WHAT IS THE LIMIT OF A CONSTANT?
Answers
The limit of a constant function is equal to the constant. The limit of a linear function is equal to the number x is approaching.
What are limits?A limit is defined as a value that a function approaches the output for the given input values.
Limit of a constant :-
We know that the limit of a function exists, only and only if the left-hand limit (LHL) and the right-hand limit (RHL) exists and are equal to one another. And, the value of the limit of that function is equal to the common value, LHL = RHL = f(x).
We need to find the limit of a constant. So, let us assume a function, f(x) = c, where c is a constant. We are assuming that we need to find the limit of this constant function at x = a, i.e. we need to find the value of
[tex]\lim_{x \to \ a} f(x)[/tex]
Plot the graph, y = c, (attached)
Let us calculate the left hand limit first.
LHL = [tex]\lim_{x \to \ -a} f(x)[/tex]
We can see that at x = -a, the value of f(x) is c.
LHL = c.....(i)
Similarly,
For right-hand limit,
We have at x = +a, the value of f(x) is c.
RHL = c....(ii)
Also, Also, the value of our function at a, i.e., f(a) = c
Thus, by equation (i), (ii) and (iii), we can say that
[tex]\lim_{x \to \ a} f(x) = c[/tex]
Hence, we can now say that the limit of any constant is the same constant.
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Related Questions
b) The growth rate of covid patient is 5% per hour. If the number of covid patients in the morning 9am is 44,100, what was the number of patient 7am sharp?
Answers
Answer:
36,900
Step-by-step explanation:
it's right I just do not know how to explain lol
In a wind tunnel experiment, the force on a projectile due to the air resistance
was measured at different velocities:
Velocity (100 ft=sec) 0 2 4 6 8 10
Force (100 lb) 0 2.90 14.8 39.6 74.3 119
Find an interpolating polynomial p(t) = a0 + a1t + a2t^2 + a3t^3 + a4t^4 + a5t^5 for these data.
What happens if you try to use a polynomial of degree less than 5?
Answers
To find an interpolating polynomial, we need to fit a polynomial to the given data points. The simplest way to do this is by using the Lagrange Interpolating Polynomial formula:
p(t) = ∑ (y_i * l_i(t))
where y_i = the y-value of the data point
l_i(t) = Lagrange basis polynomial for data point i, defined as:
l_i(t) = (∏ (t-t_j)) / (t_i-t_j) for all j ≠ i
Using this formula, we can find the interpolating polynomial for the given data points:
p(t) = 0.0006t^5 - 0.0222t^4 + 0.2436t^3 - 1.0528t^2 + 2.2080t + 2.0400
So the interpolating polynomial for this data is a 5th degree polynomial, which means that it is necessary to use a polynomial of at least degree 5 in order to accurately fit the data.
If we try to use a polynomial of degree less than 5, the polynomial will not fit the data points accurately, and the difference between the polynomial and the actual data points will be significant. This means that the results of the wind tunnel experiment would be inaccurate if we use a polynomial of lower degree.
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at which point or points (marked a-e) is the object moving the slowest without being at rest? explain your reasoning.
Answers
In the given position-versus-time graph, the object moving the slowest without being at rest is at point B.
A position-versus-time graph illustrates how far an object has travelled from its starting position at any given time since it started moving. The vertical axis describes the position of the object, and the horizontal axis describes the time.
The slope of the graph indicates the speed of the moving object. Hence, the value of the slope at a particular time indicates the speed of the object at that instant. Hence, the steeper the line is, the greater the slope of the line and the faster the object's motion is changing.
In the given graph, at points A, C and E, the slope is zero; the object is not moving, hence at rest. At the point, D slope is steeper as compared to the slope at point B. Hence, the object is moving slower at point B as compared to point D.
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--The given question is incomplete; the complete question is
"The figure shows the position-versus-time graph for a moving object. At which point or points is the object moving the slowest without being at rest?"--
The chart shows the number of rabbits a farmer observed on his farm over a period of nine weeks.
Find the third quartile of the data set.
Answers
The third quartile of the data set is 20, and option C is correct.
What are datasets?A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it. Data can be arranged for our study in the form of graphs, charts, or tables.
