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 Radicals/695216: please help me solve this math equation. { { { 4 radical 5+ 5 )^2 } } } Sorry Im Not Sure If I Showed the Problem Correctly But i Can Spell It Out Better. It Is : Parenthesis 4 radical 5 + 5 Parenthesis , exponent 2. (4rad5 + 5)^2 sorry if it is an Inconvenience.1 solutions Answer 428366 by stanbon(57377)   on 2012-12-17 14:51:34 (Show Source): You can put this solution on YOUR website!(4rad5 + 5)^2 --- = (4sqrt(5) + 5)(4sqrt(5) + 5) ---- Use FOIL: F: 4sqrt(5)*4sqrt(5) = 16*5 = 80 ----- O: 4sqrt(5)*5 = 20sqrt(5) ----- I: 5*4sqrt(5) = 20sqrt(5) ----- L: 5*5 = 25 ------ Combine those products to get: 105 + 40sqrt(5) ====================== Cheers, Stan H. ================
 Triangles/695211: I need help finding the third side of an isosceles right triangle. I gave been given the lengths radical 18, and 3. I have tried multiplying both radical 18 and 3 by radical 3 (to find the longer leg), but I been so far unsuccessful in doing so. I also have tried multiplying both numbers by 2 to find the hypotenuse. Please tell me what I should do to solve this problem. Thank you.1 solutions Answer 428364 by stanbon(57377)   on 2012-12-17 14:46:29 (Show Source): You can put this solution on YOUR website!I need help finding the third side of an isosceles right triangle. I gave been given the lengths radical 18, and 3. ---------------- Isosceles means "two equal sides". The hypotenuse has to be the longest side so it must be sqrt(18) --- You are told a 2nd side is 3; so the 3rd side must also be 3 or the triangle would not be isosceles. Cheers, Stan H. =============
 Probability-and-statistics/694956: A set of normally distributed data has mean 47 s and standard deviation 0.6 s. Find the percentage of the data within these intervals: a. Between 46 and 47 s b. Greater than 1.5s above or below the mean1 solutions Answer 428363 by stanbon(57377)   on 2012-12-17 13:24:50 (Show Source): You can put this solution on YOUR website!A set of normally distributed data has mean 47 and standard deviation 0.6 s. Find the percentage of the data within these intervals: a. Between 46 and 47 Draw a normal curve with mean = x = 47 Plot 46 on the x-axis Find the z-value of 47 z(46) = (46-47)/0.6 = -1/0.6 = -5/3 Note: The z-value of the mean is 0 ----- Percentage between 46 and 47 = P(-5/3 < z < 0) = 0.4522 ----------------------------------------------------- b. Greater than 1.5s above or below the mean If that "s" means standard deviation the answer is: normalcdf(-100,-1.5) = 0.0668 ================================ Cheers, Stan H. ==================
 Probability-and-statistics/695174: suppose you are using a=0.05 to test the claim that mu>14 using a p-value. you are given the sample statistics n=50 xbar=14.3 and s=1.2. find the p-value1 solutions Answer 428362 by stanbon(57377)   on 2012-12-17 13:14:43 (Show Source): You can put this solution on YOUR website!suppose you are using a=0.05 to test the claim that mu>14 using a p-value. you are given the sample statistics n=50 xbar=14.3 and s=1.2. find the p-value -------- Ho: u <= 14 Ha: u > 14 (claim) ------- z(14.3) = (14.3-14)/[1.2/sqrt(50)] = 1.7678 --------------------- p-value = P(z > 1.7678) = normalcdf(1.7678,100) = 0.0385 ======================== cheers, Stan H.
 Probability-and-statistics/695191: The load L that a horizontal beam can safely support is directly proportional to the square of the depth, d, of the beam. A beam with a depth of 8 inches can safely support 800 pounds. a)Find the constant variation and write the variation equation b)Find the load that a similar beam with a depth of 6 inches can safely support. I set this up at a cross multiply problem and got the wrong answer, so I'm not sure where I went wrong. As for b, I'm not sure how to even go about solving that. Thanks so much!1 solutions Answer 428361 by stanbon(57377)   on 2012-12-17 13:10:34 (Show Source): You can put this solution on YOUR website!The load L that a horizontal beam can safely support is directly proportional to the square of the depth, d, of the beam. A beam with a depth of 8 inches can safely support 800 pounds. a)Find the constant variation and write the variation equation L = k*d^2 800 = k*8^2 k = 800/64 = 12.5 ---- That is the constant of variation. ======================================= b)Find the load that a similar beam with a depth of 6 inches can safely support. L = 12.5*d^2 L = 12.5*6^2 Load = 450 pounds ====================== cheers, Stan H. =====================
 Angles/695193: if m<3=(3x+10), find m<6=(7x-110) what is the value of x and the measure of each angle plz help1 solutions Answer 428360 by stanbon(57377)   on 2012-12-17 13:05:52 (Show Source): You can put this solution on YOUR website!That depends on how the angles are related. Cheers, Stan H. ===========
 Travel_Word_Problems/695192: train A is traveling east at 70 mph. and train B is traveling west at 50 mph. how long with the two trans meet?1 solutions Answer 428359 by stanbon(57377)   on 2012-12-17 13:03:31 (Show Source): You can put this solution on YOUR website!That depends on the distance from A to B. Cheers, Stan H.
 Probability-and-statistics/694933: If five cards are drawn from a standard deck without replacement, what is the probability of drawing: A full house (a three of a kind and a pair?) I'm not sure if it should be: (52/52)*(3/51)*(2/50)*(48/49)*(3/48)*5C3*5C2 or just: (52/52)*(3/51)*(2/50)*(48/49)*(3/48)*5C3 Please explain the 5C3 and 5C2 part. 1 solutions Answer 428345 by stanbon(57377)   on 2012-12-17 10:20:11 (Show Source): You can put this solution on YOUR website!If five cards are drawn from a standard deck without replacement, what is the probability of drawing: A full house (a three of a kind and a pair?) ----- Select a card: 13 ways Select 3 of those cards: 4C3 = 4 Select a different card: 12 ways Select 2 of those cards: 4C2 = 6 ---- Total # of ways to succeed: 13*4*12*6 = 2744 --- Total # of 5 card sets: 52C5 = (52*51*50*49*48)/(1*2*3*4*5) = 2598960 ----------------- P(full house) = 2744/2598960 = 0.00106 ================= Your Questions: 5C3 means the number of groups of size 3 in a set of size 5 5C3 = (5*4*3)/(1*2*3) = 10 5C2 means the number of groups of size 2 in a set of size 5 5C2 = (5*4)/(1*2) = 10 ---- Why are the number's the same? Each time you select 3 from 5 you are automatically selecting a group of 2. ================================ Cheers, Stan H. =================
 Probability-and-statistics/695036: What is the probability of 2 aces being the show cards on a split deck of 52 cards1 solutions Answer 428343 by stanbon(57377)   on 2012-12-17 10:09:48 (Show Source): You can put this solution on YOUR website!What is the probability of 2 aces being the show cards on a split deck of 52 cards ---- # of ways to succeed: 4C2 = 6 ----- # of possible outcomes: 52C2 ----- P(2 aces) = 6/1326 ====================== Cheers, Stan H. ======================
 Probability-and-statistics/695074: There is 1 red ball, 1 blue ball, and 1 yellow ball in a hat. Two balls are selected. Construct a tree driagram and list the sample space if the selection is done. 1 solutions Answer 428341 by stanbon(57377)   on 2012-12-17 10:07:20 (Show Source): You can put this solution on YOUR website!There is 1 red ball, 1 blue ball, and 1 yellow ball in a hat. Two balls are selected. Construct a tree driagram and list the sample space if the selection is done. ---- root column has r ; b ; y --- Branch column has b & y to right of r r & y to right of b r & b to right of y --- Sample Space: rb;ry;br;by;yr/yb -------------------------------------- Cheers, Stan H. =============
 Probability-and-statistics/694977: Three identical slips of paper with the numbers 1, 2, and 3 (one number on each slip) are placed in a box.One slip is randomly selected, and then,without replacement, a second slip is selected. Find the probability that the sum of the two numbers is even. 1 solutions Answer 428340 by stanbon(57377)   on 2012-12-17 10:03:54 (Show Source): You can put this solution on YOUR website!Three identical slips of paper with the numbers 1, 2, and 3 (one number on each slip) are placed in a box.One slip is randomly selected, and then,without replacement, a second slip is selected. Find the probability that the sum of the two numbers is even. ----- Total number of results: 3*2 = 6 ------ Even results: 1+3 = 4 ; 3+1 = 4 = 2 ways ---- Ans: P(even sum) = 2/6 = 1/3 ================ Cheers, Stan H.
