Answer:
- <u>the first graph:</u> line passing through the points (3, 0) and (0,2), and the shaded region is below the line.
Explanation:
<u>1) Find the expression that represents the situation.</u>
The expression that represents the situation is an inequality:
- Number of orders of paper clips: x
- Weight of an order of paper clips: 2 lbs
- Total weight of x orders of paper clips: 2x
- Number of orders of packing tape: y
- Weight of an order of packing tape: 3 lbs
- Total weight of y orders of packing tape: 3y
- Total weight of paper clips and packing tape in a bag: 2x + 3y
- Maximum weight hold by the hook: 6 lbs
Hence, the total weight must be less than or equal to (≤) 6 lbs, which is:
<u>2) Graph of the inequality 2x + 3y ≤ 6</u>
Line:
- x-intercept: y = 0 ⇒ 2x = 6 ⇒ x = 6 /2 ⇒ x = 3 ⇒ point (3,0)
- y-intercept: x = 0 ⇒ 3y = 6 ⇒ y = 6 /3 ⇒ y = 2 ⇒ point (0,2)
Shaded region:
- Symbol ≤ means that the line is included, which is represented with a solid line, and the region is below the line.
Conclusion: the graph is the line passing through the points (3, 0) and (0,2), and the shaded region is below the line, so that is the first graph of the picture.
Note: strictly speaking, you should include the restrictions that the variables x and y cannot be negative, with which the graph would be only on the first quadrant but those constrains are not handled in the problem.
The graph is also attached.
Answer:
<em></em>
<em>The team must win 2 games to have a win : loss ratio o 2.</em>
Step-by-step explanation:
- <u>Ratio win : loss, r</u>:
r = total wins / total losses
Call n the number of new wins:
Tw =number of wins until so far + number of new win = 6 + n
Tl = number of losses so far + number of new losses = 4 + 0 = 4
r = 2 ⇒ Tw / Tl = (6 + n) / 4 = 2
Solve for n:
- (6 + n ) = 4 × 2
- 6 + n = 8
- n = 8 - 6
- n = 2
Hence,<em> the team must win 6 more games.</em>
- <u>Verification</u>: (6 + 2 ) / 4 = 8 / 4 = 2, which is the target ratio.
Using conditional probability, it is found that P(X⏐Y) = 0.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
In which:
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, we have that X and Y are mutually exclusive events, hence 
, hence:
More can be learned about conditional probability at brainly.com/question/14398287
Answers:
21. Three noncollinear points determine 3 lines and 1 plane
22. If two quadrilaterals are similar, then they are squares
23. PR = 2.6
24. Midpoint is (3,-1)
25. Angle BXD = 108 degrees
26. The complement is 18 degrees
27. A) 30
28. Corresponding angles
29. False; Change "congruent" to "supplementary"
30. Neither
31. Equation is y = (-2/5)x + 9/5
32. Obtuse scalene triangle
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Work Shown
Problem 21)
Three noncollinear points determine 3*2 = 6 pairings but half of those pairings are repeats, so we have 6/2 = 3 unique groups forming 3 lines (think of a triangle and its sides)
The three noncollinear points form a single plane. This is simply an axiom.
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Problem 22)
Original Conditional is in the form If P, then Q
The converse is the flip of that. So we go to If Q, then P.
So we have
Original Conditional: "If two quadrilaterals are squares, then they are similar"
Converse: "If two quadrilaterals are similar, then they are squares"
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Problem 23)
P is between Q and R. By the segment addition postulate, we know
QP+PR = QR
We're given PQ or QP to be 10.2 and we know that QR = 12.8, so this means,
QP+PR = QR
10.2+PR = 12.8
10.2+PR-10.2 = 12.8-10.2
PR = 2.6
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Problem 24)
Add up the x coordinates and divide by 2: (x1+x2)/2 = (8+(-2))/2 = 6/2 = 3
Add up the y coordinates and divide by 2: (y1+y2)/2 = (-6+4)/2 = -2/2 = -1
Therefore the midpoint is (3,-1)
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Problem 25)
Angle DXE = 36 (given)
Angle CXD = angle DXE (definition of bisection)
Angle CXD = 36
Angle CXE = (angle CXD)+(angle DXE)
Angle CXE = 36+36
Angle CXE = 72
Angle BXE = 2*(angle CXE) ... since XC bisects angle BXE
Angle BXE = 2*72
Angle BXE = 144
Angle BXD = (angle BXE) - (angle DXE)
Angle BXD = 144 - 36
Angle BXD = 108
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Problem 26)
From problem 25, we found that Angle CXE = 72. Since XC cuts angle BXE in half, and the other angle is BXC, this means
Angle BXE = angle CXE = 72 degrees
Now subtract that from 90
90 - (angle BXE) = 90 - 72 = 18
The complement is 18 degrees
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Problem 27)
A+B+C = 180
x+x+120 = 180
2x+120 = 180
2x+120-120 = 180-120
2x = 60
2x/2 = 60/2
x = 30
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Problem 28)
Angle 5 and angle 7 are corresponding angles. They are located on the same side of the transversal line. They both correspond to the same side of their respective parallel line counterparts. Both are on the right side of the parallel line they are attached to.
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Problem 29)
The statement in its current form is False. One way to fix it is to change the first underlined term from "congruent" to "supplementary". Angle 3 and angle 2 are same side interior angles which add up to 180 degrees.
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Problem 30)
Slope of AB = (y2-y1)/(x2-x1)
Slope of AB = (-2-6)/(-2-10)
Slope of AB = -8/(-12)
Slope of AB = 2/3
Slope of CD = (y2-y1)/(x2-x1)
Slope of CD = (2-6)/(6-(-6))
Slope of CD = -4/12
Slope of CD = -1/3
Multiply the slopes:
(Slope of AB)*(Slope of BC) = (2/3)*(-1/3) = -2/9
The result is NOT equal to -1, so the lines are NOT perpendicular
The two slopes are NOT equal, so the lines are NOT parallel
So the answer is "neither"
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Problem 31)
Anything parallel to 2x+5y = 12 is of the form 2x+5y = C where C is some fixed number
Plug in the given point (x,y) = (2,1) to find C
2x+5y = C
2*2+5*1 = C
4+5 = C
9 = C
C = 9
So we go from 2x+5y = C to 2x+5y = 9. Now solve for y
2x+5y = 9
2x+5y-2x = 9-2x
5y = -2x+9
5y/5 = (-2x+9)/5
y = (-2/5)x + 9/5
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Problem 32)
A+B+C = 180
16+B+64 = 180
B+80 = 180
B+80-80 = 180-80
B = 100
The angle B is 100 degrees, which is larger than 90 degrees. We have an obtuse triangle because of this fact.
All three angles (16, 64, 80) are different, so the side lengths are different. The three different side lengths means we have a scalene triangle.
Answer:
Any integer multiplied can give rational number
Step-by-step explanation:
