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Sergeeva-Olga [200]
3 years ago
11

A weight-management researcher was interested in whether the size of breakfast coulddeter overall food consumption throughout th

e rest of the day. He creates two breakfastgroups, a 350-calorie breakfast and a 750-calorie breakfast, assigns six participants toeach group and tracks their total calories eaten in one day. Because of the detailedattention needed to accurately interview participants about their eating, he works withthe high-calorie group and has his assistant interview the low-calorie group. How manylevels doesthe independent variable have in this study?
Mathematics
1 answer:
Damm [24]3 years ago
4 0

Answer:

Number of independent variables = 2

Step-by-step explanation:

Lets stary with definitions. First of all, variables are properties, of an experiment that take on different amounts or values, rather than a constant that has one unchanging value assigned to it.

Now, we have two kinds of variables namely dependent and independent variables. For this question, we need to know independent variables. Independent variables are variables that could be manipulated at discretion. In the question, the independent variable is "the size of breakfast" because the experimenter chose by reason of choice to either use 350-calories or 750- calories breakfast.

However, the dependent variables are those whose outcomes are with respect to the change in the independent variable. The experiment is actually out to observe how the dependent variable plays out during the experiment. In our example, the dependent variable is "overall food consumption throughout the rest of the day". Thus, the outcome of the overall food consumption throughout the rest of the day is as a result of the size of breakfast taken.

Now, the independent variable can take on various levels, and the number of levels are the number of experimental conditions that the independent variables can take. In our example the independent variable (size of breakfast), was either 350-calories breakfast or 750-calories breakfast, hence it took 2 experimental conditions.

Thus, we say that number of independent variables is 2.

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By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

  1. Define the function seen in the statement by the label f(x₀, y₀).
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    xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
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The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

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The two-way table shows the number of books of each type in Eliza's home ​what is the probability that a randomly selected refer
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Given system of equation is:

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