The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π
How to convert degrees to radians?When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Thus, since we want to find the radian measure of 170 degrees, it means that;
If 180° = π radians,
then; 170° = (170 * π)/180
= ¹⁷/₁₈π
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the solid whose base is the region bounded by x-y^2 and the line y-1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares
The solid whose base is the region bounded by the parabola y = x^2 and the line y = 1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares is a parabolic pyramid.
A parabolic pyramid is a pyramid whose base is a parabola and whose lateral faces are formed by rectangles that are perpendicular to the base. The height of the pyramid is determined by the y-coordinate of the point where the parabola and the line y = 1 intersect. The length of the side of the square cross section is determined by the x-coordinate of the point where the parabola and the line y = 1 intersect.
The base of the solid is a parabolic region, defined by the parabola y = x^2 and the line y = 1, and the cross sections are squares, perpendicular to the base, and parallel to the x-axis. This solid is called a parabolic pyramid.
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according to the social class model developed by gilbert, which is based on weber's analysis of the class structure, the upper class in the united states includes about of the population. group of answer choices 3 percent 1 percent 8 percent 12 percent
According to the social class model developed by Gilbert and Kahl, and based on the theory of Weber, the upper (capitalist) class of the United States includes about b) 1 percent of the population.
In the United States, the upper class, or capitalist class, is estimated to comprise about 1 percent of the population.
This is according to the social class model developed by Gilbert and Kahl, which is based on the theory of Weber.
This model suggests that the upper class is made up of those who own the majority of the nation's wealth and power, and are thus able to influence governmental decisions.
While the upper class may be small in size, it is highly influential and its members often have the resources to enact large-scale change.
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twenty-four workers were surveyed and asked how long it takes them to travel to work each day. the data below are given in minutes. 20 35 42 52 65 20 60 49 24 37 23 24 22 20 41 25 28 27 50 47 58 30 32 48 which of the following shows the data in a stem-and-leaf plot?
Use the data to create a stemplot.
Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.
20 35 42 52 65 20 60 49 24 37 23 24
22 20 41 25 28 27 50 47 58 30 32 48
The data in a stem-and-leaf plot:
3/0257
2/0002344578
4/12789
5/028
6/05
Stemplots (Stem-and-Leaf Plots)Another presentation that is similar to a histogram is a stemplot. In statistics, a stemplot is a tool for presenting quantitative data in a graphical format, similar to a histogram, namely to assist in visualizing the shape of the data distribution which is often used in exploratory analysis. Stemplots were introduced by Arthur Bowley in the early 1900's. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977.
Stem-and-leaf plots provide more information about true values than histograms. As in a histogram, the length of each bar corresponds to the number of events that fall into a given interval. On Histograms. we can only see the frequency value of the data but we don't know what the actual number value is. In contrast to the histogram, in SLP besides we can know the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf.
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4y=12x=3 and let y+3x+1 a solution
The system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 has the following solution: (x, y) = (1 / 24, 7 / 8)
How to solve a system of linear equations
In this question we find the case of a system of two linear equations with two variables, this case may have an unique solution. This system can be solved by algebraic properties.
First, write the system of linear equations:
4 · y - 12 · x = 3
y + 3 · x = 1
Second, clear y in the second equation:
y = 1 - 3 · x
Third, substitute in the first equation:
4 · (1 - 3 · x) - 12 · x = 3
Fourth, expand the expression and clear variable x:
4 - 12 · x - 12 · x = 3
4 - 24 · x = 3
24 · x = 4 - 3
24 · x = 1
x = 1 / 24
Fifth, determine the value of variable y:
y = 1 - 3 · (1 / 24)
y = 1 - 1 / 8
y = 7 / 8
The solution to the system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 is (x, y) = (1 / 24, 7 / 8).
RemarkThe statement reports several typing mistakes. The system of linear equations is shown below:
4 · y - 12 · x = 3
y + 3 · x = 1
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It would take Jack $4$ hours to mow the lawn if he works alone. Fortunately, after he mows for $2$ hours, Jill joins him. They finish mowing $90$ minutes later. How many minutes would it have taken for Jill to mow the entire lawn alone?
Answer: 720
Step-by-step explanation:
you can assess normality of data using what?
You can assess normality of data using D. Pearson's Measure of Normality
What is Pearson's Measure of Normality ?Pearson's Measure of Normality, also known as Pearson's Test for Normality, is a statistical test that is used to assess whether a set of data is normally distributed.