Given a chart for the number of rabbits, a farmer observed on his farm over a period of nine weeks.
week 1 2 3 4 5 6 7 8 9
rabbits 2 3 5 7 11 15 18 22 27
the formula of quartiles is
Lower Quartile (Q1) = (N+1) * 1 / 4
Middle Quartile (Q2) = (N+1) * 2 / 4
Upper Quartile (Q3 )= (N+1) * 3 / 4
here N = 9
third quartile(Q3) = (N+1) * 3 / 4
third quartile(Q3) = (9 + 1)3/4
third quartile(Q3) = 7.5 term
third quartile(Q3) is the term between 7th and 8th week
third quartile(Q3) = (7th term + 8th term)/2
7th term = 18
8th term = 22
third quartile(Q3) = (18 + 22)/2
third quartile(Q3) = 20
Hence option C is correct.
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Which is the graph of g(x)?
3,
x < -2
g(x) = - +2,
-/+2, -2
2x - 3,
x22
Answers
Step-by-step explanation:
you don't show us all possible answer options.
none of the visible graphs are correct.
just look at x=0. g(0) = -0/2 + 2 = 2
so, the correct graph has to go through (0, 2). and the 3 segments connect at the interval end points
(-2, 3) and (2, 1).
so, please pick the correct answer option based on this information.
1. Carly needed to study for of an hour for 9 days. How many hours did she study? A. 7 1/2 hours B. 9 5/6 hours C. 7 hours D. 2 1/7 hours
Answers
The total number of hours that Carly studied for 9 days is; 7¹/₂ hours
How to solve proportion problems?She wants to study 5/6 of an hour per day for 9 days.
Thus;
Number of hours studied per day = 5/6 * 1 hour = 5/6 hours
Therefore for 9 days, the total number of hours she will study is;
5/6 * 9
= 45/6
= 15/2
= 7¹/₂ hours
That value denotes the total number of hours that she studied for 9 days
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Complete question is;
Carly needed to study for 5/6 of an hour for 9 days. How many hours did she study?
1,014 is the median value of the given population parameters. This value is the middle value. in the ordered list of data values. This value in a set of 11 will be the 1014 number in order. Therefore, years will have totals at or below the median.
Answers
Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.
How is the median value determined?When working with a tiny data collection, you must first count the number of data points (n) and organise them in ascending order. In the case of an unequal distribution of data points, the rank of the data point whose value is the median is determined by adding 1 to the total number of points and dividing the results by 2.In statistics, the median is the value that, when placed in order, falls in the centre of the supplied collection of data. Either descending or ascending order can be used to arrange the data or observations.Since 1014 is at median which tells us that 50% of the values are equal.1014 * 11 = 11014.
Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.
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Please help if you can, this is due in two days.
Answers
The lengths of side [tex]\overline{AB}[/tex] and [tex]\overline{AC}[/tex], found using the angle bisector theorem are;
AB = 28, AC = 42
What is the angle bisector theorem?The angle bisector theorem states that the bisector of an angle in a triangle, intersects the opposite side at a point such that the opposite side are divided into proportions that is equivalent to the ratio or proportion of the other two sides.
AB = x - 7
AC = x + 7
According to the angle bisector theorem, we get;
8/12 = (x - 7)/(x + 7)
8·(x + 7) = 12·(x - 7)
8·x + 8 × 7 = 12·x - 12 × 7
8·x + 56 = 12·x - 84
12·x - 8·x = 56 + 84 = 140
4·x = 140
x = 140 ÷ 4 = 35
x = 35
Therefore;
AB = 35 - 7 = 28
AC = 35 + 7 = 42
The correct option is therefore;
AB = 28, AC = 42
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solve the inequality |x| < 5
Answers
The inequality is solved to x < -5/4
What is an inequality?An inequality can be defined as a mathematical relation that makes a non-equal comparison between two numbers, mathematical expressions or equations.
Inequalities are used to compare two numbers on the number line on the basis of their size.
The different inequality signs are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that;
|x| < 3x - 5
Note that the signs, "| |" represents modulus which explains that the number must be a positive number.
collect like terms
x -3x< 5
substract the like terms
-4x< 5
Make 'x' the subject
x < -5/4
Hence, the value is x < -5/4
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The complete solution is:
solve the inequality |x| < 3x - 5
A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed.
The city will have (blank) streetlights at the end of 46 weeks.
The city will have 232 streetlights at the end of (blank) weeks.
Answers
Answer:
316 street lights.
25 weeks.
Step-by-step explanation:
Linear Equations:We can set up a linear equation with the information provided expressed in slope intercept form: [tex]y=mx+b[/tex], where "m" is the slope, and "b" is the initial value.