 Probability-and-statistics/695111: if an adult male is told that hie height is whithin 2 standard deviations of the mean of the normal distribution of heights of adult males what can he assume1 solutions Answer 428338 by stanbon(57377)   on 2012-12-17 09:59:18 (Show Source): You can put this solution on YOUR website!Ans: His height is not extraordinary. Cheers, Stan H.
 Probability-and-statistics/695145: A social service agency finds that, on the average, 2.86 of every 100 families need help from the agency. About how many families can they expect to help in a town of 976 families? 1 solutions Answer 428337 by stanbon(57377)   on 2012-12-17 09:57:19 (Show Source): You can put this solution on YOUR website!A social service agency finds that, on the average, 2.86 of every 100 families need help from the agency. About how many families can they expect to help in a town of 976 families? ---- Use a proportion: x/976 = 2.86/100 ---- x = 0.0286*976 ---- x = 27.91 (round up to 28 families) =================================== cheers, Stan H. ===================
 Graphs/695140: what is the solution set of x + y = 0 x - y + 2 = 0 1 solutions Answer 428336 by stanbon(57377)   on 2012-12-17 09:54:05 (Show Source): You can put this solution on YOUR website!what is the solution set of x + y = 0 x - y + 2 = 0 ----- x + y = 0 x - y = -2 ---- Add and solve for "x": 2x = -2 x = -1 ------- Solve for "y": x + y = 0 -1 + y = 0 y = 1 ----- Solution: (-1,1) ==================== Cheers, Stan H. ==================
 test/695144: Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two digit number? Please solve using only one variable.1 solutions Answer 428333 by stanbon(57377)   on 2012-12-17 09:40:17 (Show Source): You can put this solution on YOUR website!answered
 Miscellaneous_Word_Problems/695141: When a ball is kicked in the air, its height in meter above the ground can be modeled by h(t)= -4.9t^2 + 14.7t and the distance it travels can be modeled by d(t)=16t where t is the time in seconds. a. How long is the ball in the air b. How far does it travel before it hits the ground c. What is the maximum height of the ball Can you please help? Thank you!1 solutions Answer 428332 by stanbon(57377)   on 2012-12-17 09:38:55 (Show Source): You can put this solution on YOUR website!When a ball is kicked in the air, its height in meter above the ground can be modeled by h(t)= -4.9t^2 + 14.7t and the distance it travels can be modeled by d(t)=16t where t is the time in seconds. a. How long is the ball in the air The ball starts on the ground and ends up on the ground. It's height on the ground is zero. Solve: -4.9t^2+14.7t = 0 t(-4.9t+14.7) = 0 t = 0 and t = 14.7/4.9 = 3 seconds Ans: The ball in in the air for 3 seconds ------------------------------------------------- b. How far does it travel before it hits the ground Ans: 3 meters ----------------------------------- c. What is the maximum height of the ball Vertex occurs at t = -b/(2a) = -14.7/(2*-4.9) = 3/2 h(3/2) = -4.9(3/2)^2 + 14.7(3/2) = 11.025 meters (maximum height) ======================== Cheers, Stan H. ========================
 Average/695130: How do I find the average of these numbers? 2, 4, 6, 8, 10 ,14 1 solutions Answer 428329 by stanbon(57377)   on 2012-12-17 09:27:38 (Show Source): You can put this solution on YOUR website!How do I find the average of these numbers? 2, 4, 6, 8, 10 ,14 ------ Add them up and divide by 6 to get the average. ---- Cheers, Stan H. ----------
