Answer:
In a quadratic equation of the shape:
y = a*x^2 + b*x + c
we hate that the discriminant is equal to:
D = b^2 - 4*a*c
This thing appears in the Bhaskara's formula for the roots of the quadratic equation:
You can see that the determinant is inside a square root, this means that if D is smaller than zero we will have imaginary roots (the graph never touches the x-axis)
If D = 0, the square root term dissapear, and this implies that both roots of the equation are the same, this means that the graph touches the x axis in only one point, wich coincides with the minimum/maximum of the graph)
If D > 0 we have two different roots, so the graph touches the x-axis in two different points.
Answer:
slope = -1/3, y-intercept (0, -3), x-intercept (-9 , 0)
Step-by-step explanation:
3 - x = 3(y + 4)
3 - x = 3y + 12
3y = 3 - x - 12
3y = -x -9
y = -1/3 x - 3
slope = -1/3
when x = 0 (y-intercept)
y = -1/3 × 0 - 3
y = -3
y-intercept (0, -3)
when y = 0 (x-intercept)
0 = -1/3 x - 3
1/3 x = -3
x = -9
x-intercept (-9 , 0)
The three-dimensional figure that will produce a trapezoid if its cross section was cut by a plane that is not parallel to its base is the rectangular pyramid. If a plane was cut parallel to the base of the pyramid, the shape that would be produced would be a rectangle.
Answer:
0.5 ; 0.475 ; 0.689 ; 0.4013
Step-by-step explanation:
Given that:
Rate of production of defective batteries p = 0.05
Number of batteries produced (n) = 10
The expected number of defective batteries = mean = n * p = 10 * 0.05 = 0.5 batteries
Variance of defective batteries :
Var(X) = n * p * q ; q = 1 - p
Hence,
Var(X) = 10 * 0.05 * 0.95 = 0.475
Standard deviation (X) = sqrt(variance) = sqrt(0.475) = 0.689
Probability that atleast 1 battery is defective :
Using the binomial probability function
P(x ≥ 1) = 1 - p(x = 0)
= 1 - q^n
= 1 - 0.95^10
= 1 - 0.59873693923837890625
= 0.40126306076162109375
= 0.4013