We're given the initial amount, or what the city already has is 132 street lights, that's our "b" value and they will install 4 each additional week which is our slope. So we have the equation: [tex]y=4x+132[/tex]
To find how many streetlights the city will have at the end of 46 weeks, we can plug in 46 as "x" to give us:
[tex]y=4(46)+132\\y=316[/tex]
To find when the city will have 232 streetlights we can set the equation equal to 232 and solve for "x" the number of weeks.
[tex]232=4x+132[/tex]
Subtract 132 from both sides
[tex]100=4x[/tex]
Divide both sides by 4
[tex]25=x[/tex]
So this will occur after 25 weeks.
Find the slope of the line y=2x+17.
Answers
Answer:
Step-by-step explanation:
2x + y = 17 in slope intercept form? Put the y on one side by itself. -2 is the slope and 17 is the y-intercept. Slope / gradient of a line is obtained by making an equation in the form of: where ' m ' gives the slope/gradient of the line and ' c ' gives y-intercept.
The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y", this form is called "slope-intercept form" and the reason for that name is because it easily shows both the slope and the y-intercept of the line.
Check attached image 1 to better understand this concept.
As you may see in the picture, the slope is just the number that multiplies variable "x". Hence, the coefficient of this line is 2.
Check attached image 2 to see the graph of this line. Notice that the y-intercept is 17, as shown in the slope-itercept form of the equation.6x x 6 + 75 = 10x - 9
Answers
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4. It's really common to contrast expressions and phrases.
what is expression ?It is necessary to duplicate, divide, add, or subtract in mathematics. The following is how an expression are put together: Number, expression, and mathematical operator The components of a numerical method include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It's really common to contrast expressions and phrases. An language, often known as an algebraic expression, is any mathematical statement that rating systems, numbers, and then an arithmetic function between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.
given
6x + 75 = 10x -9
Because 6x + 75 = 10x -9
6x -10 x = -9 - 75
-4x = -84
x = 21; the value of x is 4.
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4.
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3 1/3(1+2x)= 5 1/2(2x-1)
Answers
Step-by-step explanation:
=> The simplest form of
56
:
98
56:98 is
4
:
7.
4:7.
Step-by-step explanation:
Given ratio -
56
:
98
56:98
We have to reduce it to its simplest form,
For that, we have to find the GCD of the numerator as well as the denominator:
So, the GCD for
56
56 and
98
98 is
14.
14.
Now, divide both the numerator and denominator by the GCD:
=
>
56
÷
14
98
÷
14
=>
98÷14
56÷14
=
>
4
7
=>
7
4
Hence, the simplest form is
4
:
7.
4:7.
Researchers wanted to determine if a new organic pesticide Z was effective at killing grasshoppers that typically invade cornfields. The effect of the grasshoppers in the fields is a decrease in yield which has economic consequences on the farmers. For the study two ten-acre cornfields located 1 mile apart were chosen. The cornfield to the west was sprayed only with water. The cornfield on the east received the same amount of water with a 10% solution of organic pesticide Z. Samples of the numbers of grasshoppers in the field were made every week for 10 weeks.
RESULTS
West field treated only with water
The number of grasshoppers in the west field doubled after ten weeks.
East field treated with pesticide Z
The number of grasshoppers in the east field declined by 50% after 10 weeks.
The following questions relate to this experiment.
1) State a possible hypothesis for this study. 2) What was the purpose of conducting this experiment? 3) What was the independent variable in the above experiment? 4) What was the dependent variable in the above experiment? 5) Which group was the control group? 6) Why is it important to have a control group in the experimental design? 7) Which of the following is the most accurate conclusion about these results?
Pesticide Z is a good way to control most insect infestations on fields of corn, wheat, or oats. East fields are more likely than west fields to have problems with grasshoppers eating corn crops. If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later. Pesticide Z is unable to kill grasshoppers and is not suitable for the use in modern agriculture. 8) Based on the results of the experiment what will be your recommendation to the farmer in order to decrease the number of grasshoppers in the cornfield. 9) Arrange the stages of the scientific method listed below in order from first to last. Analyze data Formulate hypothesis Make observation about nature Reject or accept hypothesis Conduct experiments 10) You have noticed that after you forget to water your houseplant it wilts. This is an example of which part of the scientific method:
a. Hypothesis b. Observations c. Experiment
Answers
A possible hypothesis for this study is: "The organic pesticide Z will reduce the number of grasshoppers in cornfields compared to water treatment alone."
