To find the z-score for a weight of 196 oz., use
A table for the cumulative distribution function for the normal distribution (see picture) gives the area 0.9772 BELOW the z-score z = 2. Carl is wondering about the percentage of boxes with weights ABOVE z = 2. The total area under the normal curve is 1, so subtract .9772 from 1.0000.
1.0000 - .9772 = 0.0228, so about 2.3% of the boxes will weigh more than 196 oz.
I would say yes and no because estimations aren't exact, they're close to the correct value. Trent's estimation is correct since 53+12=65, if we were looking for the exact distance, Trent would be wrong because there are fractions too, so the exact value would be 66 (5/12) or 65 (17/12).
Hope this helped :)
For each, you'll use the slope formula
m = (y2-y1)/(x2-x1)
For function f, you'll use the two points (1,6) and (2,12) since x ranges from x = 1 to x = 2 for function f
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (12-6)/(2-1)
m = 6/1
m = 6
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For function g, you'll use (2,4) and (3,20)
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (20-4)/(3-2)
m = 16/1
m = 16
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For function h, you'll use (0,-6) and (2,-18). The y coordinates can be found by plugging in x = 0 and x = 2 respectively into h(x)
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (-18-(-6))/(2-0)
m = (-18+6)/(2-0)
m = (-12)/(2)
m = -6
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The order from left to right is: h, f, g
The first digit can be any one of the numbers 2-9 That a total of 8 numbers.
The next 6 digits can be any permutation of 6 from the numbers 0 to 9.
(10 numbers)
nPr = n! / r!
so here we have 10P6 = 10! / 6! = 10*9*8*7 = 5040
So final answer is 8 * 5040 = 40,320
Answer: P = 2x + 2y + 10
Step-by-step explanation: The perimeter (P) of a rectangle is given as
P = 2L + 2W
By factorizing the right hand side of the equation we now have
P = 2(L + W)
However, the length of the rectangle is given as x + 6 and the width is given as y - 1
If P = 2(L + W), then
P = 2(x + 6 + {y - 1} )
P = 2(x + 6 + y -1)
P = 2(x + y + 5)
After expanding the bracket, we now have
P = 2x + 2y + 10