It is based on the skewness and kurtosis of the data, and it provides a p-value which indicates the probability that the data is from a normal distribution. Pearson's test is considered as one of the most common statistical test used to check normality of data.
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The full question is:
You can assess normality of data using A. Pearson's Index of Skewness B. Pearson's Test C. Pearson's p-value D. Pearson's Measure of Normality
6/10 Darlene runs kilometer in the morning and 1 2/5 kilometers in
About how many kilometers does Darlene run?
the afternoon.
The number of kilometers that Darlene runs is given as follows:
2.4 kilometers.
How to obtain the distance that Darlene runs?The distance that Darlene runs is obtained applying the proportions in the context of the problem.
The proportion is applied to convert the mixed number to decimal, adding the integer part to the division of the numerator by the denominator.
The distances are given as follows:
Morning: 1 km.Afternoon: 1 + 2/5 = 1 + 0.4 = 1.4 km.Hence the total distance is of:
1 + 1.4 = 2.4 km.
Missing InformationShe ran 1 km in the morning.
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Question 8
A scientist determines a plot of forest has a stable population of about 100 deer. Deer live in the interior of ecosystems. Then, a highway is built, splitting the forest into two plots of equal size.
After a couple of years, the scientist checks the number of deer in the two plots and finds the total population to be 60 deer.
Why did the carrying capacity of the habitat drop when the forest was split into two plots?
Select all that apply.
Responses
The two plots of forest have more edges than a single plot, causing a decrease in interior species. The two plots of forest have more edges than a single plot, causing a decrease in interior species.
The highway changed the climate of the region, making it less suitable for deer.The highway changed the climate of the region, making it less suitable for deer.
The two plots of forest provided more interior habitat for species other than deer. The two plots of forest provided more interior habitat for species other than deer.
The highway affected the growth of many plant species, which serve as food for the deer.
Question 9
A chicken-sized, flightless bird lives on an island in the middle of an ocean. The bird has some natural predators, which it avoids.
When people arrive at this island, they bring cats with them. Cats also hunt the bird.
What is the impact in the short term of bringing cats to the island?
Responses
The number of birds will remain the same.The number of birds will remain the same.
It is not possible to know whether there will be fewer or more birds.It is not possible to know whether there will be fewer or more birds.
There will be fewer birds.There will be fewer birds.
There will be more birds.
a) The highway affected the growth of many plant species, which serve as food for the deer. Option D
b) There will be fewer population of the birds. Option C
What is the carrying capacity?The carrying capacity of an ecosystem is the maximum number of individuals of a particular species that can be supported by the available resources in that ecosystem.
It is the point at which the population growth rate becomes zero, as the resources needed to sustain the population (such as food, water, and space) become limited. Carrying capacity can change over time due to factors such as climate change, pollution, and human activity.
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compare the original function with the 1st through 4th order approximations for different values of x,
First order approximation = (sin(x+dx)/(x+dx)^3 - sin(x)/x^3)/dx and ((sin(x-(2*dx))/(x-(2*dx))3) is a formula for calculating the fourth-order
Function output for the first order approximation is first order approx (x,dx)
(x3*(cos(x)) analytical derivative =
-sin(x)*3*x^2)/x^6;
First order approximation: % forward differencing = (f(x+dx) - f(x))/dx%
first-order approximation = (sin(x)/x3 - sin(x)/x+dx)/(x+dx)3)/dx;
output is equal to Abs(FirstOrderApproximation - AnalyticalDerivative);
end
Function output for the fourth-order approximation is fourth-order approx (x,dx)
(x3*(cos(x)) analytical derivative =
-sin(x)*3*x^2)/x^6;
((sin(x-(2*dx))/(x-(2*dx))3) is a formula for calculating the fourth-order approximation. 8*(sin(x-dx))/(x-dx) + 8*(sin(x+dx))/(x+dx) - ((sin(x+(2*dx))/(x+(2*dx))3))/(12*dx);
output for the error term is abs(approximation of first order - analytical derivative);
end
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help me please (asap)!!!!
Answer:
no more Fortnight gift cards
Step-by-step explanation:
Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?
answer choices
The correlation must be 0.
The correlation must be positive.
A straight line is not a good model for the data.
The regression line might or might not be a good model for the data, depending on the extent of the curve.
If a plot of the residuals shows a curved pattern, it indicates that a straight line is not a good model for the data. This does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve.