The purpose of conducting this experiment is to determine if the new organic pesticide Z is effective at killing grasshoppers that typically invade cornfields and to study its effect on reducing the number of grasshoppers.
How to explain the variablesThe independent variable in the experiment is the treatment with organic pesticide Z.
The dependent variable in the experiment is the number of grasshoppers in the cornfield.
The west field treated only with water is the control group.
It is important to have a control group in the experimental design because it provides a baseline comparison for evaluating the effect of the treatment.
The most accurate conclusion is: "If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later."
Based on the results, my recommendation to the farmer would be to spray the cornfield with pesticide Z to decrease the number of grasshoppers in the cornfield.
The stages of the scientific method in order from first to last are: Make observations about nature, formulate hypothesis, conduct experiments, analyze data, reject or accept hypothesis.
This is an example of making observations about nature.
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HELP PLEASEE the product AB is:
Answers
Answer:
D
Step-by-step explanation:
product AB
= (x - 3)(x³ + 2x² + x - 2)
each term in the second factor is multiplied by each term in the first factor, that is
x(x³ + 2x² + x - 2) - 3(x³ + 2x² + x - 2) ← distribute both parenthesis
= [tex]x^{4}[/tex] + 2x³ + x² - 2x - 3x³ - 6x² - 3x + 6 ← collect like terms
= [tex]x^{4}[/tex] - x³ - 5x² - 5x + 6
What is the area of the triangle shown?
Responses
A 24 in2
24 in 2
B 12 in2
12 in 2
C 48 in2
48 in 2
D 36 in2
Answers
Answer:
42 in^2 <=====not in your answer choices
Step-by-step explanation:
Area of a right triangle = 1/2 base * height = 1/2 (7)(12) = 42 in^2
Need help will reward
Answers
Answer:
1296
Step-by-step explanation:
2 | 36
3 | 216
the pattern is 6^x
so 6^4 is 1296
Find the area of the shape.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
units^2
2
Answers
The area of the given shape which is a sector of the circle is 3.14 sq.units.
What is a sector of a circle?
An area of a circle that is contained within its two radii and the arc that connects them is called a sector. A semicircle, which represents one-half of a circle, is the most typical sector of a circle.
Given a sector of a circle.
The radius of the circle = 2
Given π = 3.14
Area of circle = πr²
Area of sector = ( θ / 360° ) * πr²
where θ = sector angle
For the given shape, sector angle = 90°
Area of sector = (90°/360°) × 3.14 × 2² = (1/4) × 3.14 × 4 = 3.14
Therefore the area of the given sector of the circle is 3.14 sq.units.
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Ordered: 500ml 0.45% NS with heparin 25,000 U to infuse at 500 units/hr what is the flow rate
Answers
Answer:
0.0625 mL/hr.
Step-by-step explanation:
To calculate the flow rate in mL/hr, we need to know the total volume of the solution, the concentration of the solution, and the desired infusion rate.
Given:
Volume: 500 mL
Concentration: 0.45% (or 0.0045 g/mL)
Infusion rate: 500 units/hr
We know that:
Infusion rate = Volume x Concentration / Time
We can rearrange the formula to solve for time:
Time = Volume x Concentration / Infusion rate
Now we can plug in the given values:
Time = 500 mL x 0.0045 g/mL / 500 units/hr
To convert the time to hours, we will divide the time by 3600 seconds/hour
Time = 500 mL x 0.0045 g/mL / 500 units/hr / (1 hr/3600 s)
Now we have the flow rate in mL/hr
Time = 0.0625 mL/hr
So the flow rate should be set at 0.0625 mL/hr.
It's important to note that the heparin added is 25000 U, this is not related to the flow rate calculation.
What is the answer for
( f - g )(6)=
Answers
Answer: 6f-6g
Step-by-step explanation:
Solve the proportion. X/2 = 9/27
Answers
Answer:
To solve the proportion, X/2 = 9/27, you can cross multiply to get 2x = 9*27, which simplifies to 2x = 243. Then divide both sides by 2 to get x = 243/2, which simplifies to x = 121. Therefore, the solution to the proportion is x = 121.
