Answer: c
Step-by-step explanation:
Answer:
Step-by-step explanation:
its $89,372 i did the math took the test
il 5 star your comment and thanks it and brainlist if u help me
Answer:
the 4 represents how many times 5 can go into 20
The graph below is a transformation of x^2
Give the function in the graph below
G(x)= ?
I first put it as G(x)=(x-2)^2-1
But what I put it at was wrong
The equation of the graph is g'(x) = -(x + 2)² - 1
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = x²
From the graph, we can see that the graph is inverted
This means that
g'(x) = -x²
Next, the graph is shifted left by 2 units
This implies that
g'(x) = -(x + 2)²
Lastly, the graph is shifted down by 1 unit
So, we have
g'(x) = -(x + 2)² - 1
Hence, the equation is g'(x) = -(x + 2)² - 1
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Explica que procedimiento se tiene que hacer primero para hallar la solución de la expresión: 8 - 6 ÷ 3 x 7 + 2
Answer:
dividir
Step-by-step explanation:
PEMDAS
you must Divide first, since its's left most
a student drove to the university from her home and noted that the odometer reading of her car increased by 8.00 miles. the trip took 20 min. (note: 1 mile
Vector of the average velocity = 3.33 km\hr towards the south.
Distance covered by the student=7miles 7*6 = 42km
Total displacement = 10km in the south.
Total time is taken = 20mins 20/60=0.33hr
Note:
Odometer reading is the distance covered while straight-line distance is the displacement which is the shortest route
Distance is a scaler where as displacement is a vector quantity.
Scaler has only magnitude while vector has magnitude and direction.
We have to find the average velocity.
Average velocity = Ratio of total displacement and total time.
⇒ Average velocity (v) = displacement/time.
⇒ Plugging the values.
⇒ (v) = 10/0.33
⇒ (v) =3.33 km\hr
So the vector of the average velocity = 3.33 km\hr towards the south.
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The average distance between the Sun and Neptune is 4450 x 100 km. Express this distance in AU
with two significant figures.
The distance 4450× 10⁶ km between the Neptune and the sun in AU is 29.75 AU
What is Astronomical unit?The astronomical unit is a unit of length, roughly the distance from Earth to the Sun and approximately equal to 150 million kilometres or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.
An astronomical unit is the average distance between the Earth and the Sun. Estimates of this distance have varied over time. It is now defined as exactly 149,597,870.7 kilometers.
if 149,597,870.7 kilometers = 1 AU
then 4450× 10⁶ km = 4450× 10⁶ ÷149,597,870.7
= 29.75 AU
Thefore the distance between the sun and neptune is 29.75 AU
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For groups of 80 or more people, a charter bus company determines the rate r (in dollars per person) according to the formula
r = 8 − 0.05(n − 80), n ≥ 80
where n is the number of people.
(a) Express the revenue R for the bus company as a function of n.
(b) Complete the table.
(c) Criticize the formula for the rate. Would you use this formula? Explain your reasoning.
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
(a) R(n) = r(n) * n = (8 − 0.05(n − 80)) * n
(b)
n r (dollars per person) R (dollars)
80 8 640
90 7.5 675
100 7 700
(c) This formula for the rate is not ideal, as it does not take into account factors like the distance traveled or any additional services that the bus company may offer. It also does not account for any additional fees or taxes. I would not use this formula, as it does not provide an accurate representation of the price the bus company should charge for its services.
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system using elimination.
5x + 4y = 12
3x - 3y = 18
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By solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
What is Elimination Method?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Now solving the both equation by using elimination method;
5x +4y = 12 ----------------------------eq(1)
3x - 3y = 18 ----------------------------eq(2)
Multiply equation (1) by 3 and equation (2) by 4, we get;
15x + 12y = 36
12x - 12y = 72
Now, same equation will beb together;
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
x = 4
Now, we calculate for the y ;
3x - 3y = 18
3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
3y = -6
y = -6/3
y = -2
(x, y) = (4, -2)
So, by solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
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Which of the following refers to the type of statistical methods used to draw conclusions about the population based on a sample?
