write an example of antibiotic resistance to pesticides in cockroaches. write three sentences and include the theory of natural selection.
Cockroaches that have developed an antibiotic resistance to pesticides have a higher likelihood of survival compared to those that do not, due to their ability to adapt to their environment through natural selection. As the use of pesticides increases, the surviving resistant cockroaches reproduce and pass on their genetic traits to their offspring, eventually leading to an entire population of antibiotic-resistant cockroaches. Over time, this can make it much more difficult to control cockroach infestations with traditional pesticides.
write about the evolution of beak shape in finches on the Galapagos Islands. write three sentences and include the theory of natural selection.
Finches in the Galapagos Islands evolved different beak shapes as a result of natural selection. The variation in beak shapes allowed the finches to adapt to different food availability on the islands and increase their survival and reproduction rates. As the finches with advantageous beak shapes reproduced more frequently, the population shifted towards those traits, leading to the evolution of distinct species of finches with specialized and unique beak shapes.
Use the table to answer the question.
Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the table. What is the smallest discrepancy between the experimental and the expected probability of this experiment? Write your answer in 3 decimal places, rounded to the nearest thousandth.
The theoretical probability of each outcome is 1/6 or approximately 0.167.
To find the expected frequency, we multiply the theoretical probability by the total number of trials:
0.167 × 60 = 10
Subtracting the expected frequency from the observed frequency for each outcome, we get:
-0.000 (2 - 10)
-1.000 (4 - 9)
0.000 (6 - 6)
0.000 (8 - 15)
0.333 (10 - 13)
-2.000 (12 - 8)
The smallest discrepancy is -2.000, which means that the outcome of 12 occurred 2 times less than expected.
Therefore, the answer is 2.000 rounded to the nearest thousandth, which is 2.000.
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. 2 was landed on 10 times, 4 was landed on 9 times, 6 was landed on 6 times, 8 was landed on 15 times, 10 was landed on 13 times, and 12 was landed on 8 times. What is the smallest discrepancy between the experimental and the expected probability of this experiment? Write your answer in 3 decimal places, rounded to the nearest thousandth.
The total number of trials is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The theoretical probability of each outcome is 1/6 or approximately 0.167.
To find the expected frequency, we multiply the theoretical probability by the total number of trials:
0.167 × 61 = 10.187
Subtracting the expected frequency from the observed frequency for each outcome, we get:
-0.187 (2 - 10)
-1.187 (4 - 9)
-4.187 (6 - 6)
4.813 (8 - 15)
2.813 (10 - 13)
-2.187 (12 - 8)
The smallest discrepancy is -4.187, which means that the outcome of 6 occurred 4.187 times less than expected.
Therefore, the answer is 4.187 rounded to the nearest thousandth, which is 4.187.
A spinner is divided into 4 sections labeled as K, I, N, D. Xavier reproduced the wheel and uses a computer to simulate the outcomes of 500 spins. K was landed on 120 times, I was landed on 140 times, N was landed on 105 times, and D was landed on 135. What is the approximate probability that the spinner will stop on a consonant on the next spin?
The total number of spins is 500.
The number of consonants is 3 out of 4 sections, or 0.75.
To find the expected number of consonants, we multiply the total number of spins by the probability of landing on a consonant:
500 x 0.75 = 375
The number of times a consonant (K, N, or D) was landed on is 120 + 105 + 135 = 360.
The experimental probability of landing on a consonant is the number of times a consonant was landed on divided by the total number of spins:
360 / 500 = 0.72
Therefore, the approximate probability of landing on a consonant on the next spin is 0.72.