The y-value of the vertex is positive 3, as shown by the +3 on the right hand side of the equation, and the x-value is -1, from the (x+1)^2 (remember, when the number is inside the brackets, flip the sign) The vertex would be (-1, 3)
If you are looking for a rigorous answer (calculus), we must find the mininum point of the equation: f(x) = (x+1)^2 + 3 f
f'(x) = 2(x+1) = 2x + 2
2x + 2 = 0
x = -1
f(1) = (-1 + 1)^2 + 3
f(1) = 0 + 3 = 3
(-1, 3)
25.8%
First, determine how many standard deviations from the norm that 3 tons are. So:
(3 - 2.43) / 0.88 = 0.57/0.88 = 0.647727273
So 3 tons would be 0.647727273 deviations from the norm. Now using a standard normal table, lookup the value 0.65 (the table I'm using has z-values to only 2 decimal places, so I rounded the z-value I got from 0.647727273 to 0.65). The value I got is 0.24215. Now this value is the probability of getting a value between the mean and the z-score. What I want is the probability of getting that z-score and anything higher. So subtract the value from 0.5, so 0.5 - 0.24215 = 0.25785 = 25.785%
So the probability that more than 3 tons will be dumped in a week is 25.8%
Answer:
The width of the rectangular lid is 15 cm.
Step-by-step explanation:1. Let's review the information given to us to answer the question correctly:
Length of the ribbon used by Jun = 56 cmLength of the rectangular lid = 13 cm
2. What is the width of the lid? The ribbon used by Jun is equivalent to the perimeter of the rectangular lid, therefore:Perimeter = 2 * Length + 2 * WidthReplacing with the values we have:56 = 2 * 13 + 2 * Width56 = 26 + 2Width2Width = 56 - 262Width = 30Width = 30/2Width = 15
Answer:
(6,17)
Step-by-step explanation:
2x+5=3x-1
-3x -3x
-x+5=-1
-5 -5
-x=-6
^divided by -1 on both sides
x=6
y=2x+5
y=(2)(6)+5
y=17
The exterior angles should be A & C
