Answer:
3) f(x) = 3(x + 2)^2 - 1.
Step-by-step explanation:
f(x) = 3x² + 12x +11
f(x) = 3(x^2 + 4x) + 11 Completing the square:
f(x) = 3[(x + 2)^2 - 4] + 11
f(x) = 3(x + 2)^2 -+3*-4 + 11
f(x) = 3(x + 2)^2 - 12 + 11
f(x) = 3(x + 2)^2 - 1.
Answer:
25-60+36
Step-by-step explanation:
Answer:
The probability that x will take on a value between 120 and 125 is 0.14145
Step-by-step explanation:
For uniform distribution between a & b
Mean, xbar = (a + b)/2
Standard deviation, σ = √((b-a)²/12)
For 110 and 150,
Mean, xbar = (150 + 110)/2 = 130
Standard deviation, σ = √((150-110)²/12 = 11.55
To find the probability that x will take on a value between 120 and 125
We need to standardize 120 & 125
z = (x - xbar)/σ = (120 - 130)/11.55 = - 0.87
z = (x - xbar)/σ = (125 - 130)/11.55 = - 0.43
P(120 < x < 125) = P(-0.87 < x < -0.43)
We'll use data from the normal probability table for these probabilities
P(120 < x < 125) = P(-0.87 < x < -0.43) = P(z ≤ -0.43) - P(z ≤ -0.86) = 0.33360 - 0.19215 = 0.14145
Hope this Helps!!!
Answer:
12 total possible outcomes
Step-by-step explanation:
Because these are independent events, or events that don't rely on each other, the key is to find the possibilites then multiply them all. There are four equal size sections, and three other equal sized sections, so we do 3 * 4 = 12.
Answer:
The first thing you should do for this case is to draw the ordered pairs in the plane and join the points.
The area you are looking for is the area of a rectangle plus the area of a triangle.
Thus, the total area will be
At = (8) * (4.5) + (1/2) * (4) * (2.5) = 41
answer
the area of the city is 41 units^2
Step-by-step explanation:
41 square miles If you draw the outline of the city, you'll realize that if you draw a line from point B to point D, that you can subdivide the city into a triangle and a trapezoid. After performing the division, you can then calculate the area of both polygons and the add their areas together. So first, let's deal with the trapezoid ABDE. The area of a trapezoid is the average of the length of the parallel sides multiplied by the height. The parallel sides are AB and DE. So: ((18-10)+(14-10))*(9-4.5)/2 =(9 + 4)*(4.5)/2 = 12*4.5/2 = 27 Now for the area of triangle BCD. The area of a triangle is 0.5*b*h where b is the base and h the height. I'll use BC as the base and the distance from BC to D as the height. So: (9-2)*(18-14)/2 = 7*4/2 = 14 And now to add the areas. 27 + 14 = 41 So the area of the city is 41 square miles. Note: The subdivision used is not the only possible subdivision, just one of the easier ones. I could have divided the city area into 3 triangles ABE, BDE, and BCD and solved it that way instead. It was just a happy coincidence that AB and DE were parallel and as such I was able to use trapezoid ABDE instead of the two triangles ABE and BDE.
