There are nine balls. One is slightly lighter than the rest; the difference is small enough that you can't tell just by picking them up. Using a basic two-sided scale, what's the minimum number of times you'd need to weigh balls to guarantee you find the light one?

Answers

Answer 1

Answer: You will need to weight those balls only twice.You weight 6 balls, 3 on one side of weight and 3 on another, and other3 balls you have are in your hand.

Check picture bellow

Answer 2

Answer: just my thoughts:
this is assuming the rest of the balls are of equal weight.
put 4 and 4 on either side of the scale, if by some chance they end up equal then that means the one ball not on the scale is the lighter. (can switch out with another ball to confirm) and that will be 2 weighs by just luck.
systematically, the more likely case is that the lighter ball will be in the 8 you put on the scale, and it's lightness will cause one side to be higher. this means that the lighter ball is on the higher side.
then take the four balls from the higher side and put two and two back on the scale. again higher sides means lighter. then take those two and put one and one. you will then find the lightest ball.
this method will take 3 weighs

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What is the mean of Variable A? Express answer to one decimal place. Scatter plot on a first quadrant coordinate grid. The horizontal axis is labeled Variable A. The vertical axis is labeled Variable B. Points are plotted at (two, two), (two, eight), (four, three), (five, one), (six, three), (seven, five), (eight, six), (nine, two).

Answers

Variable A is x. Variable B is y. (x,y)

2 , 2, 4, 5, 6, 7, 8, 9

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You have no more than $65 to spend after paying your bills. You want a drink that costs$2.25 including tax, and you want to buy a pair of shoes, which will have 7% sales tax.
What is the inequality that represents the amount of money you have to spend?

a. x + 0.07x + 2.25 > 65
b. x + 0.07x + 2.25 ≤ 65
c. x + 0.07x + 2.25 < 65
d. x + 0.07x + 2.25 ≥ 65

Answers

Answer: B

Step-by-step explanation: You have no more than $65 which means you will want to spend equal to or less. Since you have $65, you will be able to spend up to that amount but you will not be able to spend any more than that. So, you will need to make sure the final price remains under or equal to your amount.

If x is a real number such that $x^3 = 729$ , then $x^2+√(x)$ equals?

Answers

$x^3 = 729 \n \n x^2+√(x) =? \n \n x^3 - 729=0 \n \n x^3-9^3 = 0\n \n(x-9)(x^2+9x+81)=0$

$x^2+9x+81 =0 \ \ or \ \ x-9 = 0\n \n\Delta =b^2-4ac =9^2-4\cdot 1\cdot 81=81- 324 =-243 \n \n and \ we \ know \ when \ \Delta \ is \ negative, \ theres \ no \ solution \n or \n x-9=0 \n \nx=9$

$a^3-b^3=(a-b)(a^2+ab+b^2) \n\n \n x^2+√(x) = 9^2+√(9)=81+3 = 84$

First, we find the value of 'x.'
$x^(3)=729 \n x= \sqrt[3]{729}$
x=9

$x^(2) + √(x)$
$9^(2)$ + $√(9)$
81+3
= 84
$x^(2) + √(x)$ =84

8x-2(x+1)=2(3x-1)A.0
B.2
C.no solution <-- that's what I think it is.
D.identity.

Can someone check my answer

Answers

$8x-2(x+1)=2(3x-1)\n\n8x-2x-2=6x-2\n\n6x-6x=-2+2\n\n0=0\n\nD.\ identity$

Pierres parents ordered some pizzas for a party . 4.5 pizzas were eaten at the party . There were at least 5 1 half of 2 whole pizzas left over . How many pizzas did pierres parents order