The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 25 B, and 35 C responses. Show the frequency and relative frequency distributions (use 0 decimals for the frequency column and 2 decimal for the relative frequency column).

Answers

Answer 1

The relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

What is meant by relative frequency?

The proportion between a given event's frequency and all events' frequencies in a statistical experiment.

The ratio of the total number of occurrences occurring in a particular scenario to the frequency of an event can be used to determine relative frequency. Relative frequency is defined as Subgroup frequency divided by Total frequency.

Due to the possibility of interpreting the heights of relative frequency histograms as probabilities, they are significant. These probability histograms offer a graphical representation of a probability distribution that may be used to estimate the probability that specific outcomes will materialize within a given population.

The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.

The total samples be 60 + 25 + 35 = 10

Also, the frequency corresponding to A is: 60

Corresponding to B is: 25

and corresponding to C is: 35

Hence, the Frequency table is as follows:

Data               Frequency

A                          60  

B                           25

C                           35

The relative frequency table is given by:

Data               Relative Frequency          

A                      60/120 = 0.5

B                       25/120 = 0.20

C                       35/120 = 0.29

Therefore, the relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

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Related Questions

what is the average acce;eration of the particle over the interval 2

Answers

The particle's average acceleration between (1,3) and (3,3) is 0 m/s2.

What is coordinates?

The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections. Coordinates are a pair of numbers that are used to locate a point or shape in a two-dimensional plane. A point's position on a 2D plane is defined by two numbers called the x-coordinate and the y-coordinate.

Here,

A= velocity/time

Points: ( 1,3) (3,3)

Velocity: 3-3=0

Time: 3-1=2

0/2= 0 meters/seconds^2

The average acceleration of the particle over the interval (1,3) and (3,3) is 0 m/s^2.

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Complete question:

What is the average acceleration of the particle within the time interval 1 second to 3 seconds? A. -1 meter/second2 B. 0 meters/second2 C. 1 meter/second2 D. 1.5 meters/second2 E. 2 meters/second2

A random sample of 100 people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters in the district at a ___football gamesupermarketschool fund-raiserhigh school band concert

Answers

A random sample of 100 people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters at a football game.

Here,

Drawing the sample at a football game is more likely to provide a representative sample of the entire population of registered voters in the district.

This is because people attending football games are likely to include a diverse mix of registered voters from various backgrounds and demographics.

It can provide a broad representation of the population, which is crucial for obtaining accurate estimates of the proportion of voters who support improvements to the high school football field.

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if triangles are anions and stars are cations, which of the following situations would lead to the most positive membrane potential?
O Both channel types are open
O only star channels are open
O neither channel type is open
O only triangle channels are open

Answers

A positive cation and a negative anion makes ionic compound. So both the ions i.e cation and anions are open.

Membrane potential is a potential gradient that forces ions to passively move in one direction: positive ions are attracted by the 'negative' side of the membrane and negative ions by the 'positive' one. Generally Voltage gated channels- open and close in response to changes in the voltage or membrane potential; involved in generating action potentials. As stars and triangles represents the cations and anions both channel types are open to lead the most positive membrane potential.

Therefore , both the channel types ( triangle and star ) are open to lead the most positive membrane potential.

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ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left

Answers

Ara sells 1/2 of her apples in the morning, so she sells 35.5 / 2 = 17.75 pounds of apples.

She sells 4/19 of the remaining apples in the afternoon, so she sells 17.75 * 4/19 = 2.7 pounds of apples.

She sells 1/4 of the remaining apples in the evening, so she sells (35.5 - 17.75 - 2.7) / 4 = 4.5 pounds of apples.

