Complete Questions:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers.
a. 40
b. 48
c. 56
d. 64
Answer:
a. 0.35
b. 0.43
c. 0.49
d. 0.54
Step-by-step explanation:
(a)
The objective is to find the probability of selecting none of the correct six integers from the positive integers not exceeding 40.
Let s be the sample space of all integer not exceeding 40.
The total number of ways to select 6 numbers from 40 is 
.
Let E be the event of selecting none of the correct six integers.
The total number of ways to select the 6 incorrect numbers from 34 numbers is:
Thus, the probability of selecting none of the correct six integers, when the order in which they are selected does rot matter is
Therefore, the probability is 0.35
Check the attached files for additionals
If ~v = hv1, v2, v3i and ~w = hw1, w2, w3i are vectors and c is a scalar, then
(a) c~v = hcv1, cv2, cv3i
(b) ~v + ~w = hv1 + w1, v2 + w2, v3 + w3i
(c) ~v − ~w = hv1 − w1, v2 − w2, v3 − w3i.
Answer:
Step-by-step explanation:
slope intercept form is y = mx + b
b is the y intercept ( crossing y axis value).... by inspection b = -4
m is the slope of the line, Slope = m = 1/4 note: the slope is positive
the slope equals the 'rise' over 'run'
if the line moves up the slope is positive, if the line moves down the slope is negative
the rise is how many y units does the line go 'up' or 'down'
the run is how many x units does the line go 'left' or 'right'
the rise = 1 Y unit
the run = 4 X units
y = mx + b m =1/4 b = -4
y = (1/4)x + (-4)
y = (1/4)x - 4
graph a line stating at y = -4 and going up (rising) to the right ONE Y Unit for every FOUR X units (the run)
The answer is <span>5, 4, 2
</span>
Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
x³ - 11x² + 38x - 40
(x - 5) * x² = x³ - 5x² Subtract
____________________________
-6x² + 38x - 40
(x - 5) * (-6x) = -6x² + 30x Subtract
____________________________
8x - 40
(x - 5) * 8 = 8x - 40 Sutract
____________________________
0
Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)
Now, let's simplify x² - 6x + 8.
x² - 6x + 8 = x² - 2x - 4x + 8 =
= x² - 2*x - (4*x - 4*2) =
= x(x - 2) - 4(x - 2) =
= (x - 4)(x - 2)
Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0 or x - 4 = 0 or x - 2 = 0
x = 5 or x = 4 or x = 2
