Identify at least one confounding variable that undermines the conclusion drawn in the following fictional study:
Prof. Acosta was interested in which of two popular statistics textbooks (Statistics: It Will Change Your Life and Statistics: Bigger, Better, Stronger) was better for students. Prof. Acosta compared the two texts by assigning one text to a section of statistics taught by Prof. Agnew from 10 to 11 a.m. on Monday, Wednesday, and Friday, and the other text to a section of statistics taught by Prof. Alvarez from 7 to 10 p.m. on Wednesday evenings. At the end of the term, all students took the same comprehensive test. Students to whom Statistics: Bigger, Better, Stronger was assigned performed better on the test than did students to whom Statistics: It Will Change Your Life was assigned. Therefore, Prof. Acosta concluded that the former textbook was the better one.
Answers
Answer:
Identifying at least one confounding variable that undermines the conclusion drawn in the fictional study is:
All students took the same comprehensive test.
Step-by-step explanation:
In a study, an independent variable causes an effect on the dependent variable. But a confounding variable is the variable that influences the independent variable as well as the dependent variable. If this third variable is not controlled, it might lead the researcher to make a wrong estimate of the relationship that exists between the independent variable and the dependent variable.
Related Questions
Which of the points below correctly plots the point (−2,−5π/3)?
Select the correct answer below:
A
B
C
D
E
F
Answers
Answer: F
Step-by-step explanation:
Answer: correct answer is A
Step-by-step explanation:
Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.
What function type does the table of values represent?
Answers
Answer:
Quadratic
Step-by-step explanation:
Answer:
Linear
Step-by-step explanation:
for every one unit increase in x, there is a 3 unit increase in y
The slope of the plot line would be 3
The y intercept of the plot line would be -1
y = 3x - 1
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
See picture
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy
box? Explain how you got your answer. (5 points)
Answers
Assuming a thickness of 1 millimeter for the cardboard, the amount of cardboard utilized to build the candy box is roughly 240 cubic centimeters.
What is volume?Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.
Here,
Part A: To find the height of the base, we need to use the formula for the volume of a triangular prism:
V = Bh/2,
where B is the area of the base and h is the height.
We can assume the base of the triangular prism is an equilateral triangle with side length s. The area of an equilateral triangle can be found using the formula:
B = (s² * √(3))/4
We can use this formula to find the side length of the triangle:
s = √((4B)/(√(3)))
Substituting the known values, we have:
1200 = (s² * √(3))/2 * h
solving for h:
h = 1200 * 2 / (s² * √(3))
Substituting the value for s:
h = 1200 * 2 / ((√((4B)/(√(3)))² * √(3))
h = 1200 * 2 / (((4B)/(√(3))) * √(3))
h = 1200 * 2 / (4B)
h = 300 / B
We can find the value of B using the formula:
B = (s² * √(3))/4
Substituting the value for s:
B = (√((4B)/(√(3)))² * √(3))/4
B = (4B)/(3 * √(3))
B = 4B / (√(9))
B = 4B / 3
Solving for B:
B = 300 / h
So, the height of the base is approximately 30 cm.
Part B: To find the amount of cardboard used to make the candy box, we need to find the surface area of the triangular prism and multiply it by the thickness of the cardboard.
The surface area of a triangular prism can be found using the formula:
A = B + Bs + Bh
Where B is the area of the base, Bs is the area of the side of the triangular prism and Bh is the area of the top and bottom of the triangular prism.
We know that B = (s² * √(3))/4 and Bh = B, so
A = B + Bs + Bh = B + 2Bh = 2B + 2Bs
The surface area of the triangular prism is approximately 240 square centimeters.
Assuming the cardboard has a thickness of 1 millimeter, the amount of cardboard used to make the candy box is approximately 240 cubic centimeters.
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At a table in the college cafeteria, three deans meet and discuss class size in their departments. The Math dean remarks, “It was kind of funny thing with our numbers. We divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students. In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 1.”“Gee,” said the Biology dean, “We had something very similar happen. Like you, we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students. In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 2.”Then the History dean made his remarks: “You’re hardly going to believe this, but we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students. In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 3.”How many professors and students were there in the fall and spring in math, biology and history?