After cross multiplying, you should have the following:
27x = 18
Divide 27 from both sides, and now the equation will look like this:
x = 18/27
We can simplify further, so divide 9 from the numerator and denominator of the fraction:
x = 2/3
And there you have it!
a)A storage pod has a rectangular floor that measures 19 feet by 13 feet and a flat ceiling that is 5 feet above the floor. find the area of the floor and thr volume of thr pod.
b) A lap pool has a length of 24 yards, a width of 23 yards, and a depth of 5 yards. find the pool's suface area(the water surface) and the toral volume of water thatbthe pool hoods
c) A A raised flower bed is 40 feet long, 5 feet wide, and 1.8 feet deep. find the area of the bed and the volume of soil ot holds.
please i need answer right now help
Answers
a) The area of the floor A = 247 feet² volume of the pod is V = 1,235 feet³
b) The surface area of the lap pool is S = 1,574 yards² and the volume of the pool is V = 2,760 yards³
c) The area of the bed soil is A = 200 feet² and the volume of the bed soil is V = 360 feet³
What is the volume of a Cuboid?A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges
The volume of a cuboid is the product of its length , width and height
The volume of the cuboid is given by
Volume of Cuboid = Length x Width x Height
Given data ,
a)
Let the length of the pod be L = 19 feet
Let the width of the pod be W = 13 feet
Let the height of the pod be H = 5 feet
Now , the area of the floor = L x W
Substituting the values in the equation , we get
The area of the floor = 247 feet²
Now , the volume of the floor V = L x W x H
Volume of the pod = 247 x 5
Volume of the pod = 1235 feet³
b)
Let the length of the pool be L = 24 yards
Let the width of the pool be W = 23 yards
Let the height of the pool be H = 5 yards
Now , the surface area of the pool = 2 ( LH + LW + HW )
Substituting the values in the equation , we get
The surface area of the floor S = 2 ( 24x5 + 24x23 + 23x5 )
The surface area of the floor S = 2 ( 120 + 552 + 115 )
The surface area of the floor S = 1574 yards²
Now , the volume of the pool V = L x W x H
Volume of the pool = 24 x 23 x 5
Volume of the pool V = 2,760 yards³
c)
Let the length of the bed be L = 40 feet
Let the width of the bed be W = 5 feet
Let the height of the bed be H = 1.5 feet
Now , the area of the bed = L x W
Substituting the values in the equation , we get
The area of the bed = 200 feet²
Now , the volume of the soil V = L x W x H
Volume of the bed soil = 200 x 1.8
Volume of the bed V = 360 feet³
Hence , the volume is solved
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Please help me with this question.
Answers
For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.
What are trigonometric functions?
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions.
Now,
given function is csc^2x(1-cos^2x)=1
=csc^2x(sin^2x)
=1/sin^2x*sin^2x
=1
Hence,
For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.
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Three friends; Ghanem, Bilal and Rashed, applied for admission at ZU. Define G for "Ghanem is accepted" and G' for "Ghanem is not accepted". Similarly, you can define B & B' for Bilal and R & R' for Rashed. What is the sample space for the acceptance outcomes of the three friends?
a- S={G, B, R, G', B', R'}
b- S={GBR, GBR', GB'R, GB'R', G'BR, G'BR', G'B'R, G'B'R'}
c- S={G, GB, GBR, G', G'B', G'B'R'}
d- S={GBR, GBR', GB'R, G'BR, G'B'R, G'B'R'}
Answers
The sample space for the acceptance outcomes of the three friends is S={G, B, R, G', B', R'}. Therefore, option A is the correct answer.
What is a sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given that, Ghanem, Bilal and Rashed, applied for admission at ZU. Define G for "Ghanem is accepted" and G' for "Ghanem is not accepted". Similarly, you can define B & B' for Bilal and R & R' for Rashed.
Sample space of accepted ={G, B, R, G', B', R'}
Therefore, option A is the correct answer.
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Twenty members of an athletic club are studying the relationship between the time it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table.
TermCoefSE CoefTConstant39.884.249.41Time to fatigue3.920.715.52
Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
3.92±1.734(0.71)
Answers
The confidence interval for the slope of the regression line relating performance score is 0.71
sample size (n) = 20
slope (b1) = 3.92 and SE of slope = 0.71
Degrees of freedom = 20 - 2 = 18
Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,
tα/2=1.734
The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,
B1±Tα/2*SE
3.92±1.734(0.71) (c)
Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.
For example, how commodity prices relate to the shares of companies that trade in those commodities.
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Frankie wants to use her 8.39 m long ladder
against a wall, as shown below.
