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denis-greek [22]
2 years ago
12

3|2z-4|-6>12 Solve for z

Mathematics
1 answer:
mina [271]2 years ago
3 0

Answer:

312z-41-6>12

subtract -41-6

312z-47>12

add it on both sides

312z-47>12

      +47   +47

312z>59

divide 312 to both sides

z<0.189

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Y = 7x + b
2 = 7 + b, b = -5
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2 years ago
The distance between the point (2,1,1) and the plane x-2y=5 is​
Eduardwww [97]

The given plane has normal vector

x-2y=5\implies\mathbf n=\langle1,-2,0\rangle

Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation

\mathbf r(t)=\langle1,-2,0\rangle t+\langle2,1,1\rangle=\langle 2+t, 1-2t, 1\rangle

This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when

x-2y=5\implies(2+t)-2(1-2t)=5\implies5t=5\implies t=1

which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of \mathbf r(t)).

So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):

\sqrt{(2-3)^2+(1-(-1))^2+(1-1)^2}=\boxed{\sqrt5}

7 0
3 years ago
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6 0
3 years ago
Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At each stage, a ball is drawn and its color noted. Th
Vilka [71]

Answer:

The probability that the next two balls are blue is \frac{5}{32}

Step-by-step explanation:

There is a total number of 12 balls in the jar (7 Red and 5 blue), if the first marble drawn is a given, that is it is a Red marble, then following the instruction the Red marble and two more Red marbles are added. Therefore making the total number of marbles in the jar to be 14 marbles (9 red and 5 blue).

<u>FIRST EVENT:</u> So the probability of drawing the second marble to be a blue marble becomes = 5/14 [<em>this is the number of blue marbles/ total number of marbles in the jar</em>].

Thereafter the blue marble is returned and two more blue marbles are added to the jar making a total of 16 marbles (9 red and 7 blue}.

<u>SECOND EVENT: </u>So the probability of drawing the third marble to be a blue marble becomes = 7/16 [<em>this is the number of blue marbles/ total number of marbles in the jar</em>].

However, this is not the final answer because the first event and the second event must occur together, therefore, one has to multiply the first events probability and the second events probability to get the probability we are looking for.

So, the probability of picking the next two to be blue = 5/14*7/16 (seven can reduce the 14 to a 2 based on division)

Therefore the probability = 5/32 (the 2 multiplies the 16)

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3 years ago
Please help me and explain!
Sindrei [870]

Answer:

84

Step-by-step explanation:

See the attached document.

6 0
3 years ago
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