Population methods
Sampling methods
Descriptive statistics
Inferential statistics
The type of statistical methods used to draw conclusions about the population based on a sample is called inferential statistic.
Statistical inference refers to the process of generating inferences about a population from a sample or subset of the data. The goal of inferential statistics is to extrapolate from sample data to the population as a whole by comparing the parameters of multiple samples. Two major categories of inferential statistics use distinct strategies to extrapolate information from samples of the population. These are regression analysis and hypothesis testing. Inferential statistics, including hypothesis testing, examines sample data to draw conclusions about the whole population. It entails establishing a null hypothesis and an alternative hypothesis, then doing a statistical test of significance to determine which one is more likely to be correct. The impact of one variable on another can be measured with the use of regression analysis.
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Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a % confidence level. What does the confidence interval tell about the population of all college students in the state?
Question content area bottom
Part 1
What is the confidence interval for the population mean ?
The 95% confidence interval for the population mean is given as follows:
(3.64, 4.18).
It tells that we are 95% sure that the true population mean rating is between these two bounds.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 15 - 1 = 14 df, is t = 2.1448.
The remaining parameters for this problem are given as follows:
[tex]\overline{x} = 3.91, s = 0.48, n = 15[/tex]
Hence the lower bound of the interval is of:
[tex]3.91 - 2.1448\frac{0.48}{\sqrt{15}} = 3.64[/tex]
The upper bound of the interval is of:
[tex]3.91 + 2.1448\frac{0.48}{\sqrt{15}} = 4.18[/tex]
Missing InformationThe sample is given as follows:
3.9
3.1
3.7
4.4
3.2
4.1
3.3
4.4
4.3,
4.4
4.5
3.9
3.2
4.2,
4.0
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Write an equation to match this graph.
The equation for the line is y=x+7.
What is a linear equation's solution?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation.
In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Given, the line's points are (2,9), (3,10), (4,11), and (5,12). (6,13)
Assuming that the line's equation is y=x+7, adding the points to the equation results in
(2,9) 9=2+7
(3,10) 10=3+7
The equation is also valid for every point on the graph.
Hence, The line's equation is y=x+7.
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Complete Question -
A three-column table is given.
Part A C D
Part 25 35 50
Whole B 56 80
What is the value of B in the table?
44
40
36
30
Answer:
(b) 40
Step-by-step explanation:
You want the value of the "whole" corresponding to a "part" of 25 in the given table.
PartsBased on the relationships in the 2nd and 3rd columns, it appears that the parts on the second line are 5/8 of the whole.
This means that 25 is 5/8 of B, or ...
B = 8/5 × 25 = 40
The value of B in the table is (b) 40.
__
Additional comment
The parts on the first line will be 3/5 of the value of the parts on the second line. The sum of the two parts in each column is equal to the whole.
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This design began from the construction of a regular hexagon.
Name 2 pairs of congruent figures.
The true statements regarding the construction are statement 2) and statement 5)
What is construction?"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.
Given that, A design began from the construction of a regular hexagon.
The true statements made on the construction is;
2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
Hence, The true statements regarding the construction are statement 2) and statement 5)
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a 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works tuesday-saturday and rests on sunday and monday. the numbers of agents working every day of a week should be at least given numbers d1; :::; d7. the manager wants to meet this requirement with the minimal possible total number of agents employed, by deciding what will be the days o of the agents. assuming that di are large, so that we can ignore integrality restrictions, formulate manager's problem as an lo program.
A call center required the number of agents is equal to 18.
One of the most frequent themes in quantitative aptitude that is tested in government exams is time and work. One of the subjects that candidates are knowledgeable about even before they begin preparing for competitive exams.
The idea of time and effort is still the same, but there may be some variation in the questions that are posed. The majority of the questions on this topic are 1-2 word problems, but candidates should also be ready for questions about data sufficiency and data interpretation that may come up over the course of their work.
A 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works Tuesday Saturday and rests on Sunday and Monday.
total working day of call center = 7
agent's working day =5
so, required the minimal number of agents-
[tex]=\frac{7!}{2!.5!}\\\\=\frac{35}{2}\\\\= 17.5 = 18[/tex]
So, at least required number of agents = 18.