The instructions state that the angle between
her ladder and the ground should be in the
range 74° to 77°.
Calculate the maximum distance that the
base of her ladder should be placed from the
wall.
Give your answer in metres to 2 d.p.
Answers
Answer:
2.31m
Step-by-step explanation:
Trigonometry:
cosθ = adjacent/hypotenuse
cos(74) = adjacent/(8.39)
adjacent = 8.39 × cos(74)
adjacent = 2.3125974152
2.31 (to 2 d.p.)
Simplify: [tex]t^{2} . t[/tex]
Answers
Answer:
t ^3
Step-by-step explanation:
t^2.t
= t × t^2+1
= t^3
Quadrilateral BCDE is shown on the coordinate grid. Keisha reflects the figure across the line y=x to create B’C’D’E’. Use the connect line tool to draw quadrilaterl B’C’D’E
Answers
The vertices of quadrilateral B'C'D'E' are obtained exchanging the x and y-coordinates of the vertices of Quadrilateral BCDE.
Then the quadrilateral is drawn connecting the four vertices of quadrilateral B'C'D'E'.
What is the reflection rule?The rule for a reflection over the line y = x is given as follows:
(x,y) -> (y,x).
Meaning that a reflection over the line y = x will exchange the coordinates of the figure.
Then we apply this procedure to obtain the vertices of quadrilateral B'C'D'E', and in the drawing connect the consecutive vertices.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
More can be learned about reflection at https://brainly.com/question/27224272
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One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows.
3; 9; −1; 2; 0; 4; −3; 1; −1; 5; 4; −2
Part (a)
What is the mean change score? (Round your answer to two decimal places.)
Part (b)
What is the standard deviation for this sample? (Round your answer to two decimal places.)
Part (c)
What is the median change score? (Round your answer to one decimal place.)
Part (d)
Find the change score that is 2.2 standard deviations below the mean. (Round your answer to one decimal place.)
Answers
The mean change score is 2.00, the standard deviation is 3.91, the median change score is 2.5, and the change score is 2.2 standard deviations below the mean is -6.602.
(a) To find the mean change score, we sum up the change scores and divide by the number of change scores. The mean change score is:
(3 + 9 + -1 + 2 + 0 + 4 + -3 + 1 + -1 + 5 + 4 + -2) / 12 = (24) / 12 = 2
So the mean change score is 2.00.
(b) To find the standard deviation for this sample, we first need to find the variance. The variance is calculated as follows:
Find the difference between each change score and the mean change score.
Square each of these differences.
Find the mean of these squared differences.
Take the square root of the mean squared difference to get the standard deviation.
The variance is:
( (3 - 2)² + (9 - 2)² + (-1 - 2)² + (2 - 2)² + (0 - 2)² + (4 - 2)² + (-3 - 2)² + (1 - 2)² + (-1 - 2)² + (5 - 2)² + (4 - 2)² + (-2 - 2)² ) / 12 = 15.33
The standard deviation is:
√15.33 = 3.91
So the standard deviation is 3.91.
(c) To find the median change score, we need to sort the change scores in ascending order. The median is the middle value of this sorted list. Since there are an even number of change scores, the median is the mean of the two middle values. The sorted list of change scores is as follows:
-3; -2; -1; -1; 0; 1; 2; 3; 4; 4; 5; 9
The median is the mean of the two middle values, 2 and 3, which is:
(2 + 3) / 2 = 2.5
So the median change score is 2.5.
(d) To find the change score that is 2.2 standard deviations below the mean, we need to subtract 2.2 times the standard deviation from the mean change score:
2 - 2.2 × 3.91 = 2 - 8.52 = -6.602
So the change score that is 2.2 standard deviations below the mean is -6.602.
To know more about standard deviation, here
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six flags charges $35 per student, plus a $40 processing fee per group. If you graph this, where would the line cross the y-axis?
Answers
Answer: the line will cross the y-axis at (0, 40).
Step-by-step explanation:
the line of a function crosses the y-axis at the y intercept. to find the y-intercept, equal x to 0 in the slope intercept equation.
because we know that it is 35 per student and 40 processing fee per group, we know that the slope intercept equation is y = 35x + 40.
with the equation, we plug x in as 0 and solve for y.
y = 35(0) + 40
y = 0 + 40
y = 40
because we know the x-coordinate is 0, we now have the y-coordinate, which is 40.
therefore, the line crosses the y-axis at (0, 40)
