Answer:
Dilation
Step-by-step explanation:
A dilation changes the size of a figure by enlarging the figure of making the figure smaller. The sides will be proportional and the angles will be congruent making the figures similar.
Answer:
Sequence 1: Translate 5 units to the right, and 5 units down
Sequence 2: Reflect across the origin, translate 1 unit down, 1 unit to the right
Step-by-step explanation:
Chose 1 point to focus in, such as (-1, 1)
Move that point 5 units to the right, and 5 units down. See how it matches up with the same corner of the red square?
Now, use that same point, and change the signs of both the x and y, this is to reflect across the origin. (In reality, you are just reflecting across the x and y axis)
So you originally have: (-1,1) -> (1, -1)
Now move this point one unit to the right, and 1 unit to the left.
It may seem that you made it touch the wring corner, but do the same thing with another corner's points. They all flipped!
4x + 12x = 320
16x = 320
x = 20
P(x) = (x^2)(x - 4)^2(x + 4) + some constant(b)
2025 = (1^2)(1 - 4)^2(1 + 4) + b
2025 = 45 + b
b = 1980
Complete Equation:
p(x) = (x^2)(x - 4)^2(x +4) + 1980
or expanded form
p(x) = x^5 - 4x^4 - 16x^3 + 64x^2 + 1980
Answer:
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Explanation:
You can determine the probability of the collector has captured at least two small monsters of the same species is the complent of that all the monsters captured are of different species, i.e. none are of the same species.
The probability than none of the five captured small monsters are of the same species are:
<u>1. Probability than the one monster is of the species One, and the others are not of the species One:</u>
- (1/32) × (31/32) × (30/32) × (29/32) × (28/32)
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<u>2. Probability that the first monster is of the species Two, and the others are not of the species Two:</u>
- (1/32) × (31/32) × (30/32) × (29/32) × (28/32)
<u>3. Probability that the first monster is of the species Three and the others are not of the same species:</u>
- (1/32) × (31/32) × (30/32) × (29/32) × (28/32)
<u>4. Inference</u>
As you see you have to do this 32 times, and then add all the equal 32 probabilities, which is
- 32 × (1/32) × (31/32) × (30/32) × (29/32) × (28/32) = 0.72
That is the probability that none of the five small monsters are of the same species. Then, the probability that at leas two small monsters are of the same species is 1 - 0.72 = 0.28