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PLEASE HELP I WILL GIVE YOU BRAINLIEST AND 10 POINTS!! SHOW WORK PLS
Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?
we know that in parallelogram, opposite sides are parallel and are of equal lengths. So, we can say that line joining vertices ( 5, -2 ) and ( 6, 2 ) and line joining vertices ( x, y ) and ( 0, 2 ) will be parallel, that is line AB and DC will be parallel and equal to each other in length.We know that interior angles on the same side of a transversal are supplementary. Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?We are aware that a parallelogram has two opposed sides that are equally long and parallel. As a result, we may infer that the lines connecting the vertices (5, -2) and (6, 2) as well as the lines connecting the vertices (x, y) and (0, 2) will be parallel, making lines AB and DC parallel and of identical length. Interior angles on the same side of a transversal are understood to be supplementary. Similarly, B + C, C + D, and A + B all add up to 180 degrees. As a result, the sum of any two adjacent parallelogram angles equals 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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Mrs. Flanagan has these cans of soup in her kitchen cabinet: 2 cans of tomato soup, 3 cans of chicken noodle soup, 2 cans of Italian wedding soup, 2 cans of potato soup, & 1 can of split pea soup. If Mrs. Flanagan randomly chooses 1 can of soup, what is the probability she selects chicken noodle soup?
Answer:
3/10
Step-by-step explanation:
2 cans of tomato soup, 3 cans of chicken noodle soup, 2 cans of Italian wedding soup, 2 cans of potato soup, & 1 can of split pea soup = 10 cans of soup
P( chicken noodle soup) = cans of chicken noodle soup / total cans
= 3/10
What is the result from the expression[tex](6x-3)[/tex] is subtracted from [tex](-3x+2)[/tex]
Answer:
9 x - 5
Step-by-step explanation:
Simplify the following:
6 x - 3 - (-3 x + 2)
-(-3 x + 2) = 3 x - 2:
6 x - 3 + (-2 + 3 x)
Grouping like terms, 6 x - 3 - 2 + 3 x = (6 x + 3 x) + (-3 - 2):
(6 x + 3 x) + (-3 - 2)
6 x + 3 x = 9 x:
9 x + (-3 - 2)
-3 - 2 = -(3 + 2):
9 x + (-(3 + 2))
3 + 2 = 5:
Answer: 9 x - 5
HELP PLEASE FAST i'm not understanding how to do this (i'll give brainiest to whoever has best answer) The bar below is 7 inches long and divided into 2 equal parts. What is the length of one of those parts? Fill in the blanks in the equation using fractions or mixed numbers to show the length of one of the parts. X 7 inches = inches
The length of each bar is given as follows:
3.5 inches.
As a mixed number, the length of each bar is given as follows:
3 and 1/2 inches.
How to obtain the length of each bar?The length of each bar is obtained applying the proportions in the context of this problem.
The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:
7/2 = 3.5 inches.
The fraction equivalent to a decimal of 0.5 is given as follows:
1/2.
(which is used to construct the mixed number).
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jake has 16 toy cars. lydia has five fewer toy cars than jake. how many toy cars do they have in all?
1. 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why
2. The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. Identify which type of sampling is used and why
3. An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects ten schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? Simple random sample? Explain.
4. A polling company obtains an alphabetical list of names of voters in a precinct. They select every 20th person from the list until a sample of 100 is obtained. They then call these 100 people. Does this sampling plan result in a random sample? Simple random sample? Explain.
5. The personnel manager at a company wants to investigate job satisfaction among the female employees. One evening after a meeting she talks to all 30 female employees who attended the meeting. Does this sampling plan result in a random sample? Simple random sample? Explain.
Case Assignment Expectations:
Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.
The following items will be assessed in particular:
Your ability to identify situations when sampling is appropriate.
Your ability to draw the proper inferences about the population after the sample has been evaluated.
Your ability to describe the process of selecting and evaluating a samp
the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.
1. This is an example of stratified sampling, since the students are divided into three groups (Sophomores, Juniors, and Seniors) and a sample is taken from each group. This allows for a more representative sample of the overall population.
2. This is an example of random sampling, since each name has an equal chance of being selected from the bag. This ensures that the sample is unbiased and allows for a fair representation of the population.
3. This sampling plan results in a random sample, since the schools were randomly selected from the district. A random sample ensures that every member of the population has an equal chance of being selected.
4. This sampling plan results in a systematic sample, since the polling company selected every 20th person from the list. Systematic sampling allows for a more representative sample of the population, since it ensures that each person in the population is equally likely to be selected.
5. This sampling plan does not result in a random sample, since only the female employees who attended the meeting were selected. This means that those who did not attend the meeting had no chance of being selected in the sample, thus biasing the results.
This answer demonstrates the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.
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use dynkin's theorem to prove that the infinite product measure is uniquely defined on the product measure space
The infinite product measure [tex]$\mu$\\[/tex] is uniquely defined on the product measure space[tex]$(\Omega, \mathcal{A}, \mu)$[/tex] by Dynkin's theorem, since [tex]$\mu$\\[/tex] is finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite.
Let [tex]$\mathcal{A}_1, \mathcal{A}_2, \ldots$[/tex] be a sequence of sigma algebras defined on [tex]$\Omega_1, \Omega_2, \ldots$[/tex] respectively. Let [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] be the product measure space, where [tex]\Omega = \prod_{i=1}^{\infty} \Omega_i$ and $\mathcal{A} = \bigotimes_{i=1}^{\infty} \mathcal{A}_i$[/tex].
We want to prove that the infinite product measure [tex]$\mu$[/tex] is uniquely defined. To do this, we will use Dynkin's theorem.
According to Dynkin's theorem, a measure [tex]$\mu$[/tex] is uniquely determined on a product measure space [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] if the following conditions are satisfied:
1. [tex]$\mu$[/tex] is finitely additive on [tex]$\mathcal{A}$[/tex]
2. [tex]$\mu$[/tex] is countably subadditive on [tex]$\mathcal{A}$[/tex]
3. [tex]$\mu$[/tex] is [tex]$\sigma$[/tex]-finite on [tex]$\mathcal{A}$[/tex]
It is easy to see that the infinite product measure [tex]$\mu$[/tex]satisfies these conditions, since it is defined as a product of finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite measures. Thus, by Dynkin's theorem,[tex]$\mu$[/tex] is uniquely determined on the product measure space [tex](\Omega, \mathcal{A}, \mu)$.[/tex]
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A line passes through the point (-6, 5) and has a slope of 2 Write an equation in point-slope form for this line. 0 08
The required point-slope form for the given line is y = 3x/2 + 14.
What is equation of line?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
According to question:
We have,
A line passes through the point (-6, 5) and has a slope of 3/2
Then the equation of line is;
y - 5 = 3/2(x - (-6))
y - 5 = 3/2 (x + 6)
2y - 10 = 3x + 18
2y = 3x + 28
y = 3x/2 + 14
Thus the point slope form of the line is y = 3x/2 + 14.
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Points B and D are on the perpendicular bisector of ∠ABC. The measure of ∠ABD is 45°. Find the measure of ∠C.
Answer:
Step-by-step explanation:
Given ∠B=45,∠C=55
So, ∠A=180°−45°−55°
=80°
From △ABD,40°+45°+∠ADB=180°
⟹∠ADB=95°
From△ADC,40°+55°+∠ADC=180°
⟹∠ADC=85°.
Points D, B, and E are collinear. Find the value of x so that points A, B, and C are collinear
The value of x in the figure is calculated using the linear pair theorem to be 6 degrees
What is linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states that the sum of the measurements of two angles that make up a linear pair is 180°.
Because o the linear pair postulate we have that
150 + 5x = 180
collecting like terms
5x = 180 - 150
5x = 30
Isolating x
5x / 5 = 30 / 5
x = 6
hence x is solved to be 6
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4. Write the expression in
words.
h - 3
Answer:
h minus three
Step-by-step explanation:
The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of tL=0.5s. The force as a function of time is given by F(t)=at2+b, where a=−28N/s2 and b=7.0N. The momentum of the t-shirt will be its initial momentum (p0=0) plus its change in momentum due to the applied impulse: pf=p0+∫t=tLt=0F(t)dt. By applying the given time dependent function for F(t) and performing the integration, which of the following is the correct expression for pf?
The impulse equation is given by pf = p0 + ∫tL₀F(t)dt. With the given information, the integral is ∫tL₀(-28t² + 7.0)dt.
This integral can be solved using the power rule for integration, which states that the integral of xⁿ is xⁿ⁺¹/(n+1). Thus, the integral of -28t² + 7.0 is -28/3t³ + 7t. This can be evaluated from t=0 to t=0.5 to get the change in momentum due to the applied impulse. Substituting the values into the impulse equation, pf = 0 + (-28/3(0.5)³ + 7(0.5)) = -2.167. Thus, the correct expression for pf is pf = -2.167.
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A polling organization contacts 1398 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had attended a concert this past year. What is the population in the study? A. Teenagers who are 13 to 17 years of age and have attended a concert. B. Teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age and live in the United States and have attended a concert. D. Teenagers who are 13 to 17 years of age. What is the sample in the study? A. Teenagers who are 13 to 17 years of age and live in the United States. B. The 1398 teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age. D. The 1398 teenagers who are 13 to 17 years of age and have attended a concert.
The population of the given study in the polling organization contacts is given by :
Option B. Teenagers who are 13 to 17 years of age and live in the United States.
Total number of people attended by the polling organization = 1398
1398 are the teenagers .They are in the age group of 13 to 17 years of age.They all live in the United States .It was asked whether they have attended any concert in the past year.Population is represented by all teenagers of United States in the age group of 13 to 17 years of age.
Those who attended the concert represents the sample of particular category.
Therefore, the population of the required study is given by :
Option B. Teenagers belongs to 13 to 17 years of age and live in the United States .
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you win the lottery and get 1000000. the bank you invest your winnings in gives you a 6% interest rate compounded quaterly. how much will you have in 3 years ?
The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units
How to find the amount earned ?To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:
= Amount won x ( 1 + periodic rate ) ^ number of periods
Periodic rate :
= 6 % / 4 quarters per year
= 1. 5 %
The number of periods is:
= 3 years x 4 quarters per year
= 12 quarters
The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²
= 1, 195, 618. 17 currency units
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Part A What descriptive words, units, and intervals would you choose to label the x-axis and the y-axis?
Answer:
x on the horizontal axis and y on the vertical axis.
For counseling groups, it is recommended that the number of members for groups of children, __________, as compared to counseling groups for adults.
decrease
The number of members for counseling groups of children should generally be smaller as compared to counseling groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. Smaller groups also allow for more individualized attention and support.
The recommended number of members for counseling groups of children should generally be smaller than that of groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. This can lead to a lack of engagement and little benefit from the group counseling sessions. Smaller groups also allow for more individualized attention and support, which is important for young people to feel comfortable expressing their thoughts and feelings. Additionally, smaller groups can help create a more intimate environment for participants to safely share their experiences and feelings with one another. As such, reducing the size of the group for counseling sessions with children can help ensure a more successful therapeutic experience.
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Gianna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Gianna will earn $50 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Gianna's songs were played on twice as many commercials as movies and her total earnings on the royalties from all commercials and movies was $800. Graphically solve a system of equations in order to determine the number of commercials, x,x, and the number of movies, y,y, on which Gianna's songs were played.
A graph of each function is shown in the image attached below.
The number of commercials (x) is equal to 8 commercials while the number of movies (y) is equal to 4 movies.
How to write and solve the system of equations graphically?In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of commercials.Let the variable y represent the number of movies.Since Gianna would earn $50 every time one of her songs is played in a commercial and $100 every time one of her songs is played in a movie, an equation which models it is given by;
50x + 100y = 800
Additionally, Gianna's songs were played on twice as many commercials as movies;
x = 2y
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (8, 4) as shown in the image attached below.
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