What numbers come next in the pattern?? 1, -3, 9, -27
2 answers:
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Answer:
0.0076 = 0.76% probability that all five plants emerged from treated seeds
Step-by-step explanation:
The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
6 + 6 = 12 seeds, which means that
6 treated, which means that
Five sprouted, which means that
What is the probability that all five plants emerged from treated seeds?
This is P(X = 5). So
0.0076 = 0.76% probability that all five plants emerged from treated seeds
Answer:
To find the scale factor of the enlargement, compare the distance between a pair of corresponding points from both shapes.
<u>Shape K</u>
A = (4, 7)
B = (7, 7)
C = (7, 4)
D = (5, 5)
Horizontal distance between A (4, 7) and B (7, 7) = 3 units
<u>Shape L</u>
A' = (0, 11)
B' = (9, 11)
C' = (9, 2)
D' = (3, 5)
Horizontal distance between A' (0, 11) and B' (9, 11) = 9 units
9 ÷ 3 = 3
Therefore, Shape L is an enlargement of Shape K by scale factor 3.
To find the center of dilation (enlargement), draw two lines through 2 corresponding points (e.g. A and A', B and B') - the point of intersection of these lines is the center of dilation.
Therefore, the center of enlargement is (6, 5) (refer to the second attached image).
