Please help, find the value of x!!
1 answer:
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Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
=
n = 9
r = 3
= ⁹P₃
=
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 ×
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
<span>[–2.5, –1.6):
Check the picture attached. The half closed interval of x, </span>[–2.5, –1.6) is shown with the red line segment.
The part of the graph corresponding to this interval is also shown. f(-2.5)<f(-2,4) so f (x) in not increasing in the first interval.
second interval, <span>[–2, –1]: in this interval, f(x) is decreasing.
</span>
(for larger values of x in this interval, the graphs decreases continuously, that is f(x) decreases.
third interval, <span>(–1.6, 0]:
The graph decreases for x from -1,6 up to a value close to -0.5. Then from this value to 0, the graph is constant.
So f(x) is not increasing.
the fourth interval </span><span>[0, 0.8):
This interval is shown by the purple line segment. Similar to the third case, in this interval for approximately half of the first values of x, f(x) is constant, then in the second half, f(x) is increasing.
</span><span>(0.8, 2)
in this interval, for larger x, we have larger f(x), so the function is increasing.
Answer: </span>(0.8, 2)
Check the picture attached. The half closed interval of x, </span>[–2.5, –1.6) is shown with the red line segment.
The part of the graph corresponding to this interval is also shown. f(-2.5)<f(-2,4) so f (x) in not increasing in the first interval.
second interval, <span>[–2, –1]: in this interval, f(x) is decreasing.
</span>
(for larger values of x in this interval, the graphs decreases continuously, that is f(x) decreases.
third interval, <span>(–1.6, 0]:
The graph decreases for x from -1,6 up to a value close to -0.5. Then from this value to 0, the graph is constant.
So f(x) is not increasing.
the fourth interval </span><span>[0, 0.8):
This interval is shown by the purple line segment. Similar to the third case, in this interval for approximately half of the first values of x, f(x) is constant, then in the second half, f(x) is increasing.
</span><span>(0.8, 2)
in this interval, for larger x, we have larger f(x), so the function is increasing.
Answer: </span>(0.8, 2)
Answer:
Step-by-step explanation:
A) From the order of the exercise we already know that the intersection points lies on the Y-axis, so its coordinates are P(0;y;0). In order to find it, we only need to substitute the equation 4x+4z=0 into the equation 4x+3y+4z=1. Then,
1=4x+3y+4z = 3y + (4x+4z)= 3y+0.
From the expression above it is easy to obtain that y=1/3, and the intersection point is P(0;1/3;0).
B) To obtain the parallel vector to both planes we use the cross product of the normal vector of the planes.
As we want a unit vector, we must calculate the modulus of u:
.
Thus, the wanted vector is . Therefore,
.
C) In order to obtain the vector equation of the intersection line of both planes, we just need to put together the above results.
where is a real number.