When a least-squares regression line is fit to a set of data, it is used to determine the linear relationship between two variables. If a plot of the residuals (the difference between the observed values and the predicted values from the regression line) shows a curved pattern, it indicates that a straight line is not a good model for the data. This could mean that there is a nonlinear relationship between the two variables or that the data contains outliers that are not accounted for by the regression line. However, it does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve. To determine if the regression line is an accurate model for the data, it is important to visually inspect the plot of the residuals and assess whether the pattern is random or systematic. If the pattern is random, it indicates that the regression line is a good model for the data. If the pattern is systematic, it indicates that the regression line is not a good model for the data and alternative models should be considered.
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6. A parabola has focus (-1, 6) and directrix y = 4. Determine whether each point on
the list is on this parabola. Explain your reasoning.
a. (-1,5)
b. (1,7)
c. (3,9)
a. (-1,5) is on the parabola
b. (1,7) is NOT on the parabola
c. (3,9) is NOT on the parabola
How to find if they are on the parabolaa. (-1,5)
The distance from the point (-1,5) to the focus (-1,6) is sqrt((-1-(-1))^2 + (5-6)^2) = sqrt(0+1) = 1
The distance from the point (-1,5) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(5-4) = 1
Since the distances are equal, the point (-1,5) is on the parabola.
b. (1,7)
The distance from the point (1,7) to the focus (-1,6) is sqrt((1-(-1))^2 + (7-6)^2) = sqrt(2^2 + 1^2) = sqrt(5)
The distance from the point (1,7) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(7-4) = 3
Since the distances are not equal, the point (1,7) is not on the parabola.
c. (3,9)
The distance from the point (3,9) to the focus (-1,6) is sqrt((3-(-1))^2 + (9-6)^2) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25)
The distance from the point (3,9) to the directrix y=4 is the absolute value of the y-coordinate of the point - the y-coordinate of the directrix = abs(9-4) = 5
Since the distances are not equal, the point (3,9) is not on the parabola.
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In a cash drawer, there is $125 in $5 and $10 bills. The number of $10 bills is twice the number of $5 bills. How many of each type of bill is in the drawer?
Answer:
Step-by-step explanation:
You can use the equations:
x = 2y
where x is the number of $10 bills and y the number of $5 bills and:
10x+5y = 125
Solving gives x=10 and y = 5, or in other words there are 10 $10 bills and 5 $5 bills
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2600. How long did each mechanic work? First Mechanic hours Seconds Mechanic hours
Answer:
Step-by-step explanation:
Each mechanic worked a total of 12.5 hours each.
If 4 -letter "words" are formed using the letters A, B, C, D, E, F, G, how many such words are possible for each of the following conditions: (a) No condition is imposed. Your answer is : (b) No letter can be repeated in a word. Your answer is : (c) Each word must begin with the letter A and letters can be repeated. Your answer is : (d) The letter C must be at the end and letters can be repeated. Your answer is : (e) The second letter must be a vowel and letters can be repeated. Your answer is :
In this case, there are 8 letters, so the total number of 4-letter words possible is 8^4 = 4096.
(b) In this case, each letter can be used only once, so we must choose 4 different letters out of 8 letters. This can be done using the combination formula C(8,4) = 70.
(c) Since each word must begin with the letter A, the remaining 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(d) The letter C must be at the end, so the first 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(e) The second letter must be a vowel, so the first letter can be chosen out of 4 letters (A, E, I, O). The remaining 3 letters can be chosen out of 7 letters. This can be done using the combination formula C(4,1) x C(7,3) = 140.
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using the basic definition show that {3n-2/n}n=1 converges
The sequence (3n-2/n)n=1 converges to 1.
How to determine if the series convergesTo show that (3n-2/n)n=1 converges, we need to find the limit as n approaches infinity.
Using algebraic manipulation, we have the following steps
lim (3n-2/n)n = lim (3-2/n)^n
lim (3n-2/n)n = (3-2/∞)^∞
lim (3n-2/n)n = 1^∞
lim (3n-2/n)n = 1
The basic definition of convergence states that a sequence converges if the limit of the sequence as n approaches infinity is equal to a finite number
Since the limit of (3n-2/n)n as n approaches infinity is 1, we can conclude that the sequence converges to 1.
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determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). show how you arrived at each answer. use equivalence-style proofs.
From the given formulas, formula A is a tautology or always true. Formula B is a contradiction or never true. And, formula C is contingency or sometimes true.
Using the truth table, a given expression is said to be in tautology when all the values are true. The given expression is said to be a contradiction when all the values are false or never true. And the given expression is said to be contingency when the values are either true or false.