Ara has 35.5 - 17.75 - 2.7 - 4.5 = 10.5 pounds of apples left

Companies are interested in the demographics of those who listen and call in to the radio programs they sponsor. Suppose that only 20% of listeners phoning into a morning talk show are male.a. If the station takes a random sample of 200 callers, what is the probability that the sample proportion of males will be at least 0.30?b. The station management wonders if adding a male host to the program will increase the proportion of callers who are male. After adding the male host, the station records selects a random sample of 200 callers and finds that 30% are male. Does this provide convincing evidence to suggest that the proportion of male callers has increased from 20%? Explain.

Answers

The probability that the sample proportion of males will be at least 0.30 is 0.1043.

It can be calculated by using a binomial probability formula. The formula is P(X ≥ 30) = ΣP(X = k), where k = 30, 31, 32, . . . , 200.

The probability is 0.1043.

b. After adding the male host, the station records select a random sample of 200 callers and finds that 30% are male. This provides convincing evidence to suggest that the proportion of male callers has increased from 20%. This is because the probability of observing a sample proportion of 30% or higher is 0.1043, which is greater than the 0.05 significance level commonly used in hypothesis testing. This means that the probability of the observed sample proportion being due to chance is very low and it is likely that the proportion of male callers has increased.

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if z=1-i then find the argumed of z​

Answers

The argument of the complex number z = 1 - i is approximately -0.785 radians.

What is the argument in complex numbers?

In complex numbers, the argument (also called the amplitude or angle) of a complex number is the angle that the complex number makes with the positive x-axis in the complex plane. It is usually expressed in radians and is denoted by arg(z).

Given a complex number z = 1 - i, the argument of z can be found using the inverse tangent function (atan). In this case, we want to find the angle θ such that tan(θ) = (imaginary part of z) / (real part of z):

θ = atan((-1) / 1) = -π/4 radians

Hence, the argument of the complex number z = 1 - i is approximately -0.785 radians.

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What is (12^2*5)/4+9-1?


I am giving 15 points away and will give brainiest to the correct answer and who also show there work,

Answers

Answer:

60

Step-by-step explanation:

Calculate the sum or difference

12^2 x 5 / 12

Cancel out the common factor 12

12 x 5
Multiply the numbers

60

Solution:

60

Hope this helps!! <3

Please help me with all I’ll mark you brainly

Answers

The two lines have the same slope, therefore they are parallel and there is no solution.

y=-2x+6 y=2x+2 is linear or not?

This is an example of a simple linear function. The line you see on the graph, is an expression of the function rule "y = 2x +6".

2x+y=6 ⇒(1)

2x-y=2⇒(2)

Add equ(1) and (2)

so by adding we get,

2x+y+2x-y=6+2

adding the like terms.

we get,

4x=8

x=8/4=2

put x=2 in equ(1)

we get,

2(2)+y=6

4+y=6

y=6-4=2

so the values of x and y are 2 , 2 .

Therefore, The two lines have the same slope, therefore they are parallel and there is no solution.

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elena is proving the pythagorean theorem. she knows the goal is to prove that in a right triangle. so far she has: in a right triangle the altitude that intersects the hypotenuse decomposes the triangle into 2 smaller right triangles. these triangles are similar to the large triangle by the angle-angle triangle similarity theorem since each smaller triangle shares one angle with the larger triangle and has a right angle. similar triangles have proportional side lengths, so and . i can rewrite those equations to get and . therefore . . .

Answers

If the court of the length of the most comprehensive side of a triangle is equivalent to the sum of the squares of the additional two sides, then the triangle is good.

What is meant by Pythagorean theorem?

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem.The perpendicular, base, and hypotenuse of this triangle are its three named sides.Remember that in every right triangle, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the two legs side (the two sides that meet at a right angle).The unknown side of a right-angled triangle can be located using Pythagoras' theorem. The three traditional Pythagorean means are the harmonic mean, geometric mean, and arithmetic mean (HM).

That exists, in ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR living at the right angle.

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Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.

A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.


The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.


Select the answers from the drop-down lists to correctly complete each sentence.