Answers
First, let's define our variables.
Let:
• M, be the number of ,math, teachers and ,m, be the number of math students.
,• B, be the number of ,biology, teachers and ,b, be the number of ,biology, students.
,• H, be the number of ,history, teachers and ,h, be the number of ,history, students.
Similarly, we'll have that:
• Cm, will be the number of students in a ,math, class.
,• Cb, will be the number of students in a ,biology, class.
,• Ch, will be the number of students in a ,history, class.
Now, we'll traslate what each dean said into mathematic expressions, so we can work on them and get our solution.
FOR MATH:
The dean said:
1. "We divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."
\(\frac{m}{M}=C_m\)2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 1.”
\(\frac{m+1}{M+1}=C_m-1\)Now, let's clear Cm from equation 2 and equal both equations, as following:
\(\begin{gathered} \frac{m+1}{M+1}=C_m-1 \\ \\ \rightarrow1+\frac{m+1}{M+1}=C_m \\ \\ \Rightarrow1+\frac{m+1}{M+1}=\frac{m}{M} \end{gathered}\)Solving for m, we'll get an expression for the number of students asigned to a certain number of teachers:
\(\begin{gathered} 1+\frac{m+1}{M+1}=\frac{m}{M} \\ \\ \rightarrow\frac{M+1+m+1}{M+1}=\frac{m}{M}\rightarrow\frac{M+m+2}{M+1}=\frac{m}{M} \\ \\ M(M+m+2)=m(M+1) \\ \rightarrow M^2+Mm+2M=Mm+m \\ \rightarrow M^2+2M=m \\ \\ \Rightarrow m=M^2+2M \end{gathered}\)Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.
For instance, we can choose 10 teachers, and we'll get that:
• There were 10 teachers and 120 students in the fall semester
,• There were 11 teachers and 121 students in the fall semester
FOR BIOLOGY:
The dean said:
1. "...we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."
\(\frac{b}{B}=C_b\)2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 2."
\(\frac{b+1}{B+1}=C_b-2\)Similarly, we'll clear Cb from equation 2 and equal both equations, as following:
\(\begin{gathered} \frac{b+1}{B+1}=C_b-2 \\ \\ \rightarrow2+\frac{b+1}{B+1}=C_b \\ \\ \Rightarrow2+\frac{b+1}{B+1}=\frac{b}{B} \end{gathered}\)Solving for b, we'll get an expression for the number of students asigned to a certain number of teachers:
\(\begin{gathered} 2+\frac{b+1}{B+1}=\frac{b}{B} \\ \\ \rightarrow\frac{2B+2+b+1}{B+1}=\frac{b}{B}\rightarrow\frac{2B+b+3}{B+1}=\frac{b}{B} \\ \\ \rightarrow B(2B+b+3)=b(B+1) \\ \rightarrow2B^2+Bb+3B=Bb+b \\ \rightarrow2B^2+3B=b \\ \\ \Rightarrow b=2B^2+3B \end{gathered}\)Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.
For instance, we can choose 10 teachers, and we'll get that:
• There were 10 teachers and 230 students in the fall semester
,• There were 11 teachers and 231 students in the fall semester
FOR HISTORY:
The dean said:
1. "...we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."
\(\frac{h}{H}=C_h\)2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 3."
\(\frac{h+1}{H+1}=C_h-3\)Just as we did, we'll clear Ch from equation 2 and equal both equations, as following:
\(\begin{gathered} \frac{h+1}{H+1}=C_h-3 \\ \\ \rightarrow3+\frac{h+1}{H+1}=C_h \\ \\ \Rightarrow3+\frac{h+1}{H+1}=\frac{h}{H} \end{gathered}\)Solving for h, we'll get an expression for the number of students asigned to a certain number of teachers:
\(\begin{gathered} 3+\frac{h+1}{H+1}=\frac{h}{H} \\ \\ \rightarrow\frac{3H+3+h+1}{H+1}=\frac{h}{H}\rightarrow\frac{3H+h+4}{H+1}=\frac{h}{H} \\ \\ \rightarrow H(3H+h+4)=h(H+1) \\ \rightarrow3H^2+hH+4H=hH+h \\ \rightarrow3H^2+4H=h \\ \\ \Rightarrow h=3H^2+4H \end{gathered}\)Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.
For instance, we can choose 10 teachers, and we'll get that:
• There were 10 teachers and 340 students in the fall semester
,• There were 11 teachers and 341 students in the fall semester
look at attachment!!!!
Answers
Answer:
x = 5
Step-by-step explanation:
We know that BD = 2x - 1 and BC + CD = BD. Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:
BC + CD = BD
x - 3 + 7 = 2x - 1
x + 4 = 2x - 1
x + 5 = 2x
5 = x
Thus, x = 5
Checking the validity of our answer:
We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:
5 - 3 + 7 = 2(5) - 1
2 + 7 = 10 - 1
9 = 9
Thus, our answer is correct.
Marcus was showing how he solved a division problem with the area model below. His pen exploded ink on some of his work.
What is the divisor that is covered with ink on the left side of the model?
A. 100
B. 80
C. 56
D. 29
Answers
Answer:
C
Step-by-step explanation:
a owner increases the rent office house by 5% at end of each year if current its rent is ₹2500pm how much will be the rent after two years
Answers
Answer:
2950$
Step-by-step explanation:
2500×5%=125$
125×2=250$
2500+250=3960$
WILL GIVE BRAINLIEST
Answers
Answer:
Option (D)
Step-by-step explanation:
Pythagoras theorem states,
(Hypotenuse)² = (leg 1)² + (leg 2)²
(13)² = (5)² + (12)²
By the converse of Pythagoras theorem,
If we draw two sides 5cm and 12cm of a triangles with a right angle between them, third side 13 cm will fit to form a right triangle.
Therefore, Option (D) will be the answer.
Simplify. Please help.
Answers
Answer:
I believe it is B
Step-by-step explanation:
if correct pls mark brainliest
Answer:
4^8
Step-by-step explanation:
When multiplying powers, keep the base the same and add the exponents.
4^6 x 4^2 = 4^8
Find the slope of the line that goes through the points (4,-3) and (5,0)
Answers
Answer:
the slope of the points (4,-3) and (5,0) is 3
Step-by-step explanation: I used the formula y2-y1 over x2-x1 will give you the answer hope this helped!
Answer:
\(\boxed {\boxed {\sf m=3}}\)
Step-by-step explanation:
We are asked to find the slope of the line that passes through (4, -3) and (5,0).
The slope is the number that tells us the steepness and direction of a line. It is the rise over run, or the change in y over the change in x.
\(m= \frac{ \Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}\)
In the slope formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through. The points we are given are (4, -3) and (5,0). If we match the value with its corresponding value, we see that:
x₁ = 4 y₁ = -3x₂ = 5 y₂ = 0Substitute the values into the formula.
\(m= \frac{0 - -3}{5-4}\)
Solve the numerator. Remember that 2 back to back subtraction signs become an addition sign.
0--3 = 0+3=3\(m= \frac{3}{5-4}\)
Solve the denominator.
5-4 =1\(m= \frac{3}{1}\)
Divide.
\(m=3\)
The slope of the line is 3.
DON'T SOLVE IT
I know the answer. I just need to know the TOPIC in geometry.
What is the topic???
Answers
Answer:
Triangles in Geometry
Step-by-step explanation:
Management of natural resources can affect the sustainability of human populations. For example, consider an effort to decontaminate a small village’s water supply. This effort is projected to increase the carrying capacity from an initial population of 400 people (P=400) to 450 people (K = 450) during the course of 10 years (x=10). Use the simulation to determine the growth rate r of the population in this village.
Answers
The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.
How to find the growth rate ?To find the percent change or growth rate of a quantity between two different values, you can use the formula:
Percent change = ( new value - old value ) / old value x 100%
The new value would be the population of the village after 10 years which is 450 people.
The old value is the initial population of the village which is 400
The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %
= 12. 5 %
The growth rate for the village is therefore 12. 5 % every ten years.
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© Express the ratio below in its simplest form.
2.5 : 3.5
Answers
Answer:
5:7
Step-by-step explanation:
A veterinarian polled her clients own dogs as to whether or not they used dry food only for their dogs which of the following describes the population of this survey
Answers
Answer:
Can you describe this question
Step-by-step explanation:
In the survey study above, in other to get valuable information that would help the veterinarian find answers to the research question, he correct description of the population of the survey is: this veterinarian's dog-owning clients.
What is the Population of a Survey Study?In a survey, the population of the study is the group of people that can provide valuable information to a researcher regarding the research questions.
Thus, in the survey study above, in other to get valuable information that would help the veterinarian find answers to the research question, he correct description of the population of the survey is: this veterinarian's dog-owning clients.
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find two whole numbers that are closest to v42. explain your reasoning
Answers
Answer:
The numbers are 6 and 7.
Step-by-step explanation:
4² = 16
5² = 25
6² = 36
7² = 49
√36 = 6
√42 = ?
√49 = 7
The numbers are 6 and 7.
I need help please help me is it 30?
Answers
Answer:
i think is 30$
Step-by-step explanation:
Answer:
B. $15.00
Step-by-step explanation:
Think about it this way:
3 = 1.50
6 = 3.00
8 = 4.00
12 = 6.00
If you divide each of the first numbers by the second, you'll get 2.
This means that every doughnut costs $0.50.
From there you just multiply .5 by 30
30
x .5
15
30 Donuts would cost 15 dollars.
Ok so the above is a little bit more of a complicated way to do it, but it'll be more efficient for a similar, but more difficult problem. The general goal of these problems is to find out what 1 of the item would cost. In this case it's $0.50, but you need to find that out in all of these problems.
brainliest is appreciated.
Amelia grabbed 50% of the M&M's from a bowl. Then, Jess took 50% of what was left. Dominick takes 50% of the remaining M&M's. There were 3 left. How many M&M's were in the bowl before Amelia arrived.
Answers
The number of M&M's that were in the bowl before Amelia arrived is; 12
How to solve Percentage problems?Let the original amount in the bowl be x. Thus;
If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x
Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x
Now, we are told that there were finally 3 left after all the deductions. Thus;
0.25x = 3
x = 3/0.25
x = 12
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The graph of the function f is shown. The domain of f is [0, 50]. What is the range of g(x) = 4f(x)?
The graphs with the X-coordinate marks 0, 10, 20, 30, 40 and 50. The Y-coordinate mark 0, 0.5, 1, and 1.5. There is an absolute value function with vertex at (25, 1.75). It starts at origin and ends at (50, 0).
A. [0, 50]
B. [0, 70]
C. [0, 1.75]
D. [0, 7]
![The graph of the function f is shown. The domain of f is [0, 50]. What is the range of g(x) = 4f(x)?The](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/3axp1bHYGDvxp9zA5DlOgJnTLJS5NdNO.png)
Answers
Based on the calculations using the given graph, the range of g(x) is equal to: D. [0, 7].
How to identify the range and domain of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Similarly, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph of f(x) shown, we can infer and logically deduce the following:
Domain = (0, 50) i.e the domain is all real numbers.
Range = (0, 1.75).
What is the range of g(x) = 4f(x)?At the minimum f(x) = 0, we have:
g(x) = 4 × 0
g(x) = 0.
At the maximum f(x) = 1.75, we have:
g(x) = 4 × 1.75
g(x) = 7.
Therefore, the range of g(x) is equal to [0, 7].
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15. Find the surface area of the figure.
Answers
Answer:
Well personally I would use your fomula because its different ways to do this and is taught differnet but the way I was taught was to add up all the sides and multiply
Step-by-step explanation:
add all of them
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answers
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
Which of the following are solutions to the equation below?
Check all that apply.
x² + 6x + 9 = 20
A. x= 2√5-3
B. x= √3+ 20
C. x= -2√5 +3
D. x = -√3+20
☐ Ex= 2√5 +3
OF x=-2√5-3
Answers
The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
x = [-b± (√b²-4ac )] / 2a
The quadratic equation:
x²+6x+9=20
x²+6x -11 = 0
a = 1, b = 6, c = -11
x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)
x = -3 + 2√5 , x = -3 - 2√5
Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
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What is the correct solution to the expression 3+5^2. Using scientific calculator
Answers
Answer:
5^2 is 5 squared in which case this Is essentially 3+25 which is 28.
Step-by-step explanation:
Its simple 5^2 Is 5 times 5, 5^3 is 5 times 5 times 5 and so on.
Which value of x will make ab perpendicular to cd?
Answers
Answer:
Step-by-step explanation:
m∠CGE = m∠FGD = (2x + 4)° [vertically opposite angles]
If m∠BGC = 90° Or AB⊥CD,
m∠CGE + m∠EGB = 90°
(2x + 4)° + (11x - 5)° = 90°
13x - 1 = 90
13x = 91
x = 7
This isnt the answer but its an example of what the equation looks like
Evaluate the expression
12 - 3 2+429,- 4) for y = 3.
Answers
Answer:
9,427) y=5
is correct answer
The interest rate on a car loan has decreased 40% over the last 10 years and is now 8.3%. What was the rate 10 years ago?
Answers
Answer:
The interest rate on the car loan 10 years ago was 13.83%
Step-by-step explanation:
Let's assume that the interest rate on the car loan 10 years ago was "x" percent.
According to the problem, the interest rate has decreased by 40% over the last 10 years. We can express this mathematically as:
x - 0.4x = 0.6x
This means that the current interest rate (8.3%) is equal to 60% of the interest rate from 10 years ago (0.6x).
So we can write:
0.6x = 8.3%
To solve for x, we can divide both sides by 0.6:
x = 8.3% / 0.6
x = 13.83%
Therefore, the interest rate on the car loan 10 years ago was 13.83%.
Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]
help with homework pls
Answers
Answer:
no
Step-by-step explanation:
orka:sweet potato
15:8 = 1.875
350:160 = 2.1875
apply the distributive property to factor out the greatest common factor
18d + 12=
Answers
which of these is a simplified form of the equation 6 y + 4 equals 8 + 2y + 2y
Answers
Answer:
2y = 4
Explanation:
The initial equation is:
6y + 4 = 8 + 2y + 2y
First, we need to add like terms, so we get:
6y + 4 = 8 + (2y + 2y)
6y + 4 = 8 + 4y
Then, subtract 4y from both sides:
6y + 4 - 4y = 8 + 4y - 4y
(6y - 4y) + 4 = 8
2y + 4 = 8
Finally, subtract 4 from both sides:
2y + 4 - 4 = 8 - 4
2y = 4
So, the simplified expression is:
2y = 4
What is the probability that a junior non-Nutrition major and then a sophomore Nutrition major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
0.0032
The complete question as seen in other website:
There are 111 students in a nutrition class. The instructor must choose two students at random Students in a Nutrition Class Nutrition majors Academic Year Freshmen non-Nutrition majors 17 18 Sophomores Juniors 13 Seniors 18 Copy Data. What is the probability that a senior Nutrition major and then a junior Nutrition major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Step-by-step explanation:
Total number of in a nutrition class = 111 students
To determine the probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major, we would find the probability of each of them.
Let the probability of choosing a junior non-Nutrition major = Pr (j non-N)
Pr (j non-N) = (number of junior non-Nutrition major)/(total number students in nutrition class)
There are 13 number of junior non-Nutrition major
Pr (j non-N) = 13/111
Let the probability of choosing a sophomore Nutrition major = Pr (S N-major)
Pr (S N-major)= (number of sophomore Nutrition major)/(total number students in nutrition class)
There are 3 number of sophomore Nutrition major
Pr (S N-major) = 3/111
The probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major = 13/111 × 3/111
= 39/12321
= 0.0032
Q. 9 [Decimals] (10 Points)
Write the following as a decimal:
nine tenths