At a physical therapy center, doctors work with patients to develop an exercise treatment plan to combat injuries. Assume that the time spent doing pool exercises per week has an unknown distribution with a mean of 4.5 hours and a standard deviation of 0.9 hours. A doctor believes most patients at the physical therapy center swim more per week. If the doctor randomly selects 32 physical therapy patients, what is the probability that the average time spent swimming per week is over 4.7 hours? Drag and move the blue dot to select the appropriate probability graph area from the four options on the left. (Note - there are four graphs available to choose from. Only select between less than, greater than, and area between graphs.); Use the Central Limit Theorem to find μx¯ and σx¯; Calculate the z-score for x¯=4.7 and move the slider along the x-axis to the appropriate z-score; The purple area under the curve represents the probability of the event occurring. Interpret the purple area under the curve. Round μx⎯⎯⎯ to one decimal, σx⎯⎯⎯ to three decimals, and P(x⎯⎯⎯>4.7) to four decimal places.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

2x^2+5x+17

your welcome. : )

1010: 3030

is it i think

something over 10 so ? /10

step-by-step explanation: