Answer:
The world population in 2030 will be of 9.0062 billion.
The would population in 2060 will be of 13.71 billion.
Step-by-step explanation:
The exponential model for population growth is as follows.
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(t) is the population in t years from now, P(0) is the population in the current year and r(decimal) is the growth rate.e = 2.71 is the Euler number.
If the world population is 7.0 billion in 2012.
2012 is the initial year, so P(0) = 7.
P(t) will be measured in billions of people.
The growth rate is constant at 1.4%.
This means that [tex]r = 0.014[/tex]
Calculate the population in 2030.
2030 is 2030-2012 = 18 years after 2012, so this is P(18).
[tex]P(t) = 7e^{rt}[/tex]
[tex]P(18) = 7e^{0.014*18} = 9.0062[/tex]
So the world population in 2030 will be of 9.0062 billion.
What will be the population in 2060.
This is 2060-2012 = 48 years after 2012. So this is P(48).
[tex]P(t) = 7e^{rt}[/tex]
[tex]P(48) = 7e^{0.014*48} = 13.71[/tex]
The would population in 2060 will be of 13.71 billion.
Suppose that you have measured a length of 6 cm on one board and 8 cm on the other. You would adjust the two boards until the length of the string had value c to ensure that the boards made a right angle. What is c? Express your answer in centimeters to three significant figures.
Answer:
c = 10.000cm
Step-by-step explanation:
If the 2 boards made the right angle, c would be the hypotenuse with 2 sides of 6 cm and 8 cm. We can then use Pythagorean formula to solve for c
[tex]c^2 = 6^2 + 8^2 = 36 + 64 = 100[/tex]
[tex]c = \sqrt{100} = 10.000 cm[/tex]
Evaluate the line integral Z C z2 dx 2y dy 2xz dz where C is any closed curve in the space.
Answer:
Some other information should be given, I have added those necessary information, should in case you come across a similar question on line integral.
Step-by-step explanation:
To evaluate line integral, some other information has to be given, Assume (so when you see a similar question, you will know how to evaluate line integral) as part of the question X =t2, Y = 2t and Z = 3t and at interval 0≤t≤1
A step by step explanation and calculation has been attached.
Find g(-x) when g(x) = 2x^2 -5x + 5
Answer: g(-x) = 2x^2 +5x + 5
Step-by-step explanation:
This Is a topic under functions in mathematics, it deals with substituting "x" for the new entity that has been placed in the new function you're asked to look for.
Hence, to solve this, we simply substitute "-x" for "x" wherever "x" appears in the equation.
By doing so, we go straight to the given function.
2x^2 -5x + 5
And we go ahead with our substitution which goes thus:
2(-x^2) -5(-x) + 5
On simplifying, we then finally have have:
2x^2 +5x + 5.
This means:
g(-x) = 2x^2 +5x + 5
A top-fuel dragster ran a 1/4-mile (1320 ft) race. It had traveled 1305.48 feet after 3.58 seconds and it traveled the entire 1320 feet in 3.61 seconds. What was its speed, approximately, in feet per second at the end of the race? In miles per hour?
The speed approximately of this top-fuel dragster is given as 330 miles per hour.
How to solve for the speedWe have 1320 feet distance in 3.61 sec
then we have 1305.48 feet in 3.58
Such that 1320-1305.48 = 14.52 feet
we have to do the conversions of feet into miles and seconds to become hours
1 mile = 5280feet
hence we have 14.52 feet as 14.52/5280
= 0.00275miles
then 0.03 seconds to hour = 0.03/3600
= 0.0000083
Speed = distance / time
0.00275miles/ 0.0000083
= 330 miles per hour
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To find the speed of the top-fuel dragster at the end of the race, divide the total distance traveled by the time taken. The speed at the end of the race is approximately 365.098 ft/s or 249.340 mph.
Explanation:To find the speed of the top-fuel dragster at the end of the race, we can divide the total distance traveled (1320 ft) by the time it took to cover that distance (3.61 s). This will give us the average velocity of the dragster.
So, the speed at the end of the race is approximately 365.098 ft/s.
To convert this speed to miles per hour, we can multiply it by the conversion factor 0.6818. This gives us the speed of the dragster at the end of the race in miles per hour, which is approximately 249.340 mph.
George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options:
(1) a bond fund and
(2) a stock fund.
The projected returns over the life of the investments are 9% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 60% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 8.5%.
A) Formulate a linear programming model that can be used to determaine the percentage that should be allocated to each of the possible i nvestment alternatives
B) Solve the problem using the graphical solution procedure.
Answer:
Max 0.09B+0.2s
B>=0.6 Bond fund minimum
0.06B+0.2S>=0.085 Minimum Return
B+S=1 All funds invested
B,S>=0
Step-by-step explanation:
(a) In linear programming, the mathematical model and the linear objective function set of linear constraints the variables are not negative.
B=% funds invested in the bond fund
S=% of funds invested in the stock fund
Max 0.09B+0.2s
B>=0.6 Bond fund minimum
0.06B+0.2S>=0.085 Minimum Return
B+S=1 All funds invested
B,S>=0
Solve the above by using the graphical solution procedure?
steps to solve the graphs
1)draw the graphs, making sure the constraints are consider
2)consider all the constraints
3)draw the objective function line to the decision variables to
4) place the parallel lines of objective function towards larger objective function
5) consider as optimal function the feasible solution on the objective function line with the largest value ia
An aptitude test known as the Gesell adaptive score test is given to children to measure their level of cognitive development. It is of interest to know whether or not a relationship exists between this test score and the age (in months) at which a child speaks his/her first word. To examine this, the following data were collected for 21 children: (a) Treating the Gesell score as the response variable (y) and the age at first word as the explanatory variable (x), make a scatterplot of these data.
Does there appear to be a linear relationship among these variables?
To assess if there's a linear relationship between the Gesell score and the age at first word, one would create a scatterplot with the Gesell score as (y) and age as (x). The presence of a linear trend could be indicated by a clustering of points near a line, while the strength of the relationship would be further analyzed using the least-squares regression line and correlation coefficient.
Explanation:To determine whether there is a linear relationship between the Gesell adaptive score test (Gesell score) and the age at which children speak their first word, you would start by plotting a scatterplot with the Gesell score as the response variable (y) and the age at first word as the explanatory variable (x). In the scatterplot, each point represents one child's data with their corresponding age at first word on the x-axis and Gesell score on the y-axis.
After plotting the data, you would examine the scatterplot to see if the points suggest a linear trend. If the points cluster around a line that slopes upwards or downwards, this could indicate a positive or negative linear relationship respectively. Conversely, if the points are widely scattered without any discernible pattern, it might suggest that there is no significant relationship between the variables.
If there seems to be a potential linear relationship, you might proceed to calculate the least-squares regression line to find the best-fitting line through the data and the correlation coefficient to measure the strength and direction of the relationship between the variables. Significant correlation coefficients (typically those near -1 or 1) would support the presence of a linear relationship, while coefficients near zero would suggest little to no linear relationship.
Final answer:
To analyze the relationship between the Gesell adaptive score test and the age of first word spoken by children, one would plot a scatterplot with Gesell score on the y-axis and age at first word on the x-axis. This visualization aids in identifying any potential linear or non-linear patterns.
Explanation:
To investigate if there is a relationship between the Gesell adaptive score test and the age at which a child speaks their first word, we would create a scatterplot with the age at first word (in months) as the x-axis (explanatory variable) and the Gesell score as the y-axis (response variable). By analyzing the pattern of the dots on the scatterplot, we could determine if there is any apparent linear relationship or if the data suggests a more complex relationship, such as an inverted U-shaped relationship.
It's important to note that an absence of linear correlation from a statistical test doesn't necessarily deny the existence of any relationship between two measures; the relationship could be non-linear or might change over time. An example of this would be a change in problem-solving strategies in children causing an inverted U-shaped relationship in cognitive ability over different stages. Therefore, a scatterplot is a crucial tool for visually identifying patterns and potential relationships in data.
Derive the equation of motion of the spring-mass system given below. Please show and MARK your derivation step by step. Missing steps will result in losing points. Use the assumptions sin(θ) = θ and cos(θ) = 1.
Answer:
Ö + θ ( (k/m) + (g/l)) = 0
Step-by-step explanation:
Use the FBD attached:
Apply Newtons 2 nd Law in tangential direction:
Sum ( Ft ) = m*a
Sum of all tangential forces is:
m*g*sin(θ) + k*l*sin(θ)*cos(θ) = - m*l*Ö
Using small angle approximations:
sin (θ) = θ
cos (θ) = 1
Ö = angular acceleration.
m*g*θ + k*l*θ = -m*l*Ö
Ö + θ ( (k/m) + (g/l)) = 0
Associations: Describe the relationship between the predictor and response variables in cach of the four scatterplots below. a) Describe plot (1) above: Negative, non-linear Positive, non-linear Negative, linear Positive, linear No association b) Describe plot (2) above: Negative, linear Positive, non-linear Positive, linear O No association Negative, non-linear c) Describe plot (3) above: Positive, non-linear Negative, lincar Negative, non-linear Positive, linear No association d) Describe plot (4) above: Negative, non-linear Positive, non-linear No association Positive, linear Negative, linear
Answer:
Step-by-step explanation:
The relationship between predictor and response variables in scatterplots can be analyzed in terms of direction (positive or negative), form (linear or non-linear), and strength. Each plot is described based on this analysis.
Explanation:To determine the relationship between the predictor and response variables in each of the provided scatterplots, we need to analyze the form, direction, and strength of the scatterplots.
For plot (1), if the points are following a downward path but not a straight line, we would classify this as Negative, non-linear.
For plot (2), if the points are following an upward path but not a straight line, we would classify this as Positive, non-linear.
For plot (3), if the points are increasing in a straight line, we would classify this as Positive, linear.
For plot (4), if the points are decreasing in a straight line, we would classify this as Negative, linear. However, if the points seem to be randomly scattered with no discernible pattern, then we would classify this as No association.
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Determine if the collection is not well defined and therefore is not a set. The collection of current NHL players
Answer:
Step-by-step explanation:
The collection of current NHL players cant be defined as some may be on injury so therefore the current NHL players is ill-defined thereby they are described as Not well defined set
Final answer:
A collection of current NHL players is a well-defined set. We can precisely determine what is and is not a member of this set.
Explanation:
A collection of current NHL players is a well-defined set. A set is a collection of distinct objects, and in this case, the objects are the current NHL players. It is possible to precisely determine what is and is not a member of this set. We can provide a clear and concise definition of the set by listing the names of all current NHL players.
For example:
Auston Matthews
Connor McDavid
Alex Ovechkin
Sidney Crosby
Nathan MacKinnon
These are just a few examples, but by listing all the current NHL players, we can determine exactly what is included in the set and what is not.
49. If a statistician specifies a 5% level of significance, then she will reject the null hypothesis only if her sample result differs from her hypothesized value by an amount that would occur by chance a) Less than 5% of the time. b) More than 5% of the time. c) 95% of the time or more. d) 2.5% of the time or less.
Answer:
The answer is a) less than 5% of the time
Step-by-step explanation:
By definition, the level of significance is the probability that one rejects a null hypothesis of a test when it is true. Denoted as alpha α, it shows how convincing the sample data is and concludes if it is statistically significant.
A level of significaance of 5% or 0.05, shows that you need more convincing power before determining whether you willreject the null hypothesis
By way of rule,
-If p-value ≤ level of significance α , then reject the null hypothesis.
-If p-value ≥ level of significance α , then do not reject the null hypothesis.
This implies that a statistician with a 5% level of significance will reject the null hypothesis if her hypothesized value falls below this mark.
Answer:
c) 95% of the time or more.
Step-by-step explanation:
The level of significance in a statistical research is the probability of rejecting the null hypothesis when it is actually true. A possible example is a significance level of 0.02 which indicates a 2% risk of concluding that a difference exists when there is no actual difference. The lower the significance level, the stronger the evidence required before you can reject the null hypothesis. 5% significance level may imply 95% confidence interval which means the range of values that occurs 95% of the time.
Therefore, rejecting the null hypothesis at 5% significance level means that the alternative hypothesis differs from the null hypothesis by 95% or more of its possible values (95% of the time or more).
Let Y1 and Y2 have the joint probability density function given by:
f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere.
(a) Find the value of k that makes this a probability density function.
(b) Find P(Y1 ≤ 3/4, Y2 ≥ 1/2).
The question involves computing parameters of a joint probability density function given a specific function and ranges. The process involves setting up and evaluating appropriate double integrals over the given ranges.
Explanation:The subject of this problem is related to joint probability density functions (pdfs) and probability theory which comes under mathematics, specifically statistics.
(a) To find the value of k that makes this a valid probability density function, we use the property that the integral of a pdf over its range should equal 1:
So, we integrate the function f(y1, y2) = k(1 – y2) over the range 0 <= y1 <= y2 <= 1. This gives us a double integral: We first integrate with respect to y1, from 0 to y2. Then we integrate with respect to y2, from 0 to 1. Finally, we set this equal to 1 and solve for k.
(b) To find P(Y1 ≤ 3/4, Y2 ≥ 1/2), you integrate the joint pdf over the given intervals:
Integrate from 0 to 3/4 with respect to y1, and from 1/2 to 1 with respect to y2. Learn more about Joint Probability Density Functions here:
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One coin in a collection of 65 coins has two heads; the rest of the coins are fair. If a coin, chosen at random from the lot and then tossed, turns up heads six times in a row, what is the probability that it is the two-headed coin?
There is only 1 two-headed coin in the collection of 65 coins.
The probability of selecting the two headed coin is 1/65.
The outcome achieved when any of the other coins is tossed a number of times is based purely on chance.
Although if the 2-headed coin is selected, the only possible outcome is having a head, but It also possible to have 6 heads in 6 tosses with a coin that is not 2-headed.
What we're concerned with, is the probability that the 2-headed coin was selected from the lot of 65 coins, which is 1/65.
Answer:
There is only 1 two-headed coin in the collection of 65 coins.
The probability of selecting the two-headed coin is 1/65.
The outcome achieved when any of the other coins is tossed a number of times is based purely on chance.
Although if the 2-headed coin is selected, the only possible outcome is having a head, but It is also possible to have 6 heads in 6 tosses with a coin that is not 2-headed.
What we're concerned with, is the probability that the 2-headed coin was selected from the lot of 65 coins, which is 1/65.
Step-by-step explanation:
The share of aggregate income held by middle-income households in 1970 was 62%, whereas that held by upper-income households was 29%. The corresponding figures in 2014 were 43% and 49%, respectively. The models describing the fall and the rise in the share of the aggregate incomes of these two groups are approximately linear over the period under consideration.† (a) Find the mathematical models describing the percent share of aggregate income held by each group from 1970 through 2014. (Let t denote the time, in years, with t = 0 corresponding to the beginning of 1970.) middle-income households y = Incorrect: Your answer is incorrect. upper-income households y = Incorrect: Your answer is incorrect. (b) Find the time when the aggregate income held by upper-income households first exceeded that held by middle-income households. (Give the calendar year in which the change occurred.)
Answer:
a) y = -19/44t +62; y = 5/11t +29
b) 2007
Step-by-step explanation:
(a) The two-point form of the equation of a line is useful when two data points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Middle Income
The two given points are (0, 62), (44, 43), so the equation is ...
y = (43 -62)/(44 -0)(t -0) +62
y = -19/44t +62
__
Upper Income
The two given points are (0, 29), (44, 49), so the equation is ...
y = (49 -29)/(44 -0)(t -0) +29
y = 20/44t +29
y = 5/11t +29
__
(b) The year in which the shares are equal is found by setting the y-values equal:
-19/44t +62 = 5/11t +29
33 = 39/44t
t = (33)(44)/39 ≈ 37.2
The upper income share exceeded the middle income share in the year 1970 +37.2 = 2007.
The mathematical models for the middle-income and upper-income households are y1(t) = 62% - 0.38% * t and y2(t) = 29% + 0.40% * t, respectively. The aggregate income held by upper-income households first exceeded that held by middle-income households in the year 2014.
Explanation:In order to find the mathematical model, we will first determine the slope for each data set. The slope is calculated as the change in y divided by the change in x. Here, 'y' represents the share of aggregate income and 'x' represents time.
For the middle-income households, the slope (m1) is: m1 = (43% - 62%)/(2014 - 1970) = -0.38% per year. So, the equation becomes: y1(t) = 62% - 0.38% * t.
For the upper-income households, the slope (m2) is: m2 = (49% - 29%)/(2014 - 1970) = 0.40% per year. So, the equation becomes: y2(t) = 29% + 0.40% * t.
To find out when the aggregate income held by the upper-income households first exceeded that held by middle-income households, we set the two equations equal to each other and solve for 't'. This gives us t = (62% - 29%)/(0.40% + 0.38%) = 43.7, or roughly 44 years after 1970 which is the year 2014.
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I understand sum I just need more help
Answer:
Step-by-step explanation:
The Pythagorean theorem is expressed as
Hypotenuse² = opposite side² + adjacent side²
If the distances of the routes given are Pythagorean triples, then they obey the Pythagorean theorem hence, they would form a right angle triangle.
1) for the bus routes between stop A, B and C,
13² = 12² + 5²
169 = 144 + 25 = 169
A Pythagorean triple is formed hence, stop A, B and C form a right angle triangle.
2) for the bus routes between stop C, E and E,
22² = 14² + 18²
484 = 196 + 324 = 520
A Pythagorean triple is not formed hence, stop C, E and E do not form a right angle triangle.
3) 25² = 9² + HJ²
625 = 81 + HJ²
HJ² = 625 - 81 = 544
HJ = √544 = 23.32
4) EG² = 15² + 8²
EG² = 225 + 64
EG² = 289
EG = √289 = 17
what is the total area of this prism?
T.A=
Answer:
The answer to your question is 61.8 in²
Step-by-step explanation:
Process
1.- Calculate the height of the triangle
3² = h² + 1.5²
h² = 3² - 1.5²
h² = 9 - 2.25
h² = 6.75
h = 2.6 in
2.- Calculate the area of the triangles
Area = [tex]\frac{base x height}{2}[/tex]
Area = [tex]\frac{3 x 2.6}{2}[/tex]
Area = 3.9 in²
There are 2 triangles = 2(3.9) = 7.8 in²
3.- Calculate the area of the rectangles
Area = base x height
Area = 6 x 3 = 18 in²
There are 3 rectangles = 3(18) = 54 in²
4.- Total area
At = 7.8 + 54
= 61.8 in²
Answer:
(104 +16√13) ft
Step-by-step explanation:
Let C(x) be the statement "x has a cat," let D(x) be the statement "x has a dog," and let F(x) be the statement "x has a ferret." Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.
a) A student in your class has a cat, a dog and a Ferret is Ex(C(x)∧D(x)∧F(x)).
b) All students in your class have a cat, a dog or a Ferret is ∀x(C(x)∨D(x)∨F(x)).
c) Some student in you class has cat and Ferret but not a dog is Ex(C(x)∧D(x)∨¬F(x)).
The various types of logical connectives include conjunction (“and”), disjunction (“or”), negation (“not”), conditional (“if . . . then”), and biconditional (“if and only if”).
Let C(x) : x has a cat
D(x) : x has a dog
F(x) : x has a Ferret
a) A student in your class has a cat, a dog and a Ferret.
Ex(C(x)∧D(x)∧F(x))
b) All students in your class have a cat, a dog or a Ferret.
∀x(C(x)∨D(x)∨F(x))
c) Some student in you class has cat and Ferret but not a dog
Ex(C(x)∧D(x)∨¬F(x))
Therefore,
a) A student in your class has a cat, a dog and a Ferret is Ex(C(x)∧D(x)∧F(x)).
b) All students in your class have a cat, a dog or a Ferret is ∀x(C(x)∨D(x)∨F(x)).
c) Some student in you class has cat and Ferret but not a dog is Ex(C(x)∧D(x)∨¬F(x)).
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The statements can be expressed using logical connectives and quantifiers in mathematical logic. They express different combinations of students owning cats, dogs, and ferrets.
Explanation:The statements can be expressed in terms of C(x), D(x), F(x), quantifiers, and logical connectives as follows:
a) ∃x (C(x) ∧ D(x) ∧ F(x)): This states that there exists a student 'x' such that 'x has a cat, a dog, and a ferret'. b) ∀x (C(x) ∨ D(x) ∨ F(x)): This states that for all students 'x', 'x has a cat, a dog, or a ferret'. c) ∃x (C(x) ∧ F(x) ∧ ¬D(x)): This states that there exists a student 'x' such that 'x has a cat and a ferret, but not a dog'. d) ¬∃x (C(x) ∧ D(x) ∧ F(x)): This states that there does not exist a student 'x' such that 'x has a cat, a dog, and a ferret'. e) ∃x C(x) ∧ ∃x D(x) ∧ ∃x F(x): This states that for each animal (cats, dogs, ferrets), there exists a student 'x' that has this animal as a pet. Learn more about Mathematical Logic here:https://brainly.com/question/30928478
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A pitcher holds 12 cups of juice. If each glass holds 24 ounces of juice, how many glasses can be filled from the pither
Answer:
A pitcher can hold only 2 cup in his hands
Given f(x)= a×e−bx , where a = 1 and b = 6,
calculate g(x)=dfdx and obtain g(1) (that is, evaluate the derivative of f(x) at x = 1).
Report your answer with three significant figures.
Answer:
g(1) = -0.015
Step-by-step explanation:
We are given he following in the question:
[tex]f(x) = ae^{-bx}[/tex]
For a = 1 and b = 6, we have,
[tex]f(x) = e^{-6x}[/tex]
We have to find the the derivative of f(x) with respect to x.
[tex]g(x) = \dfrac{d(f(x))}{dx} = \dfrac{d(e^{-6x})}{dx}\\\\g(x) = -6e^{-6x}\\\\g(1) = \dfrac{d(f(x))}{dx}\bigg|_{x=1} = -6e^{-6} = -0.015[/tex]
Thus, g(1) = -0.015
If r1 , r2 , and r3 represent rotations from Dn and f 1 , f 2 , and f 3 represent reflections from Dn , determine whether r1 r2 f 1 r3 f 2 f 3 r3 is a rotation or a reflection.
The combined transformation operation r1 r2 f1 r3 f2 f3 r3 is a reflection. This is because a sequence of transformations combining rotations and reflections, when arranged and executed in order, still produces a reflection.
Explanation:The problem is understanding whether the composition of certain transformations, namely rotations (r1, r2, r3) and reflections (f1, f2, f3) from Dn, results in another rotation or a reflection. In mathematics, a composition of transformations means applying several transformations in sequence.
Here, think about the properties of rotations and reflections. A rotation followed by another rotation will result in a rotation. Similarly, a reflection followed by another reflection is equivalent to a rotation. However, a reflection followed by a rotation or vice versa results in a reflection.
The sequence provided is r1 r2 f1 r3 f2 f3 r3. Assuming each transformation in the sequence is executed in order, we can see that it is divided into four segments: rr, rf, fr, and r. The first segment, rr, will result in a rotation. The second segment, rf, will result in a reflection. That reflection followed by the next r, resulting in another reflection. Finally, the last segment is just a rotation. Therefore, reflection followed by a rotation results in a reflection.
So, the combined transformation r1 r2 f1 r3 f2 f3 r3 is a reflection.
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Researchers wanted to determine if there was an association between the level of satisfaction of an individual and their risk of diabetes. The researchers studied 1621 people over the course of 5 years. During this 5-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of diabetes over the 5-year period. After their analysis, the researchers concluded that the satisfied individuals were less likely to experience diabetes.
Complete parts (a) through (c).
(a) What type of observational study was this? Explain.
(b) What is the response variable? What is the explanatory variable?
(c) In the report, the researchers stated that "the research team also hasn't ruled out that a common factor like genetics could be causing both the emotions and the lung cancer."
Explain what this sentence means. Choose the correct answer below.
A. The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study, but that affect the value of the response variable
B. The researchers thought that genetics had greater influence than level of happiness.
C. It is not important to adjust for explanatory variables.
Answer:
Step-by-step explanation:
Hello!
To see if there is an association between the variables:
"Level of satisfaction of an individual"
"Risk of diabetes of an individual"
The researchers studied 1621 people over 5 years.
Observations recorded:
Interviews of daily lives and hassles and hypothetical situations that were studied to assess their emotions.
Determination, if in the course of these 5 years the individuals experienced any type of diabetes.
Conclusion "Satisfied individuals are less likely to have diabetes"
a) This is a prospective cohort study.
In this type of study, a group of individuals that share the same characteristics is observed over some time, recording the events of interest.
b) Considering that the experiment concluded that "satisfaction" reduces the "risk of diabetes", we can determine that the response variable is "Risk of diabetes of an individual" and the explanatory variable is "Level of satisfaction of an individual".
Remember, the explanatory variable is the one considered to have a direct effect over the response variable.
c) "the research team also hasn't ruled out that a common factor like genetics could be causing both the emotions and the lung cancer."
There is a new variable that may affect the experiment. Be "genetic factor" the new variable and it affects directly "emotions and lung cancer", we can say that if some of those individuals are genetically predisposed to have lung cancer, this affects their emotions (satisfaction) and therefore, modifying their risk of having diabetes.
If this is so, then the genetic factor could be a lurking variable affecting directly the result of the observational experiment. Then the correct answer is:
A. The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when some explanatory variables were not considered in a study, but that affects the value of the response variable.
I hope it helps!
Final answer:
This response explains the type of observational study conducted, identifies the response and explanatory variables, and clarifies the researchers' concern about confounding due to genetics.
Explanation:
(a) Type of observational study: This study is an observational study because the researchers are observing and analyzing individuals to determine a relationship between satisfaction levels and the risk of diabetes without intervening or manipulating variables.
(b) Response and explanatory variables: The response variable in this study is the occurrence of diabetes, while the explanatory variable is the level of satisfaction of the individuals.
(c) Explanation of sentence: The sentence suggests that a common factor like genetics could be influencing both the emotions and the risk of diabetes, indicating that the researchers are considering the possibility of confounding where unaccounted variables may affect the relationship observed.The statement indicates concern about confounding variables, where genetics might influence both satisfaction and diabetes risk, suggesting they have not separated the effects of these intertwined factors fully. (Option A)
Simplify (4x - 6) – (3x + 6).
1) ×- 12
2)-x - 12
3) x + 12
4) -x + 12
Answer:
1) x-12
Step-by-step explanation:
(4x-6)-(3x+6)
4x-6-3x-6
x-12
Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-intercept, and vertex of the function. f(x) = -(x + 1)2 + 4
Answer:
Part A: vertex at (-1,4)
Part B: line of symmetry x =-1
Part C: x-intercept x = -3 and x = 1
Part D: y-intercept y = 3
Step-by-step explanation:
Given f(x) = - (x+1)² + 4
The given equation represents a parabola.
The general equation of the parabola with a vertex at (h,k)
f(x) = (x-h)² + k
Part A: To find the vertex, compare the general equation with the given function.
So, the vertex of the function will be at (-1,4)
Part B: the line for the axis of symmetry of function will be at x =-1
Part C: To find x-intercept, put y = 0
So, - (x+1)² + 4 = 0
- (x+1)² = -4
(x+1)² = 4
x + 1 = ±√4 = ±2
x + 1 = 2 OR x + 1 = -2
x = 1 OR x =-3
x-intercept at x = 1 and x = -3
Part D:To find y-intercept, put x = 0
So, y = - (0+1)² + 4 = -1 + 4 = 3
y-intercept at y = 3
See the attached figure.
Answer:
Vertex at (-1,4)
Line of symmetry x =-1
x-intercept x = -3 and x = 1
y-intercept y = 3
.Using the laws of logic to prove tautologies. Use the laws of propositional logic to prove that each statement is a tautology. (a) (p ∧ q) → (p ∨ r) (b) p → (r → p)
Answer:
See explanation below.
Explanation:
If the statement is a tautology is true for all the possible combinations and we can check this with the table of truth for the statements
Part a
[tex] (p \land q) \Rightarrow (p \lor r)[/tex] lets call this condition (1)
[tex] (p \land q)[/tex] condition (2) and [tex](p \lor r)[/tex] condition (3)
We can create a table like this one:
p q r (2) (3) (1)
T T T T T T
T T F T T T
T F T F T T
T F F F T T
F T T F T T
F T F F F T
F F T F T T
F F F F F T
So as we can see we have a tautology since for all the possibilites we got true the final result.
Part b
[tex] p \Rightarrow (r \Rightarrow p)[/tex] let's call this condition (1)
And let [tex] (r \Rightarrow p)[/tex] condition (2)
We can create the following table:
p r (2) (1)
T T T T
T F T T
F T F T
F F T T
So is also a tautology since the statement is true for all the possibilities or combinations.
Identify the type of sampling used. Thirty-five math majors, 52 music majors and 38 history majors are randomly selected from 447 math majors, 480 music majors and 451 history majors at the state university. What sampling technique is used?
Answer:
Stratified
Step-by-step explanation:
The stratified sampling is defined as the type of random sampling when the population is divided into non-overlapping groups known as strata and then sample is selected from each of the stratum.
The sampling technique used is stratified sampling because the population is divided into 3 strata math, music and history and then sample of 35,52 and 38 is selected from these 3 strata respectively.
One group, which contains 28 dogs, averages 20.5 inches. Another group that contains 19 dogs, averages 32.1 inches.
What is the average height of poodles in your kennel?
Answer:
The average height of poodles in your kennel is 25.19 inches.
Step-by-step explanation:
This is a weighed average problem.
To find the weighed average, we sum each value of the set multiplied by it's weight, and then we divide by the sum of the weights.
In this problem, we have that:
Average 20.5 inches has weight 28.
Average 32.1 inches has weight 19.
What is the average height of poodles in your kennel?
[tex]A = \frac{32.1*19 + 20.5*28}{19+28} = \frac{1183.9}{47} = 25.19[/tex]
The average height of poodles in your kennel is 25.19 inches.
To start with, in finding the height of the poodle, we consider both groups. We then add the multiplication of the number of dogs by the average, and finally, we divide them all by the number dogs. Mathematically, i am saying that;
Group 1 = 28 * 20.5 = 574Group 2 = 19 * 32.1 = 609.9Adding the number of dogs together, we have 28 + 19 = 47Finally,
[tex]\frac{574+609.9}{47}[/tex] = 25.19
Therefore, the average height of the dogs in the kennel is 25.19 inches
learn more about calculating averages here: https://brainly.com/question/20118982
If a population mean is 300 and the sample mean is 400, the difference of 100 is called:
A.Standard error
B.Sampling error
C.Allowable error
D.None of the above.
Answer:
B. Sample error.
Step-by-step explanation:
Such type of error is called Sample error.
Sample error occurs when
Sample error is a statistical error when an expert fails to choose a sample which symbolizes the whole data population and the outcomes of the sample do not reflect the outcomes from the whole population.
If a population mean is 300 and the sample mean is 400, the difference of 100 is called sampling error. So, option b is correct.
Sampling error represents the difference between the population mean and the sample mean, which arises purely by chance because a sample rather than the entire population is observed.
The other options are incorrect in this context:
Standard error: This measures the spread of the sample means around the population mean.Allowable error: This term refers to the acceptable range of error in forecasting or measurement but is not applicable in this context.The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age ¯ x x¯ of these residents is to be computed. We know the random variable ¯ x x¯ has approximately a Normal distribution because____________.
a. of the central limit theorem.
b. of the 68‑95‑99.7 rule.
c. the population from which we’re sampling has a Normal distribution.
d. of the law of large numbers.
Answer:
a. of the central limit theorem.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size, larger than 30, can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, the sample size is 100, so it is sufficiently large to use the Central Limit Theorem. The mean of the sample in 69 and the standard deviation of the sample is 0.58.
So the correct answer is:
a. of the central limit theorem.
Data is collected from a:
A. sample
B. population
C. variable
D. None of the above answers is correct
Data is collected from a sample, which is a smaller subset of the population.
Explanation:The correct answer is A. sample. When data is collected, it is usually infeasible or impractical to collect information from an entire population. Therefore, a sample, which is a smaller subset of the population, is selected for data collection and analysis. For example, if we want to know the average height of students in a school, it would be time-consuming and costly to measure the height of every student. Instead, we can select a sample of students from different grades or classrooms to represent the entire population and collect data from them.
Learn more about Data Collection here:https://brainly.com/question/32425922
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Find the appropriate percentile from a t-distribution for constructing the following confidence interval.
99% t-interval with n = 3.
Answer: 9.9248
Step-by-step explanation:
We know that the critical t- value for confidence interval is a two-tailed value from the t-distribution table corresponding to degree of freedom (df = n-1 , where n is the sample size) and the significance level ([tex]\alpha/2[/tex]) .
The given confidence interval = 99%
⇒ Significance level = [tex]\alpha=100\%-99\%=1\%=0.01[/tex]
Sample size : n=3
DEgree of freedom : df = n-1 = 2
Then, the critical t- value for 99% confidence interval will be;
[tex]t_{\alpha/2, df}=t_{0.01/2,\ 2}[/tex]
[tex]t_{0.005 , 2}=\pm9.9248[/tex] [From t-distribution table]
Hence, the appropriate percentile from a t-distribution for constructing the 99% confidence interval with n = 3 is 9.9248.
On one of its routes across Asia, Alpha Airlines flies an aircraft with checked-in luggage capacity of 8500 lbs. There are 121 seats on the flight.
The average (per passenger) weight of checked-in luggage is 68 lbs with a standard deviation of 11 lbs.
What is the probability that on a randomly selected full flight on this route the checked-in luggage capacity will be exceeded?
Answer:
the probability is P=0.012 (1.2%)
Step-by-step explanation:
for the random variable X= weight of checked-in luggage, then if X is approximately normal . then the random variable X₂ = weight of N checked-in luggage = ∑ Xi , distributes normally according to the central limit theorem.
Its expected value will be:
μ₂ = ∑ E(Xi) = N*E(Xi) = 121 seats * 68 lbs/seat = 8228 lbs
for N= 121 seats and E(Xi) = 68 lbs/person* 1 person/seat = 68 lbs/seat
the variance will be
σ₂² = ∑ σ² (Xi)= N*σ²(Xi) → σ₂ = σ *√N = 11 lbs/seat *√121 seats = 121 Lbs
then the standard random variable Z
Z= (X₂- μ₂)/σ₂ =
Zlimit= (8500 Lbs - 8228 lbs)/121 Lbs = 2.248
P(Z > 2.248) = 1- P(Z ≤ 2.248) = 1 - 0.988 = 0.012
P(Z > 2.248)= 0.012
then the probability that on a randomly selected full flight, the checked-in luggage capacity will be exceeded is P(Z > 2.248)= 0.012 (1.2%)