A.
–12.6
B.
–3.15
C.
12.6
D.
3.15
Answer:
x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)
Step-by-step explanation:
In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x:
Answer:
(x³ - 5)(x³ + 4)
Step-by-step explanation:
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
- x³ - 20 = (x³ - 5)(x³ + 4)
The correct answer is (c) The experimental probability is 4.06 percentage points greater than the theoretical probability.
To compare the theoretical probability and the experimental probability of drawing a blue tile, we need to first calculate each one.
Theoretical probability of drawing a blue tile:
Total number of tiles = 5 + 6 + 2 + 4 + 1 + 10 + 5 + 3 = 36
Number of blue tiles = 10
Theoretical probability of drawing a blue tile = number of blue tiles / total number of tiles = 10 / 36 = 27.78%
Experimental probability of drawing a blue tile:
Number of draws in the five trials = 54 + 36 + 80 + 22 + 75 = 267
Number of blue tiles drawn in the five trials = 18 + 11 + 20 + 4 + 32 = 85
Experimental probability of drawing a blue tile = number of blue tiles drawn / number of draws = 85 / 267 = 31.84%
To compare the two probabilities, we subtract the experimental probability from the theoretical probability:
Theoretical probability - experimental probability = 27.78% - 31.84% = -4.06%
The result is negative, which means that the experimental probability is greater than the theoretical probability.
However, we need to express this difference as an absolute value (i.e., without the negative sign) and as a number of percentage points.
The absolute value of -4.06% is 4.06%, and this is the amount by which the experimental probability is greater than the theoretical probability.
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Answer:
c.
The experimental probability is 4.06 percentage points greater than the theoretical probability.
Step-by-step explanation:
The answer is A) On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
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The distance between each tree planted along the 2 kilometers and 50 meters road is 205 meters. This is achieved by dividing the length of the road (2050 meters) by the number of spaces between the trees (10).
To solve this problem, first, we need to understand that a kilometer is equal to 1000 meters. Therefore, 2 kilometers 50 meters is equal to 2050 meters. Given that the 11 trees are planted at an equal distance apart along the 2050 meter road, we would have to divide the total road length by the number of spaces between the trees. The number of spaces is always one less than the number of trees, so we have 11-1 = 10 spaces. Therefore, the distance between each tree is 2050 meters divided by 10, which equals to 205 meters.
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