Find the slope of the line that passes through (6, 15) and (10, 10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer 1

Answer:

m=-5/4

Step-by-step explanation:

the slope is always defined as "the change in y over the change in x" m= y2-y1/x2-x1


Related Questions

Please answer this question for me

Please answer this question for me

Answers

Answer:

11, 12 is right

Step-by-step explanation:

if you do the equation the answer is 11.7473etc, and is in the middle of 11 and 12

Answer:

you marked the right one

Step-by-step explanation:

Given KW is perpendicular to JO, JP is perpendicular to KO, KN intersects with JP=Q. Prove that triangle OKW ~ triangle OJP

Answers

Answer:

Proved

Step-by-step explanation:

m∠JPO  = 90  =  m∠OWK, and angle O is common between both triangles [reflexive property]. Therefore by Rule AA, ΔOKW~ΔOJP

Given KW is perpendicular to JO, JP is perpendicular to KO, KN intersects with JP=Q. Prove that triangle

Triangle OKW similar to triangle OJP by angle-angle or AA or ΔOKW ~ ΔOJP by AA.

What is the similarity law for triangles?

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Please refer to the attached picture for the diagram.

We have:

KW is perpendicular to JO, JP is perpendicular to KO.

KN intersects with JP=Q.

From the figure:

Angle JPO =Angle OWK = 90 degrees

By using the reflexive property:

Angle O = Angle O

Thus, triangle OKW similar to triangle OJP by angle-angle or AA or ΔOKW ~ ΔOJP by AA.

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Given KW is perpendicular to JO, JP is perpendicular to KO, KN intersects with JP=Q. Prove that triangle

DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!
Here is a graph of f given by f(Θ) = tan(Θ). What are the Θ-intercepts of the graph of f? Explain how you know.

DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!Here is a graph of f given by f() = tan(). What

Answers

the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

What area the Θ-intercepts of the graph of f?

The Θ-intercepts of a graph of a function f are the values of Θ where the graph intersects the Θ-axis, i.e., where f(Θ) = 0.

In the case of f(Θ) = tan(Θ), we know that the function has vertical asymptotes at Θ = π/2, 3π/2, etc., where the function is undefined. Therefore, the graph of f will intersect the Θ-axis at these values of Θ, since the function is negative for Θ between π/2 and 3π/2 and positive for Θ outside of that interval.

Thus, the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

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Find the slope of the line that passes through the points (5,10) and (-6,19).

Answers

Answer:

-11 over positive 9

Step-by-step explanation:

5 -11 is -6, and 10 + 9 is 19

Which of the following equations will produce the graph shown below?

Answers

Answer:

You didn't attach anything.

Step-by-step explanation:

You bike 11.2 miles in 1.4 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you​ travel?

Answers

Answer:17

Step-by-step explanation:

Answer:

Y=8x

Hope this helped

Step-by-step explanation:

two arithmetic sequences and both begin with and have common differences of absolute value , with sequence increasing and sequence decreasing. what is the absolute value of the difference between the st term of sequence and the st term of sequence ?

Answers

The difference between the 51st term of a and the 51st term of b is 1000.

the nth term of an arithmetic series is given by \(a_{n}= a_{0}+(n-1)*d\)

where \(a_{0}\) is the first term of the arithmetic series, \(a_{n}\) is the nth term of the series and d is the common difference

Given that,

\(a_{0}=b_{0}=30\)

Common difference of both series that have absolute value = 10

common difference of series a is 10 as this series is increasing

similarly, the common difference of series b is -10 as it is decreasing

Putting the values in the above equation we get:

\(a_{51}= a_{0}+(n-1)*d\\\)

=> 30 + (51-1)*10

=> 30 + 500 = 530

Thus, the value of \(a_{51}\) is 530.

\(b_{51}= b_{0}+(n-1)*d\\\)

=> 30 + (51-1)*-10

=> 30 -500 = -470

Thus, the value of \(b_{51}\) is -470.

so we have to find the value of \(a_{51}-b_{51}\) which is 530 - (-470) =530 +470 =1000

Therefore, The difference between the 51st term of a and the 51st term of b is 1000.

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: Prove that a) X'Y' + X'Y +XY = X' +Y b) A'BC' + ABC' + BC'D = BC' Find the complement of the following function a) WX(Y'Z+YZ') + W'X'(Y' +Z)(Y+Z') b) (A+B'+C') (A'B' +C)(A + B'C') Find Dual of question 2 (a, b),

Answers

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Alex has six candy bars he wants to cut into fifths. How many 1/5 size pieces will he have

Answers

Answer:

30 pieces.

