500= (19.50-8.00)x
500 = 11.50x
x=500/11.50=43.48
so he needs to sell approximately 44 centerpieces to break even
Answer:
Axis of Symmetry is x = 2
Vertex is (2, -9)
X Intercepts are (5, 0) and (-1, 0)
Step-by-step explanation:
Quadratic Equation is in standard form. Formula find the x value of the vertex in standard form is -b/2a
a=1
b=-4
c=-5
--4/2(1) = 2
Plugin to find the y value of the vertex.
2^2-4(2)-5=y
4-8-5=y
y = -9
The x value of the vertex (in this case is 2) is the axis of symmetry. Therefore the axis of symmetry is x=2
Factor the equation to put into intercept form.
(x-5)(x+1) = y
The equation can be FOIL-ed to get back to standard form.
Separate the 2 parentheses and whatever can cancel the parentheses are your intercepts.
For (x-5) your intercept is (5, 0)
For (x+1) your intercept is (-1, 0)
The x intercepts are where the parabola will cross the x axis on the graph.
It takes 3/9 to make 1/3.
You multiply the 1 (in 1/3) by 3, and you multiply the 3 (in 1/3) by 3. You get 3/9. You needed to multiply by 3 to make 1/3 have a common denominator is 9.
Answer: a) 0.996, b) 0.253, c) 0.02.
Step-by-step explanation:
Since we have given that
Probability of success = Probability of the math majors belong to ethnic minorities = 33% = 0.33 =p
Probability of failure = q = 1-0.33 = 0.67
Number of students selected = 7
a) No more than 5 belong to an ethnic minority
So, using "binomial distribution", we get that

b. Exactly three of them belong to an ethnic minority
So, it becomes,

c. None of them belong to an ethnic minority

Hence, a) 0.996, b) 0.253, c) 0.02.
Answer:
When we know all 3 sides we use the law of cosines
a = 47
b = 11
c = 38
cos (A) = (b^2+c^2-a^2) / (2bc)
cos (A) = -0.7703349282
Angle A = 140.38
cos (B) = (a^2 + c^2 -b^2) / (2ac)
cos (B) = 0.9888017917
Angle B = 8.5826 degrees
cos (C) = (a^2 + b^2 -c^2) / 2ab
cos (C) = 0.8568665377
cos (C) = 31.033 degrees
Angle W would be the smallest angle so it equals
31.033 degrees or rounded to nearest tenth
31.03
Step-by-step explanation: