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Answers by Garnet H.

Your null hypothesis always suggests equality and that any differences detected are simply due to chance. So a rejection of the null will be suggesting just the opposite, that observed differences are most likely not due to chance.   answer: A

The F-ratio is a ratio of the variation between your treatments to the variation within your treatments. Or, put algebraically, F = (variation between treatments) / (variation within treatments).   The within-treatment variation is the variation due to chance. So, obviously,...

find profit (answer)

okay, that's an upside-down U and the maximum value is at the top  if you put the function in vertex form you can easily find the vertex: group the first two terms and factor out the negative (essentially factoring out -1): p = - (x²-14x) + 54 complete the square by taking...

4n^2=-12n-6 (answer)

bring all terms to one side and set equal to 0 4n²+12n+6=0 factor out 2 2(2n²+6n+3)=0 ===> 2n²+6n+3=0   complete the square 2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4 take square root of...

separate the first two terms on the left and factor out 5 5(m² + (12/5)m ) + 6 = 0 take half the middle coefficient (12/5), square it, and add it to the terms in parentheses 5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides) simplify...

9/2x+1=4/x (answer)

assuming those are 3 terms and not 2 you should start by noting all restrictions for x. In this case, x cannot be 0 because we can't divide by 0. multiply both sides by the lcm (2x) 9 + 2x = 8 ===> 2x = -1 ===> x = -1/2

if the roots are r1 and r2, then the simplest equation is the quadratic: (x-r1)(x-r2) = 0 since yours are -3 and 5, the simplest (quadratic) equation is: (x - -3)(x - 5) = 0 (x+3)(x-5) = 0 which expands to x²-2x-15 = 0

check the number of digits in the number you have 3 possibilities: 1-digit numbers 2-digit numbers 3-digit numbers the only 3-digit candidate you have is 100 and that results in a 1, so this is an easy case for a 1-digit number the only way for the digits to add to 1 is for that number to be =...

suiye is right, and that way is probably even quicker, but another way to arrive at the answer is to set up an equation four consecutive integers: x, (x+1), (x+2), and (x+3) sum them up and get 86 x + x+1 + x+2 + x+3 = 86 now solve for x, the smallest...