Step-by-step explanation:

According to the word problem, Alex wants to cut all six of his candy bars into fifths.

5/5 = one whole candy bar.

If there will 5 pieces for every candy bar, we can multiply 5 by 6.

5 x 6 = 30.

There will be 30 of the 1/5 size pieces.

Factorize: 6x² + 13x + 6

Answers

Hello!

6x² + 13x + 6

= (6x² + 9x) + (4x + 6)

= 3x(2x + 3) + 2(2x + 3)

= (3x + 2)(2x + 3)

I need help on this asap!

I need help on this asap!
I need help on this asap!

Answers

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

How to write the required system of linear inequalities?

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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I need help on this asap!

7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = { vt ++3 dt Jo Answer 8. g(x) = {* In (1+tº) dt

Answers

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived.

Determine which inequality describes the dogs at the park.

d < 20
d > 20
d ≥ 20
d ≤ 20

Answers

Answer:

 (b)  d > 20

Step-by-step explanation:

You want an inequality that represents "more than 20 dogs."

More than

The English description "more than" is represented by the math symbol for "greater than." If we let "d" represent the number of dogs running around the park, then the math representation can be ...

  more than 20 dogs

  d > 20 . . . . . . . . the number of dog is greater than 20

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How do you do this I need help

How do you do this I need help

Answers

Answer:\(\frac{11}{12}\)>\(\frac{8}{9}\)

Step-by-step explanation:

multiply 12x9 to get 108 as your common denominator so then whatever I do to the bottom I have to do to the top so I would multiply 11x9 which would give me my first fraction \(\frac{99}{108}\) and then 9x12 I get 108 so then I multiply the top by 12 and 8x12 is 96 which u would have \(\frac{96}{108}\)

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Given a triangle on a coordinate plane, Steve found its circumcenter. How can he check the answer?
Use midpoint formula to find the midpoint of each side

Use distance formula to verify that each vertex is equidistant from the circumcenter

Use distance formula to verify that each side is equidistant from the circumcenter

There is no way to verify the coordinates of the circumcenter
Given a triangle on a coordinate plane, Kim found its incenter. How can she check the answer?
Use distance formula to verify that each side is equidistant from the incenter

Use midpoint formula to find the midpoint of each side

There is no way to verify the coordinates of the incenter

Use distance formula to verify that each vertex is equidistant from the incenter

Answers

Answer:

ihnc

Step-by-step explanation:

ihnc

Answer:

The answer is D - Use distance formula to verify that each vertex is equidistant from the incenter.

Step-by-step explanation:

I know because I just toke the test and got it right.

If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent. True or False?

Answers

The statement "If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent" is true.

Let's understand why?

Explanation:

An argument with a tautology conclusion is an argument that arrives at a conclusion that is always true, regardless of the truth values of the premises. In other words, it is impossible for the premises to be true while the conclusion is false.

This means that any attempt to find a counterexample that disproves the conclusion will always fail, as there is no possible scenario in which the conclusion is false.

The counterexample set of an argument is the set of all possible scenarios in which the premises are true but the conclusion is false. If the conclusion is a tautology, then there is no possible scenario in which the conclusion is false, and thus the counterexample set is empty. An empty counterexample set is equivalent to an inconsistent counterexample set, as it means that there is no consistent scenario in which the conclusion is false.

Therefore, if the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent.

Hence, the statement is true.

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16×25×15 =?
4+11÷2=?
?-?=?

Answers

Answer:

16x25x15=6000

4+11÷2=9.5

Step-by-step explanation:

1) 16x25x15 is 16 times 25 times 15, which is 6000

2) This question requires BIDMAS/BODMAS. As you start with the multiplication (Brackets Indices Multi Divide Add Subtract) 11÷2 = 5.5, 5.5+4=9.5

Liam bought a plant and planted it in a pot near a window in his house. Let H represent the height of the plant, in inches, t months since Liam bought the plant. A graph of H is shown below. Write an equation for H then state the y-intercept of the graph and determine its interpretation in the context of the problem.

Liam bought a plant and planted it in a pot near a window in his house. Let H represent the height of

Answers

The equation of the function is: H = 4t + 10.

The y-intercept of the function is 10, which is the height of the plant when Liam initially bought it.

How to Write the Equation of a Function?

To write the equation of a function, first, find the slope (m) = rise / run. You can pick any two points on the line to find the slope. Next, find the y-intercept (b) which is the point where the line intercepts the vertical axis of the graph.

Find the slope using the two points from the given graph, (5, 30) and (10, 50):

Slope (m) = change in H / change in t = (50 - 30) / (10 - 5) = 20/5

m = 4

The y-intercept is b = 10 [in this context, it is the height of the plant when Liam initially bought it]

To write the equation of the function, substitute m = 4 and b = 10 into H = mt + b:

H = 4t + 10

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find the measure of angle 2 and 3​

find the measure of angle 2 and 3

Answers

Answer: angle 2 is 38

Angle 3 is 79

Step-by-step explanation:

SOLVE THHE EQUATION QUICK WILL GUVE BRAILIEST: -3y-4>26

Answers

Answer:

342

Step-by-step explanation:

Answer: y<10

Explanation:
-3y-4>26
+4. +4
-3y/3>30/3
Y<-10

Consider the logistic differential equation:
dy/dx = y/8(6 - y)
Let f(t) be the particular solution to the differential equationwith f(0) = 8
a. What is the limiting factor?
b. Use Euler's method, starting at t=0 with two steps of equalsize, to appropriate F(1).
c. What is the range of f for t > 0

Answers

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Please, let me get the answers in 15 mins. Explain what a
strategy canvas is and how it is used

Answers

A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.

It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.

The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.

The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.

To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.

A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.

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Find an
angle 0 coterminal to -301°, where 0°

Answers

Answer:

what do you mean?!??!!!!

I don’t understand...What do you mean

what did ada Lovelace do

Answers

Answer:

She was considered the first computer programmer.

Step-by-step explanation:

She wrote about one called the Analytical Engine, and even though it was never built, it came to her conclusion that the computer could follow a series of simple instructions to perform a complex question.

Beach Cruises prints brochures and fliers to advertise their dolphin watching tours. To print, the brochure requires three pages while the flier requires two. They are limited to 500 sheets of paper, but need to print at least 80 brochures and 100 fliers. Each brochure cost 10 cents to print and each flier cost 6 cents to print. How many of each should their print to minimize their cost? Include: Constraints (inequalities), shaded graph, feasible region, labeled vertices, Objective Function, Max/Min

Answers

Answer:

500 divided by 80 equals 6.25. 6.25 divided by 100 equals 0.0625

Step-by-step explanation:

500 divided by 80 equals 6.25. 6.25 divided by 100 equals 0.0625

True False: ANOVA, Part II. Determine if the following statements are true or false, and explain your reasoning for statements you identify as false. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a 5% significance level, then (a) we can then conclude that all the means are different from one another. (b) the standardized variability between groups is higher than the standardized variability within groups. (c) the pairwise analysis wi identify at least one pair of means that are significantly different. (d) the appropriate o to be used in pairwise comparisons is 0.05 /4 0.0125 since there are four groups.

Answers

(a) False. If the null hypothesis is rejected using ANOVA, it means that there is significant evidence to suggest that at least one of the means is different from the others.

However, it does not necessarily mean that all the means are different from one another. Additional tests such as pairwise comparisons are needed to determine which specific means are significantly different from one another.

(b) True. When ANOVA is used, the F-statistic is calculated by dividing the variability between groups by the variability within groups. Therefore, if the null hypothesis is rejected, it means that the variability between groups is higher than the variability within groups.

(c) True. Pairwise comparisons are used to determine which specific means are significantly different from one another. If the null hypothesis is rejected using ANOVA, then pairwise comparisons will identify at least one pair of means that are significantly different.

(d) True. When conducting pairwise comparisons, it is important to adjust the significance level to account for the multiple comparisons being made. In this case, there are four groups, so the appropriate level of significance is 0.05/4 = 0.0125. This helps to control the overall type I error rate.

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A recipe called for the ratio of sugar to flour to be 10: 1. If you used 90 ounce of sugar, how
many ounces of flour would you need to use?

Answers

Answer:9 ounces of flours

Step-by-step explanation:90:9 ratio or sugar to flour

Dogan
Dog Years
It is said that dogs age seven years for every "people year." Mason's dog. Shep, was
born on Mason's eighth birthday. When Mason was nine years old, Shep was seven
dog years old. In dog years, how old will Shep be on Mason's twelfth birthday?

Answers

Answer:

84 years old

Step-by-step explanation:

A simple 12 x 7 Since for ever 7 dog years= 1 human year

the mean and the standard deviation of scores on an accounting exam are 74 and 8, respectively. the mean and the standard deviation of scores on a marketing exam are 78 and 10, respectively. find the z-scores for a student who scores 90 in both classes.

Answers

The z-scores for a student who scores 90 in the accounting exam and marketing exam is 2 and 1.2, respectively.

A z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean of a data set. To find the z-score for a student who scores 90 in both classes, you can use the following formula:

z = (x - μ) / σ

Where:

x is the student's score

μ is the mean of the data set

σ is the standard deviation of the data set

For the accounting exam:

z = (90 - 74) / 8 = 2

For the marketing exam:

z = (90 - 78) / 10 = 1.2

So a student who scores 90 in both the accounting and marketing exams has a z-score of 2 for the accounting exam and 1.2 for the marketing exam. This means that the student's score on the accounting exam is 3 standard deviations above the mean, and their score on the marketing exam is 1.2 standard deviations above the mean.

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Sarah has four sisters and three brother. a) what fraction of her siblings are boys? b) what fraction of her siblings are girls? c) if her parents have another baby boy, what fraction of her siblings are boys now?

Answers

The correct answer is a) The fraction of Sarah's siblings who are boys is 3/7.b) The fraction of Sarah's siblings who are girls is 4/7.

c) If her parents have another baby boy, the fraction of her siblings who are boys becomes 4/7.

a) To determine the fraction of Sarah's siblings who are boys, we divide the number of brothers by the total number of siblings. Sarah has three brothers, so the fraction of her siblings who are boys is 3/7.

b) Similarly, to determine the fraction of Sarah's siblings who are girls, we divide the number of sisters by the total number of siblings. Sarah has four sisters, so the fraction of her siblings who are girls is 4/7.

c) If Sarah's parents have another baby boy, the number of brothers would increase to four, while the total number of siblings remains the same. So, the fraction of her siblings who are boys would become 4/7.

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Basalt, with a density of 3 g/cm is found in an area with a thickness of more than 10 km. Granite with a density of 2.5 g/cm is found is also found in the same area, with the granite having intruded the basalt. Carbonates rocks are also present in the whole area and have a density of 2 g/cm.Three sections have been identified, (i) the first having a carbonate sequence of 5 km, followed by a basalt layer of 3 km and finally a granite section of 6 km. Calculate the lithostatic and hydrostatic pressures at the bottom of the carbonate layer, at the base of the basalt layer and at the base of the granite layer.[4, 5, 7](ii) The second section goes through a complete section of granites to a depth of 7 km. Calculate the lithostatic and hydrostatic pressures at the base of the granite 7 km from the surface. [4](iii) Discuss what would happen in an underground mine when the lithostatic pressure is higher than the hydrostatic pressure at a particular level? [5] What would likely be found on an organic farm? Synthetic fertilizersGenetically engineered seedsFeed that contains no antibiotics Feed additives Ben wants to put wall-to-wall carpeting in a small rectangular room. The roommeasures 12 feet by 10 feet. Carpet cost $3.60 per square foot. How much will it costBen to re-carpet the small room? Which compound has only ionic bonds? a)CO2. b)Al2O3. c)H2O2. which one of the following would random dispersion most likely be observed? I will give brainliest to whoever answers this question right Who made up the Redeemers? imagine you are the mother in hanging fire and the son in summer of his fourteenth year. write a poetic response from these points of view to the narrators of the two poems sarah was recently contacted by a prospective buyer. what should sarah have the buyer do before viewing any properties? Communication problems often plague ethical dilemmas, which of the following is often at the forefront of communication problems regarding clinicians?Question 3 options:Failure to speak upPoor independenceLanguage BarriersPoor knowledge of the situation Over the past 15 years, a business owner has made at most $4,000 in profits each week .Which graph represents the business owner's possible profits each week ? Prepare an FMEA with between five and ten failure modes you can even conduct an FMEA on whether or not you will get your MBA! This is an extremely important quality tool for all senior managers, entrepreneurs...any leader, really.formulate your response and post it. You may take a screen shot or build a simple table right in your response in the forum. You may also attach an excel spreadsheet. question of the testing In paragraph 9, what does the phrase the dying suns rays suggest about the setting of the story? Density=6g/ml Volume=42ml a client has just been diagnosed with multiple myeloma (a cancer of the plasma) and will be initiating chemotherapy. the nurse, in an outpatient clinic, reviews the medications the client has been taking at home. the medications include pantoprazole for gastroesophageal reflux disease (gerd) and an over-the-counter calcium supplement to prevent osteoporosis. what interventions should the nurse take? select all that apply. Why is I-330s costume so appealing to D-503? suppose this lab allowed you to mix two of the solutions. what type of solution would you expect to result from mixing the drain cleaner with the battery acid? What was the main responsibility of the war Production Board during WWII? Find the area of the shaded region.