In the given formulas, formula A (p→q)∨(q→r) is a tautology. This is because the values in all rows are true (T).
In the given formulas, formula B (¬(¬(p∧q)→(p→¬q))) is a contradiction. This is because the values in all rows are false (F).
In the given formulas, formula C ((¬p∨q)→q) is a contingency. This is because some values are true and some are false.
The complete question is -
Determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). Show how you arrived at each answer. Use equivalence-style proofs.
A. (p→q)∨(q→r)
B. ¬(¬(p∧q)→(p→¬q))
C. ((¬p∨q)→q)
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a circular disk is to be manufactured with a radius of 26 cm. use differentials to estimate the maximum error in the calculated area of the disk if the possible error in measuring the radius is 0.25 cm.
The maximum error in calculating the area of the disk is approximately 0.25 cm * 2π * 26 cm = 16.3 cm².
The maximum error in the calculated area of the disk can be estimated using differentials. A = r2, where r is the circle's radius, is the formula for calculating a circle's area.. Differentiating this equation with respect to r gives us A' = 2πr. Plugging in the given values, we get A' = 2π * 26 cm = 161.6 cm². If the possible error in measuring the radius is 0.25 cm, then the maximum error in calculating the area of the disk is 0.25 cm * A' = 0.25 cm * 161.6 cm² = 16.3 cm². Therefore, the maximum error in the calculated area of the disk is approximately 16.3 cm².
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a picture is enlarged by keeping its width the same and increasing its length. the scatter plot shows the perimeter of the picture (y) for different lengths (x):plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140which function best represents the data in the scatter plot?
The function best represents the data in the scatter plot is y = 2x + 20.
The function of the straight line has the general formula: y = mx + c
where m is the slope of the line, and c is the y-intercept
So first, we will need to find the slope (m):
The slope can be calculated with the points (x₁, y₁) and (x₂, y₂) as follows:
m = (y₂ - y₁)/(x₂ - x₁)
= 120 - 60/50 - 20
= 60/30
= 2/1
So, now we have the slope of our equation y = 2x + b but we still need to find b (or where the y intersects.)
Now, consider the ordered pair (20, 60)
y = 2x + b
60 = 2 × 20 + b
b = 60 - 40
b = 20
Now, put the value of b in y = 2x + b, and we get
y = 2x + 20
Also, b can not be -20 because this is a positive y-intercept, and we know it has a slope of 2.
Therefore the function is y = 2x + 20
--The given question is incomplete; the complete question is
"A picture is enlarged by keeping its width the same and increasing its length. The scatter plot below shows the perimeter of the picture (y) for different lengths (x):
Plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140
Which function best represents the data in the scatter plot?
y = 2x − 20
y = 2x + 20
y = x − 20
y = x + 20"--
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help pls i need the answer and fast !!!
Answer: The slope of the line is 2/3.
The line is not solid, it is dashed.
The area below the line is shaded.
A solution to the inequality is (2,3).
The x-intercept of the boundary line is (-3/2,0)
All the statements except the first one are true about the graph of y< 2/3 x +1.
Step-by-step explanation:
The expression 16n-24 factored using GCF
The G.C.F. of the expression 16n - 24 is evaluated to be 8(2n - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - 16n - 24.
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor).
First of all find the G.C.F of 16n and 24 separately.
It can be written that -
16n = 2 × 2 × 2 × 2 × n
24 = 2 × 2 × 2 × 3
The common prime factor between the two is 2 × 2 × 2 = 8.
So, the GCF of 16n and 24 is 8.
Now use the GCF to factor the expression -
= 16n - 24
= 8(2n) - 8(3)
Using the distributive property -
= 8(2n) - 8(3)
= 8(2n - 3)
Therefore, the GCF value is 8(2n - 3).
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Which is greater -6, 6, or -2
Find the equation for the plane through the points Po(5,5,2), Qo(-4,0,-2), and Ro(-4,-1,1).
Using a coefficient of - 19 for x, the equation of the plane is
Ax+by is c is the equation for a line in two dimensions, the equation for a line in three dimensions.
