signed up for the bus tour.
1 answer · Mathematics · 2 weeks ago