The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52 B) 84.78 C)127.17 D) 169.56


This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88 B) 2.25 C) 1.8 D) 1.5

Answers

The volume of the large container is given as follows:

508.68 in³.

The ratio of the volumes is of:

B) 2.25

How to obtain the volume of a cylinder?

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for the large container are given as follows:

h = 4.5, r = 0.5 x 8 x 1.5 = 6.

(as the diameter is half the radius).

Hence the volume of the large container is obtained as follows:

V = 3.14 x 6² x 4.5 = 508.68 in³.

The ratio is of 2.25, as the radius is squared.

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Solve.
How much pure acid is in 780 milliliters of a 14% solution?
The answer is ml.
(Tung an integer or a decimal.)

Answers

The amount of pure acid in the solution is 109.2ml. The solution has been obtained using the concept of proportion.

What is proportion?

When a ratio is expressed as a/b and two ratios are equal, the expression is a proportion. A and B can be any two integers in this case. Understanding many ideas in mathematics and science requires a solid understanding of ratios and proportions.

According to the direct proportion formula, we can state y = kx given a constant k if the quantity y is directly proportional to the quantity x. The direct proportion equation also has a generic form, which is y = kx.

Let 'x' ml be the quantity of pure acid in the solution.

We are given that we have 780 ml of a 14% solution

This means that 780ml is 100%.

So, using proportion:

⇒780/x= 100/14

⇒780*14/100=x

109.2ml = x

Hence, the amount of pure acid in the solution is 109.2ml.

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Dominic collected data on the location where students of two grades would most like to visit and displayed it on a table.


Aspen, Colorado New York, New York Chicago, Illinois Total
Under age 15 21% 16% 12% 49%
Age 15 and above 17% 24% 10% 51%
Total 38% 40% 22% 100%


Which term best describes the entry of 51%?
Marginal frequency
Marginal relative frequency
Joint frequency
Joint relative frequency

Answers

The term that best describes the entry of 51% in this table is "Marginal relative frequency. The correct option is B.

What is Marginal relative frequency.?

The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single category of data.

For instance, the number of female students would be one marginal frequency in a table of students classified by sex and area of study, and the number of students enrolled in a particular area of study would be another, regardless of sex.

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TRUE OR FALSE question 8 collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in your data.

Answers

True. Collaborating with a social scientist can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results.

Collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in data. Social scientists can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results. This can be done in several ways. Firstly, they can help identify potential sources of bias, such as demographic variables, cultural norms, and other external factors that may affect the data. Secondly, they can help devise strategies to counter the potential sources of bias. For example, they can suggest methods of incorporating diverse perspectives into the data collection process, or of analyzing data in a way that takes into account the potential effects of bias. Finally, they can provide insights into how social contexts can shape the interpretation of data, and can help ensure that any conclusions drawn from the data take into account the complexity of the social environment. By collaborating with a social scientist, researchers can help ensure that their data is free from bias, allowing for more meaningful and accurate results.

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Triangles LMN and FGH are shown.
Select the correct button in the table to show whether each statement is true or false.​

Answers

The answer to the true and false questions are given below:

1. MN/NL=GH/HF=true2. LM+MN+NL=FG+GH+HF=false3. Triangle LMN is similar to triangle FGH.=true

How to solve:

Coordinates of L = (-1, -3)

M= (1, 3)

N = (1, -3)

Coordinates of F = (2, 6)

G= (3, 9)

H= (3, 6)

To find the distance b/w the points:

\sqrt(x2-x1)^2 + (y2 -y1)^2)

MN/NL =3

GH/HF = 3

Hence, it is true.

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Pam takes her truck in for basic service. The service agent says a few extra repairs are also needed, so Pam adds the cost of those repairs in her head, rounding to the nearest $10. The costs are as follows: Wheel alignment: $110 Transmission fluid flush: $75 Cabin air filter: $23 What is her total estimate for the repairs? Note: 4 or less: round down, 5 or more: round up. For example, 14 becomes 10, while 15 becomes 20.

Answers

Answer:

$210 when round up

Step-by-step explanation:

To find the total estimate for the repairs, we need to add up the cost of each individual repair.

Wheel alignment: $110

Transmission fluid flush: $75

Cabin air filter: $23

Total estimate = $110 + $75 + $23 = $208

Pam rounded the costs to the nearest $10, so the total estimate may not be exactly $208, but it will be close to it.

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answers

The steps that she could use to solve the quadratic equation are determined as:

2(x² + 6x + 9) = 18 + 3(x + 3)² = 21/2

What is a Quadratic equation?

ax2+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of the coefficient of x, square it and add it to both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation are determined as 2(x² + 6x + 9) = 18 + 3 and then (x + 3)² = 21/2.

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Complete question:

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.

2(x2 + 6x + 9) = 3 + 182(x2 + 6x) = –32(x2 + =6x) = 3(x + 3)² = 21/22(x2 + 6x + 9) = –3 + 9(x + 3)2 = 6/2

For 3-4, use the table at the right.
3. Emma has $100 to spend at the pet store. She needs
to buy 1 bag of dog food and 2 chew toys. Will
Emma have enough money left over to buy 3 times
as many catnip toys as chew toys? Explain.

Answers

No, Emma will not have enough money left over to spend 3 times as many catnip toys as chew toys.

How does math relate to money?

For planning our spending, saving, and investing, we need math. In each scenario, having a solid grasp of mathematical ideas will be advantageous to your own finances. We are all effectively "bankers" in our individual lives because the term "banking" relates to handling money.

In this question,

1. Emma needs to spend $35 on 2 chew toys and 1 bag of dog food, which comes out to $20 + $15.

2. She has $65 in leftover funds because she has $100 to spend and $35 to spend it on.

3. She would need to spend $30 on 6 catnip toys, which is three times the amount she would spend on chew toys.

4. Nevertheless, she has just $65 left over, which is insufficient to pay for six catnip toys.

5. Consequently, Emma does not have enough cash on hand to purchase three times as many catnip toys as chew toys.

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I have attached a picture of the question but have typed out the option, i know a little bit about the function and what it would look like but im confuzed on what the plane y=?z=sin(xy)Give reasons for your choices. This function is [zero / linear / parabolic / period] in both x and y, and the function is [the same / not the same]when x is interchanged with y, so its graph is [ symmetric / not symmetric] about the plane y =[ ] . In addition, the function is [zero / linear / parabolic / periodic ] along the x- and y-axes. These conditions are satisfied only by [A / B / C / D / E / F ] and [ I / II / III / IV / V / VI ].

Answers

The function is periodic in both x and y, and the function is the same when x is interchanged with y, so its graph is symmetric about the plane y = 0. In addition, the function is periodic along the x- and y-axes. These conditions are satisfied only by C and IV.

A: The function plane does not have a zero or linear behavior, so this option is not correct.

B: The function does not have a linear behavior, so this option is not correct.

C: The function is periodic in both x and y, so this option is correct.

D: The function does not have a parabolic behavior, so this option is not correct.

E: The function does not have a periodic behavior, so this option is not correct.

F: The function does not have a linear behavior, so this option is not correct.

I: The function is the same when x is interchanged with y, so this option is correct.

II: The function is not symmetric about the plane y = 1, so this option is not correct.

III: The function is not symmetric about the plane y = 2, so this option is not correct.

IV: The function is symmetric about the plane y = 0, so this option is correct.

V: The function is periodic along the x- and y-axes, so this option is correct.

VI: The function is not linear along the x- and y-axes, so this option is not correct.

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Evaluate this expression for the given values of x and y 2x^2 - y x=3 y=8 QUICK FAST PLEASE HURRY

Answers

Answer:

-6

Step-by-step explanation:

2 * 3^2 - (8 * 3) = 18 - 24 = -6

please help i cant figure it out
5(2x-6) + 8 - 2x = x + 2(x-11)

Answers

Is this a true or false question?

Answer:

Step-by-step explanation:

10x - 30 + 8 - 2x = x + 2x - 22

8x - 22 = 3x - 22

-3x          -3x

5x-22=-22

    22 22

5x=0

/5  /5

x=0?

Sarah borrows $100. she earns $ 300 per day. Let y represent the number of dollars Sarah has in X days. An equation represent this situation is entered into a graphing calculator

Answers

The graphing window that will correctly graph the linear function is given as follows:

-1 <= x <= 15 and -150 <= y <= 3700.

How to define the linear function?

The linear function in slope-intercept format for this problem is defined as follows:

y = mx + b.

In which:

m is the slope, representing the daily amount earned.b is the intercept, representing the initial amount borrowed.

Hence the function for this problem is defined as follows:

y = 100 + 300x.

Meaning that the amounts of the initial and final days are given as follows:

Day 0: 100.Day 12: 100 + 300 x 12 = 3700.

And the graph window is given as follows:

-1 <= x <= 15 and -150 <= y <= 3700.

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Shane and Daniel are simplifying the expression 24 ÷ 6 x 2. Daniel says the correct answer is 8, while Shane says the correct answer is 2. Who is correct and why?

Answers

The correct response to the equation 24 ÷ 6 x 2 is 8. As a result, Daniel is right whereas Shane is wrong.

In mathematics, there are certain principles for simplifying various expressions or equations. As a result, 8 is the correct answer since it satisfies to the BODMAS rule. In which case, division comes before multiplication and must come before addition.

In this statement, divide comes first, therefore 24 will be divided by 6, then the result of division will be multiplied by 2 to provide an answer of 8.

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Which of the following measurements is the GREATEST in magnitude? Hint: be sure
to convert all the measurements to the same units before comparing them!!!
520 g
52 kg
699 g
O2354 mg

Answers

Answer:

52kg

Step-by-step explanation:

5 integers have a
mean = 6
mode = 5
range = 9.
What could the 5 numbers be?

Answers

Answer:

5, 5, 3, 12, 5

Step-by-step explanation:

This is because the criteria for the numbers are;

*** It must sum up to 30 to get a mean of 6

*** 5 must occur more than once

*** The difference between the largest and smallest number is 9

H=10.00+0.07x after 20 months

Answers

The numeric value of the function H(x) = 10 + 0.07x when x = 20 is given as follows:

11.4.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function in this problem is defined as follows:

H(x) = 10 + 0.07x.

When x = 20, the numeric value is found replacing the lone instance of x by 20, hence:

H(20) = 10 + 0.07(20)

H(20) = 10 + 1.4

H(20) = 1.4.

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A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p= the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0,5, 100 simulated proportions for samples of size 25 are shown in the dotplot. Using the dotplot, what do the two dots above 0.70 represent? O There is a 2 in 100 chance that the true proportion of heads is 0.7 O In two simulated samples of 25 spins, the proportion of heads is 0.7. O There is a 2 in 100 chance that the sample proportion of heads is 0.7 O In two simulated samples of 25 spins, the true proportion of heads is 0.7.

Answers

We have an option that says in 2 simulated samples of 25 spins, the proportion of heads is .7 and that would be our best option(d).

A student decides to spin a dim and determine the proportion of times it's lands on heads and the student spins the time 25 times and records that it lands on heads 17 times. So we have a leads on head of 17 out of 25,

So, probability 17/25 =0.68

Let p be the true proportion of times that time would land on heads 1 spun and under this assumption, p is going to be 0.5 simulated proportions for samples of size.

25 are shown to us in a dot plot. So, I'm assuming you can see your dot plot and when you look at the dot plot, you can see that again, each 1 of those dots represents a simulation of sample size, 25 . So basically, almost think of it like 100 different experiments where we did. This 25 times,

so, the question is using the dot plot. What do the 2 dots above .70 represent?

We have an option that says in 2 simulated samples of 25 spins, the proportion of heads is .7 and that would be our best option(d).

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If me.hernandez turns in a late order for 1 turkey sandwich

Answers

Answer:

C.

Step-by-step explanation:

If by "turns in" they mean order, than its not a 3:4 ratio

One of the top 10 occupations in terms of job growth in the next few years is expected to be registered nurses. The number of​ people, y, in​ thousands, employed as registered nurses in a certain country can be estimated by the linear equation
559 x minus 10 y equals negative 27 comma 010
559x−10y=−27,010​, where x is the number of years after 2012.
a. Find the slope and the​ y-intercept of the linear equation.
b. What does the slope mean in this​ context?
c. What does the​ y-intercept mean in this​ context?

Answers

Answer: a. To find the slope and y-intercept of the linear equation, we need to write it in slope-intercept form (y = mx + b). To do this, we can add 10y to both sides and divide both sides by 10 to get:

y = -559x/10 - 2701/10

y = -55.9x - 270.1

The slope of the equation is -55.9, and the y-intercept is -270.1

b. The slope of a linear equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope of -55.9 means that for every year after 2012, the number of people employed as registered nurses is expected to decrease by 55.9 thousand.

c. The y-intercept of a linear equation is the point where the line crosses the y-axis. In this context, the y-intercept of -270.1 means that in 2012, there were expected to be 270.1 thousand people employed as registered nurses.

Step-by-step explanation:

Explain the Fundamental Theorem of Calculus Part 1 (the antiderivative part) and Part 2 (the evaluation part). Then compare each part and specify when one part would be used over the other. Give a real-world example that involves Part 2 of the Fundamental Theorem of Calculus.
I already have an explanation for each separate part but I need help with examples of comparing the two parts, when each part should be used over the other, and a real-world example.
Thanks!

Answers

The Fundamental Theorem of Calculus (FTC) has two parts: Part 1 and Part 2.

What is the parts in calculus?

Part 1 (The Antiderivative Part) states that if f is a continuous function on an interval [a, b], then there exists an antiderivative F of f on [a, b], meaning that F'(x) = f(x) for all x in [a, b].

This means that given a function, we can find a new function that when differentiated, returns the original function.

Part 2 (The Evaluation Part) states that if F is an antiderivative of f on [a, b], then the definite integral of f over [a, b] can be calculated as the difference of the values of the antiderivative F evaluated at the endpoints, i.e., ∫_a^bf(x)dx = F(b) - F(a).

This means that we can evaluate the definite integral of a function by finding its antiderivative and evaluating it at the endpoints of the interval.

Part 1 is used to find antiderivatives, while Part 2 is used to evaluate definite integrals. They are complementary and are used in tandem to solve problems involving integration.

A real-world example that involves Part 2 of the FTC is the calculation of the total distance traveled by a moving object. If the velocity of the object is given as a function of time, we can use the FTC to calculate the total distance traveled by finding the definite integral of the velocity function over the time interval and evaluating it at the endpoints. The result is the difference between the final and initial positions of the object.

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A company is investigating working conditions throughout its operations and has offered employees the opportunity to complete a questionnaire on this subject.
Select the type of sample that has been formed in each presented situation:
Simple random sample
Stratified random sample
Voluntary response sample
Multistage sample

Answers

Correct answer is :- Voluntary response sample

'What is Voluntary response sample?'

A sample made up of people who have voluntarily decided to take part in the sample group is known as a voluntary response sample.

Those who want to participate in a voluntary response sample typically do so because they are passionate about the topic of the survey. This is why voluntary response samples frequently produce results that are considerably biased, as the majority of participants will have strong opinions on the subject. The ease of joining the survey is another factor in people's participation.

An example would be a TV show host asking his audience to visit his website and participate in an online survey.

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