The least-squares regression line can be used to predict the number of hours of pain relief given a certain dose.
This is done by taking the sum of the squares of the residuals and finding the minimum value. The residuals are the differences between the observed values and the predicted values. The plot of the residuals versus the dose would reveal the variation in the hours of pain relief across the doses.
For example, the formula for finding the least-squares regression line is
Y = b0 + b1X
where Y is the predicted value, b0 is the intercept, b1 is the slope, and X is the dose.
To calculate the residuals, we take the difference between the observed values and the predicted values for each dose.
residual = Y (observed) - Y (predicted)
The plot of the residuals versus the dose would reveal if the variation in the hours of pain relief is not the same across the doses. This is because if the variation is not the same, then the residuals would not be evenly distributed. If the residuals were evenly distributed, then the sum of the residuals would be equal to zero.
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Sally has a leaking faucet in her bathroom. When she first noticed the leak, there was a puddle that was 2 inches in diameter. Each hour, the diameter will triple in size. If Sally doesn’t do anything to stop the leak, how large will the puddle be after 10 hours?
The required size of the hole after 10 hours will be 118098 inches.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Sally has a leaking faucet in her bathroom. When she first noticed the leak, there was a puddle that was 2 inches in diameter.
According to the given condition
let Y be the size of the hole after 10 hours
Y=2×3¹⁰
Y=118098
Thus, the required size of the hole after 10 hours will be 118098 inches.
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according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.) A. P( z>(0.27-0.22)/root((0.22)(0.73))/300 B. P( z>(0.27-0.22)/root((0.27)(0.73))/300 C. P( z>(0.22-0.27)/root((0.22)(0.78))/300 D. P( z>(0.22-0.27)/root((0.27)(0.73))/300
The probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex] Hence, the correct answer is option D.
This probability can be calculated using the normal approximation to the binomial distribution, with the sample proportion (p-hat) being 0.27, the population proportion (p) being 0.22, and the sample size (n) being 300.
The formula for the standard error of a sample proportion is -
[tex]\sqrt{p(1-p)/n}[/tex]
substituting the values, we get,
[tex]\sqrt{(0.27)(0.73)/300}.[/tex]
Then, we use the formula for a standard normal probability -
P(z > (p-hat - p)/standard error),
substituting the values, we get,
[tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]
Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]
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In the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.
The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday. (Select all that apply.)
A. Students who are skipping class cannot be sampled.
B. Home-schooled students cannot be sampled.
C. Students who are not taking statistics cannot be sampled.
D. Dropouts cannot be sampled.
E. Students who are on a school trip cannot be sampled.
F. Students who are out sick cannot be sampled.
Answer:
c
Step-by-step explanation:
Determine how (if possible) the triangles can be proved similar.
Select one:
A. SAS~
B. SSS~
C. Not Similar
D. AA~
The triangles are proved similar by; D. AA similarity.
What are similar angles of triangles?When on comparing the sides and measures of internal angles of two or more triangles, if there is a common properties among them, then the triangles are similar. Note that being similar does not imply that they are congruent.
So that on comparing the properties of the two triangles given, it can be inferred that:
the two traingles are similar by Angle-Angle theorem which states that; when two angles of two triangles are the same, then the triangles are similar.
Therefore, the statement to prove that the triangles are similar is giben in option D. AA similarity.
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What is the value of x in this proportion?
56=−4x+2
Responses
x=−2 4/5
x equals negative 2 and 4 over 5
x=−4 2/5
x equals negative 4 and 2 over 5
x=−5 1/5
x equals negative 5 and 1 over 5
x=−6 4/5
x equals negative 6 and 4 over 5
The value of x or the expression 56 = -4x + 2 is -27/2.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
56 = -4x + 2
Solve for x.
56 = -4x + 2
Subtract 2 on both sides.
56 - 2 = -4x
54 = -4x
Divide -4 into both sides.
-54/4 = x
x = -54/4
x = -27/2
x = -13(1/2)
Thus,
The value of x is -27/2.
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the directions are : The table shows a proportional relationship between x and y. What is the unit rate of y per x.
Since the table shows a proportional relationship between x and y, the unit rate of y per x is equal to 4.
What is a proportional relationship?In order to have a proportional relationship and equivalent ratios, the variable (x) and the variable (y) must have the same constant of proportionality.
Next, we would calculate the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 12/3 = 20/5 = 24/6 = 32/8
Constant of proportionality (k) = 4.
In this context, we can reasonably infer and logically deduce that the unit rate for this proportional relationship is equal to 4.
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Complete Question:
The table shows a proportional relationship between x and y what is the unit rate of y per x (3, 5, 6, 8) (12, 20, 24, 32)?
Select all the equations that are NOT equivalent to p-7=22
The equivalent expressions are B. p-7-p = 22 -, C. p - 7 + 22 = 22 - 7, D. p - 7 + 7 = 22 - 22
What are algebraic expressions?Algebraic expressions are simply defined as expressions that comprised of terms. coefficients, factors, constants and variables.
They are also made up of some operations which are arithmetic. They include;
AdditionMultiplicationBracketFloor divisionParenthesesSubtractionDivisionFrom the information given, we have the equation as;
p- 7 = 22
To solve the equation, collect like terms
p = 22 + 7
Add the like terms
p = 29
Hence, the value is 29
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The complete question:
Which equation is NOT equivalent to p- 7 = 22? Select all that apply.
A. p-p-7 = 22-p
B. p-7-p = 22 -
C. p - 7 + 22 = 22 - 7
O
D. p - 7 + 7 = 22 - 22
Ep-7 + 7 = 22 +7
Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?
The number of questions that were answered per minute 20 questions
How to determine the number of questions?the question reads: Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?
You should number that a minute is made up of 60 seconds
This implies that 4/5 of a minute is given as 4/5 * 60
This is equal to 48 seconds
So every 48 seconds, Jamie answers 16 questions
This implies that (16*60)/48 = 20
Therefore in one minute Jamie would answer 20 questions
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