 Linear_Equations_And_Systems_Word_Problems/695137: How much pure alcohol must be added to 1200 ml of a 20% solution to make its strength 36%?1 solutions Answer 428328 by stanbon(57377)   on 2012-12-17 09:25:46 (Show Source): You can put this solution on YOUR website!How much pure alcohol must be added to 1200 ml of a 20% solution to make its strength 36%? ------- Equation: alc + alc = alc 0.20*1200 + 1*x = 0.36(1200+x) ----- 20*1200 + 100x = 36*1200 + 36x 64x = 16*1200 x = 300 ml (amt. of pure alc needed) =================== cheers, Stan H. ==============
 test/695133: Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two digit number? 1 solutions Answer 428327 by stanbon(57377)   on 2012-12-17 09:22:39 (Show Source): You can put this solution on YOUR website!Sum of the digits of a two digit number is 9. When We interchange the digits it is found that the resulting new number is greater than the original number by 27. WHAT is the two digit number? ---- Let the original number be 10t+u ------ Interchanged number is 10u+t ==================================== Equations: t + u = 9 10t+u - (10u+t) = 27 ------ Substitute for "t" using t = 9-u ---- 10(9-u)+u -10u-(9-u) = 27 90 - 10u + u -10u-9+u = 27 -18u + 81 = 27 -18u = -54 u = 3 (the unit's digit) ---- Solve for "t" using t = 9-u t = 9-3 = 6 (the ten's digit) ------ Original Number: 10t+u = 63 =============================== Cheers, Stan H. ==========================
 Miscellaneous_Word_Problems/695134: How would I factor: 8x^2z^2-4xz^2-12z^2 So far I have 4z^2(2x-3)(x+1) but I am completely lost. Thank you!1 solutions Answer 428326 by stanbon(57377)   on 2012-12-17 09:13:42 (Show Source): You can put this solution on YOUR website!How would I factor: 8x^2z^2-4xz^2-12z^2 ----- = 4z^2[2x^2 - x -3] --- = 4z^2(2x-3)(x+1) You are correct -------------- cheers, Stan H.
 Age_Word_Problems/695124: Aga was 9 yrs. old. When his sister was born. Now, he is 6 yrs less than twice his sister's age. What are their present ages?1 solutions Answer 428325 by stanbon(57377)   on 2012-12-17 09:10:39 (Show Source): You can put this solution on YOUR website! Aga was 9 yrs. old. When his sister was born. Now, he is 6 yrs less than twice his sister's age. What are their present ages? ---- Equations: a-s = 9 --- a = 2s-6 ---- Substitute for "a" and solve for "s": 9+s = 2s-6 s = 15 yrs: (sister's age now) ---- Solve for a using a = s+9 a = 15+9 = 24yrs (Aga's age now) =============== Cheers, Stan H. ===============
 Permutations/695121: How many unordered 2-letter subsets of the letters A,B, and C are there?1 solutions Answer 428324 by stanbon(57377)   on 2012-12-17 08:58:45 (Show Source): You can put this solution on YOUR website! How many unordered 2-letter subsets of the letters A,B, and C are there? ---- Ordered subsets: ab ; ac ; bc-------3 Total # of 2 letter subsets: 3*2 = 6 ----- Ans: # of unordered 2-letter subsets = 6-3 = 3 ======================================== Cheers, Stan H. ============
 Linear-systems/695050: find the slope if it exists of the line containing the pair of points (-3,14) and (-5,-15)1 solutions Answer 428309 by stanbon(57377)   on 2012-12-16 22:58:45 (Show Source): You can put this solution on YOUR website!find the slope if it exists of the line containing the pair of points (-3,14) and (-5,-15) ---- m = (-15-14)/(-5--3) = -29/-2 = 29/2 ======================================= Cheers, Stan H.
 Linear-equations/695043: Which is an equation of the line that passes through (0,2) and has a slope of 9?1 solutions Answer 428306 by stanbon(57377)   on 2012-12-16 22:54:48 (Show Source): You can put this solution on YOUR website!Which is an equation of the line that passes through (0,2) and has a slope of 9? ------- y = 9x + 2 ============== Cheers, Stan H.
 test/695038: Marinna gives apple to her children. If she give 5 apples to each child, she will have 4 left, but if she gives 8 apples to each child, she will be 8 short. How many children does she have?1 solutions Answer 428305 by stanbon(57377)   on 2012-12-16 22:50:58 (Show Source): You can put this solution on YOUR website!Marinna gives apple to her children. If she give 5 apples to each child, she will have 4 left, but if she gives 8 apples to each child, she will be 8 short. How many children does she have? ----------- Equations: Let x be the # of children: ----- y1 = (x-4)/5 y2 = (x+8)/8 ------ x must be a whole number solution. --- x = 24 (# of children) =========================== cheers, Stan H.
 Expressions-with-variables/695039: what value of x makes the equation true? 4(x-2)=-3(2x-5) 1 solutions Answer 428300 by stanbon(57377)   on 2012-12-16 22:33:16 (Show Source): You can put this solution on YOUR website!what value of x makes the equation true? 4(x-2)=-3(2x-5) ------------ 4x-8 = -6x+15 ------ 10x = 23 --- x = 2.3 ============ Cheers, Stan H. ===========
 Proportions/695034: a waitress has 3 time as many dimes as nickles, one more quarter than nickles that worth \$2.65 in total. find how many dimes she has?1 solutions Answer 428299 by stanbon(57377)   on 2012-12-16 22:29:15 (Show Source): You can put this solution on YOUR website!a waitress has 3 time as many dimes as nickles, one more quarter than nickles that worth \$2.65 in total. find how many dimes she has? ----------------- Equations: d = 3n q = n+1 5n + 10d + 25q = 265 cents --------------------------------- Substitute for d and for q: solve for "n": 5n + 10(3n) + 25(n+1) = 265 ----- 5n + 30n + 25n = 240 ================== 60n = 240 n = 6 (# of nickels) --- d = 3n = 18 (# of dimes) ============================== Cheers, Stan H. ================
 Age_Word_Problems/694988: In 9 years olga will be four times older than she is now. how old is olga1 solutions Answer 428272 by stanbon(57377)   on 2012-12-16 20:40:21 (Show Source): You can put this solution on YOUR website!In 9 years olga will be four times older than she is now. how old is olga ---- Equation: a+9 = 4a ------ 3a = 9 a = 3 yrs old (Olga's age now) ================================= Cheers, Stan H. ==================
 Linear-systems/694987: Solve the system of linear equations by graphing 3x-y=0 6x+y=9 what is the solution of the system of equations? 1 solutions Answer 428271 by stanbon(57377)   on 2012-12-16 20:37:22 (Show Source): You can put this solution on YOUR website!Solve the system of linear equations by graphing 3x-y=0 6x+y=9 ----------- Note: 9x = 9, so x = 1 Then y = 3 ------- ----- Pt. of intersection: (1,3) ====================== Cheers, Stan H. ======================
 logarithm/694828: Given that 2log to the base y of x =3 find the relation involving x and y1 solutions Answer 428269 by stanbon(57377)   on 2012-12-16 20:26:24 (Show Source): You can put this solution on YOUR website!Given that 2log to the base y of x =3 find the relation involving x and y ---- 2logy(x) = 3 ----- logy(x^2) = 3 --- y^3 = x^2 ---- y = x^(2/3) =================== Cheers, Stan H. =============
 logarithm/694980: Write in exponential form. Log1/5 625=-41 solutions Answer 428267 by stanbon(57377)   on 2012-12-16 20:23:13 (Show Source): You can put this solution on YOUR website!Write in exponential form. Log1/5 625=-4 ----- base = (1/5) log = exponent = -4 result = 625 ----- (1/5)^(-4) = 625 ======================= Cheers, Stan H. =====================