What is the equation of plane formula?The equation of a plane in R has the generic form an x + b y + c z + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.A line and a point that is not on the line can only be crossed by one plane.Ax+by=c is the equation for a line in two dimensions. It is logical to assume that ax+by+cz=d is the equation for a line in three dimensions. However, this assumption is incorrect since it turns out that this is really the equation for a plane. In contrast to a line, a plane lacks an evident "direction."(5,5,2), Qo(-4,0,-2), and Ro(-4,-1,1).5x + 5y =2-4x + y = -2-4x -y = 1To learn more about equation of the plane refer to:
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14. A brand-new school district needs to generate ID numbers for its student body. The district anticipates a total
enrollment of 75,000 students within the next ten years. Will a five-digit ID number using the symbols 0, 1,…, 9
be enough? Explain your reasoning using logarithms
The different combinations of the five-digit number formed are enough to create ID numbers.
What is meant by combinations?
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant.
We first find the total number of 5-digit enrollment IDs that can be created using all possible combinations of numbers possible.
Since each digit of the five-digit number can be from 0-9, there are ten possible values for each digit.
So the total number of ways a five-digit number can be formed
= 10*10*10*10*10 = 100,000
For the given question, it is mentioned that only 75,000 students are expected to be enrolled in the next ten years,
Since 100,000 is greater than 75,000 the five-digit ID number will be enough.
But if the school is to last longer than ten years, it is safe to use a six or seven-digit ID number.
Therefore a five-digit Id number using symbols from 0-9 will be enough.
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Need help with #4 please :)
Answer:
Step-by-step explanation:
the answer is 69
Answer:yes
Step-by-step explanation:
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Here we see two sides being congruent and one angle, this means that the other angles are also congruent, as only one triangle can be formed with two set sides and an angle. therefore we know both triangles are congruent
What is 4 ÷ 1⁄5?
- Answers are appericated.
Answer: 20
Step-by-step explanation:
Answer:
[tex] \sf \: 4 \div \frac{1}{5} = 20[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 4 \div \frac{1}{5} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 4 \div \frac{1}{5} [/tex]
[tex] \sf \rightarrow \: 4 \times \frac{5}{1} [/tex]
[tex] \sf \rightarrow \: 4 \times 5[/tex]
[tex] \sf \rightarrow \: 20[/tex]
Hence, the answer is 20.
please help me with math
Answer: 3rd Picture
Step-by-step explanation: Equation: y=1/3x+4
Intercepts y axis at 4, and with the slope equation (rise/run), then it rises 1 and runs 3, thus being the 3rd picture.
Which of the following variables are quantitative?Number zip codeFavorite colorShoe sizeArea code
Quantitative variables can be used to measure and contrast data because they have numerical values. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables.
Quantitative variables can be used to measure and contrast data because they have numerical values. They come in discrete or continuous forms. While continuous variables have an infinite number of possible values, such as decimal numbers, discrete variables have specific values, such as integers or whole numbers. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables. Quantitative variables can be used to describe a population's varied characteristics, such as the median age or annual income of a given group. The average height of men and women, for example, might be used to compare two populations. The use of quantitative variables is crucial for comprehending and analyzing data. They enable academics to spot patterns and trends in data They enable researchers to find patterns and trends in data, anticipate the future, and form conclusions.
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the complete question is
Which of the following variables are quantitative? Number zip codeFavorite colorShoe sizeArea code and Shoe size.
What is the ratio of 1.5-inch screws to 2.5-inch screws, written in three different ways? Do not reduce.
The ratio of two screws written in three different forms are,
2.5 : 1.5, 5 : 3 and 1.5/2.5.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Two screws are in the ratio of 1.5 inches and 2.5 inches.
It can be written as 2.5 : 1.5
It can also be written as 2.5×10 : 1.5×10 = 25 : 15 = 5 : 3.
It can also be written as a fraction as, 1.5/2.5.
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For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. f(x)=4x²-7 on (1,b)
On the interval (1,b), f(x)=4x2-7 changes at an average rate of 8b-11. To determine this, divide the difference between the function at b and 1 (4b2-7-3) by the difference between the intervals (b-1).
The average rate of change of a function on an interval is a measure of the change in the output of the function over the given interval. It can be calculated by taking the difference of the output between the endpoints of the interval, and dividing by the difference between the endpoints of the interval. For the given function f(x)=4x²-7 on the interval (1,b), the average rate of change is 8b-11This is obtained by dividing the output difference between 1 and b (4b2-7-3) by the output difference between the intervals (b-1). Our average rate of change is given by this formula: (4b2-7-3) / (b-1) = 8b-11. This average rate of change provides us with a general understanding of the function's rate of change across the specified interval. The output of the function increases at a constant rate as the input increases in this situation because the rate of change grows linearly as b increases.
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