In three to five sentences explain how resource scarcity, competition, and the survival of organisms are connected.
Resource scarcity refers to the limited availability of resources in a given ecosystem. Competition arises when multiple organisms require the same resources for their survival. This competition for resources can be fierce, particularly when resources are scarce, and only the fittest and most adapted organisms are able to survive and thrive. Therefore, the survival of organisms depends on how well they can compete for the limited resources available in their ecosystem.
Your teacher asks you to write a paper that supports a claim with evidence. In three to five sentences, describe one claim you would like to make and discuss different forms of evidence you can collect to support your claim. Where would you look for this evidence?
One claim that I would like to make is that regular exercise promotes physical and mental health. Evidence to support this claim can be gathered from scientific studies that have investigated the effects of exercise on health outcomes like weight loss, cardiovascular health, and mood. Data and statistics from government health agencies like the Centers for Disease Control and Prevention can also be used to support this claim. Additional evidence can be sourced from personal testimonials and case studies from individuals who have experienced health benefits as a result of regular exercise. I would look for this evidence in academic journals, online databases, and reliable health and fitness websites.
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Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can use proportions. We know that 7 out of 12 martial artists practice every day, so we can set up a proportion:
7/12 = x/144
To solve for x, we can cross-multiply and simplify:
12x = 7 * 144
12x = 1008
x = 84
Therefore, we can predict that 84 martial arts students practice every day.
b. The sample size is the total number of martial arts students at the school, which is given as 144.
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You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
There are six possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6. Three of these outcomes are even: 2, 4, and 6. To calculate the probability of rolling an even number on the first roll and not rolling a 2 on the second roll, we need to multiply the probability of rolling an even number on the first roll (3/6) by the probability of not rolling a 2 on the second roll (4/6):
P(even, then not 2) = (3/6) * (4/6) = 12/36 = 1/3
Therefore, the probability of rolling an even number on the first roll and not rolling a 2 on the second roll is 1/3.
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A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is 1/6 since there is one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6). Therefore, the theoretical probability of rolling a 3 is:
1/6
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 comes up by the total number of rolls:
Experimental probability = Number of times a 3 comes up / Total number of rolls
Experimental probability = 67 / 450
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 1:
Experimental probability = 67/450
Therefore, the experimental probability of rolling a 3 is 67/450.
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You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent