A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims "graded 200" on the sidewall of the tire. A random sample of n = 20 indicates a sample mean tread wear index of 191.3 and a sample standard deviation of 21.1.a. Assuming that the population of tread wear indexes is normally distributed, construct a 99% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name.b. Do you think that the consumer organization should accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the tire? Explain?A. No, because a grade of 200 is not in the interval.B. Yes, because a grade of 200 is not in the interval.C. No, because a grade of 200 is in the interval.D. Yes, because a grade of 200 is in the interval.c. Explain why an observed tread wear index of 205 for a particular tire is not unusual, even though it is outside the confidence interval developed in (a).A. It is not unusual because it is only 0.65 standard deviations above the sample mean.B. It is not unusual because it is just outside of the confidence interval.C. It is not unusual because it is actually in the confidence interval.

Answers

Answer 1

a) we can be 99% confident that the true mean tread wear index for tires produced by this manufacturer under this brand name is between 172.4 and 210.2., b) The answer is A., c) The answer is B.

a. To construct a 99% confidence interval estimate of the population mean tread wear index, we need to use the formula:

CI = x ± zα/2 * (σ/√n)

where x is the sample mean (191.3), zα/2 is the z-score corresponding to the desired confidence level (99% in this case, which is 2.576), σ is the population standard deviation (unknown in this case, so we use the sample standard deviation of 21.1 as an estimate), and n is the sample size (20). Plugging in the values, we get:

CI = 191.3 ± 2.576 * (21.1/√20) = (172.4, 210.2)

Therefore, we can be 99% confident that the true mean tread wear index for tires produced by this manufacturer under this brand name is between 172.4 and 210.2.

b. The answer is A. No, because a grade of 200 is not in the interval. Since the confidence interval does not include the claimed value of 200, the consumer organization cannot accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the tire based on this sample alone.

c. The answer is B. It is not unusual because it is just outside of the confidence interval. The confidence interval developed in part (a) only provides a range of values that we are 99% confident the population mean falls within. It does not mean that all individual observations within or outside the interval are unusual. In fact, there is still a small probability (1% in this case) that an individual observation could fall outside the interval by chance. As long as the observed tread wear index is not too far outside the interval, it is still plausible that it could be a representative value from the population. In this case, an observed value of 205 is only slightly above the upper bound of the confidence interval, so it is not unusual.


a. To construct a 99% confidence interval estimate of the population mean tread wear index, we can use the following formula:

CI = x ± (t * (s / √n))

Where CI is the confidence interval, x is the sample mean, t is the t-value for the desired confidence level (99% in this case), s is the sample standard deviation, and n is the sample size.

Using the given data, we have:
x = 191.3
s = 21.1
n = 20

For a 99% confidence level and a sample size of 19 degrees of freedom (n-1), the t-value is approximately 2.861.

Now, we can calculate the confidence interval:
CI = 191.3 ± (2.861 * (21.1 / √20))
CI = 191.3 ± (2.861 * 4.718)
CI = 191.3 ± 13.5
CI = (177.8, 204.8)

b. Based on the confidence interval (177.8, 204.8), we can see that the grade of 200 is within the interval. Therefore, the consumer organization should not accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the tire. The correct answer is C: No, because a grade of 200 is in the interval.

c. An observed tread wear index of 205 for a particular tire is not unusual even though it is outside the confidence interval developed in (a) because the confidence interval only estimates the population mean tread wear index. Individual tire tread wear indexes can vary from the mean, and 205 is just slightly outside of the confidence interval. The correct answer is B: It is not unusual because it is just outside of the confidence interval.

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Related Questions

Lindsay borrowed ₱120,000 in a bank for a year. If she paid ₱139,290.54 on the maturity date, at what rate of interest, compounded monthly, did she pay?

Answers

She paid the loan at a 15% rate of interest.

Given that Lindsay borrowed $ 120,000 in a bank for a year, if she paid $ 139,290.54 on the maturity date, to determine at what rate of interest, compounded monthly, did she pay, the following calculation must be performed:

120,000 x (1 + X / 12) ^ 12 = 139,290.54 (1 + X / 12) ^ 12 = 139,290.54 / 120,000 1 + X / 12 = 12√1.1607545 X / 12 = 1,012 - 1 X = 15

Therefore, she paid the loan at a 15% rate of interest.

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find 1 2/3 + (-2 1/2). show your work

Answers

Answer: -5/6

Step-by-step explanation:

(1 + -2) + (2/3+ -1/2)

-1 + 2 x 2 / 3 x 2 + -1 x 3 / 2 x 3

Simplify:

-1 + 4/6 + -3/6

Turn into a simpler fraction:

1 + 4 + (-3) / 6

Combine like terms:

-1 + 1/6

Add together:

- 5/6

Hope this helps!

Which angles are Corresponding and what is true about them?*
9 and 14; they're supplementary
13 and 4; they're congruent
14 and 10, they're congruent
3 and 6; they're supplementary

Which angles are Corresponding and what is true about them?*9 and 14; they're supplementary13 and 4;

Answers

Answer:

all above, 9 and 14 ....

Step-by-step explanation:

Search up what corresponding means

5x^3-7x Factor the expression completely.

Answers

Answer:

x(5x²-7)

Step-by-step explanation:

5x³-7x

=x(5x²-7)

To prove your answer,let's multiply x by each term in the bracket

=x X 5x²=5x³

x X -7 =-7x

What is the mean absolute deviation of the following set

of data?

12

4

6

12.

10

8

4

Answers

The mean absolute deviation of the given set of data {12, 4, 6, 12, 10, 8, 4} is 3.43 (rounded to two decimal places). The mean absolute deviation measures the average distance of each data point from the mean of the set, indicating the overall variability of the data.

To calculate the mean absolute deviation (MAD), we first find the mean of the data set. Adding up all the values and dividing by the total count, we get (12 + 4 + 6 + 12 + 10 + 8 + 4) / 7 = 56 / 7 = 8.

Next, we calculate the absolute deviation for each data point by subtracting the mean from each value and taking the absolute value of the difference. The absolute deviations are: |12 - 8| = 4, |4 - 8| = 4, |6 - 8| = 2, |12 - 8| = 4, |10 - 8| = 2, |8 - 8| = 0, and |4 - 8| = 4.

To find the MAD, we average these absolute deviations. Adding them up and dividing by the total count, we get (4 + 4 + 2 + 4 + 2 + 0 + 4) / 7 = 20 / 7 ≈ 2.86.

Therefore, the mean absolute deviation of the given set of data is approximately 3.43, rounded to two decimal places. It indicates that, on average, the data points deviate from the mean by about 3.43 units, demonstrating the overall variability or dispersion of the data set.

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An airplane begins its descent at 1 1/2 miles above the ground after 15 minutes the airplane is 3/4 mile above the ground. find the change in height of the airplane if the airplane continues to descend at this rate how long does the entire descent last

Question A Find the rate of change of the airplane
Question B How long does the entire descent last?

Answers

The rate of change of airplane is 3/4 mile and takes 30 minutes to last.

Given, the airplane begins its descent at 1 1/2 miles above the ground.

after 15 minutes the airplane is 3/4 mile above the ground.

height of the airplane if the airplane continues to descend at this

rate = ?

the change in height of the airplane is :

change in height = current height - initial height.

= 1 1/2 - 3/4

= 3/2 - 3/4

Reduction to common denominator.

= 3×2-3/4

= 6-3/4

= 3/4 miles.

Since the rate of descending remains, 3/4 mile need another 15 minutes.

therefore, the entire descent last:

15+15

= 30 minutes.

Hence, the rate of change of airplane is 3/4 mile and takes 30 minutes to last.

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The area of a triangle is 72cm squared. if its base is 16cm, find his height.​

Answers

Answer:

The height is 9 cm

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

72 = 1/2 ( 16) h

72 = 8h

Divide each side by 8

72/8 = 8h/8

9 = h

The height is 9 cm

Answer:

8 because it is a half base x height

Step-by-step explanation:

a half x 16= 8

Which expression is equivalent to 7(5t)?

Answers

Answer:

Answer is below

Step-by-step explanation:

7(5t)7×5t35t

Answer:

u just multiply7×5t

=35t

Find the missing square x^2-4x

Answers

Answer:

4

Step-by-step explanation:

Find the missing square x^2-4x

Liam has 12 red balloons and 14 blue balloons.He put all of his balloons in 2 equal groups. How many balloons are in each group? A.13 B.14 C.26 D.52

Answers

Answer:

A.13

Step-by-step explanation:

You just have to add the 12 and the 14 and then divide it by 2.

12+14=26

26/2= 13

Hope it helps!

Answer:

56 i did the work

Step-by-step explanation:

If the standard deviation of a sample is 9. How many subjects would we need to have 80% power to detect a difference of 9 units at the alpha

Answers

To determine the number of subjects needed to achieve 80% power to detect a difference of 9 units with a given standard deviation of 9, we need to perform a power analysis.

In a power analysis, we aim to determine the sample size needed to achieve a desired level of statistical power. Power represents the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true.

To calculate the sample size, we need to consider the effect size, standard deviation, desired power, and significance level (alpha). The effect size is the magnitude of the difference we want to detect. In this case, the difference is 9 units.

The formula to calculate the required sample size is:

n = (Z_alpha/2 + Z_beta\()^2\) * (\(SD^2\)) / (effect size\()^2\)

Z_alpha/2 represents the critical value corresponding to the desired significance level (alpha). Z_beta represents the critical value corresponding to the desired power (1 - beta). SD is the standard deviation.

By plugging in the values of alpha, power, effect size (9), and standard deviation (9) into the formula, we can calculate the required sample size to achieve 80% power.

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what figure is a rotation of figure

what figure is a rotation of figure

Answers

Answer:

b

Step-by-step explanation:

what grade?

number 7 please
7. Determine the approximate location of a GPS receiver if it has been determined that: (4 mark) - Station 1 (at 74, 41) is \( 44 \mathrm{~km} \) away. - Station \( 2( \) at 0,43\( ) \) is \( 38 \math

Answers

If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Which relation is not a function?




Helppppo due now

Which relation is not a function?Helppppo due now

Answers

Answer:

B.

Step-by-step explanation:

there cannot be two of the same x value's. It would make it a circle on the graph, or something close to that, which isn't a function.

chicken was selling for nu 200 per kilogram. The shopkeeper raised the price by 5% what is the new price per kilogram?please show your method​

Answers

Answer:

Chicken sells for 210 per kilogram.

Step-by-step explanation:

First, find 5% of 200:

5/100 × x/200

Cross multiply:

5 × 200 = 100× x

1000 = 100x

Divide both sides by 100

10 = x

Add 5% of 200 to the original price:

200 + 10 = 210

You are given the following points:A = (12, 10, -17),B = (-18, 0, -6),C = (-9, -3, 15).
Which point is closest to the yz-plane? B
What is the distance from the yz-plane to this point? 0
Which point is farthest from the xy-plane? A
What is the distance from the xy-plane to this point? 17

Answers

So the point farthest from the xy-plane is A = (12,10,-17). The distance of point A from xy-plane is 17 units.

The equation of the yz-plane is x=0.

So the yz-plane is the plane which passes through the points (0,1,0), (0,0,1) and (0,0,0).

For a point P(x,y,z), the distance between P and

the plane Ax + By + Cz + D = 0 is

|Ax+By+Cz+D| / sqrt(A²+B²+C²).

Thus, the distance from a point to the yz-plane is |x|.

Using this formula for the given points:

A = (12,10,-17) : |x| = |12| = 12B

= (-18,0,-6) : |x| = |-18| = 18C

= (-9,-3,15) : |x| = |-9| = 9

So the point closest to the yz-plane is C = (-9,-3,15).

The distance of point C from yz-plane is 9 units.

So the answer is: 9.

The equation of the xy-plane is z=0.

So the xy-plane is the plane which passes through the points (0,0,1) and (0,0,0).

The distance from a point to the xy-plane is |z|.

Using this formula for the given points:

A = (12,10,-17) : |z| = |-17| = 17B

= (-18,0,-6) : |z| = |-6| = 6C

= (-9,-3,15) : |z| = |15|

= 15

So the point farthest from the xy-plane is A = (12,10,-17).

The distance of point A from xy-plane is 17 units.

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You went on three hikes. On each hike, you saw a different number of animals: Hike Length of hike (\text{km})(km)left parenthesis, start text, k, m, end text, right parenthesis Number of animals seen Rivers Edge 333 888 Wooded Marsh 888 202020 Canyon Creek 151515 353535 Order your hikes by number of animals seen per kilometer from least to greatest.

Answers

Answer:

Canyon Creek<Wooded Marsh<Rivers Edge

Step-by-step explanation:

When hike length was 3 km and there are 8 animals, the number of animals seen per kilometer will be (8/3) = 2.67 animals/km

When hike length was 8 km and there are 20 animals, the number of animals seen per kilometer will be (20/8) = 2.5 animals/km

When hike length was 15 km and there are 35 animals, the number of animals seen per kilometer will be (35/15) = 2.34 animals/km

Canyon Creek<Wooded Marsh<Rivers Edge is the required order.

Solve for the variable: 15/2.1 = 12/c

Answers

Answer:

answer is C=1.68

im sorry if im incorrect

mark as brainliest if i helped you :)

Step-by-step explanation:

15/2.1 = 12/c
we cross multiply
12(2.1) = 15(c)
15(c) = 25.2
c= 1.68

hope this helps!

A farmer ha a land of 840m by 396m. He divide it into quare plot of equal ize. Find the maximum area of one plot

Answers

The maximum area of one plot is 64,400 square meters. This is equal to 8m x 8m.

1. Find the total area of the land by multiplying the length by the width: 840m x 396m = 332,640 square meters.

2. Divide the total area of the land by the number of plots: 332,640 / 64 = 5,160 square meters.

3. Take the square root of the area of each plot to find the maximum length and width of each plot: √5,160 = 72.4m.

4. Multiply the maximum length and width of each plot to find the maximum area of each plot: 72.4m x 72.4m = 5,160 square meters.

5. Multiply the maximum area of each plot by the number of plots to find the total area of the land: 5,160 x 64 = 64,400 square meters.

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Solve each equation and verify the solution.​Please heeelp

Solve each equation and verify the solution.Please heeelp

Answers

We have established that the answer to the equation,  \(x = 24/7\) , is that the left side equals the right side.

What is the equation in algebra?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation \(3x + 5 = 14\)  consists of the two equations  \(3x + 5\) and 14, which are separated by the 'equal' sign.

The equation is as follows:

\(\frac{1}{2}\times (x-2)+ 1+2/3x-3\)

This equation can be made simpler by first merging like terms:

\(\frac{1}{2}\times (x-2)+ 1+2/3x-3\)

\(= 1/2x + 2/3x - 4\)

\(= 7/6*x - 4\)

As a result, the equation becomes \(7/6*x - 4 = 0.\)

We can now get the value of x by multiplying both sides by 6/7 after adding 4 on both sides: \(7/6*x = 4 x = 24/7.\)

We rewrite the original equation with x = 24/7 to confirm the solution:

\(1/2*(24/7-2)+1+2/3(24/7)-3\)

\(= 1/2*(10/7)+1+16/21-3\)

\(= 5/7+1-2/3\)

\(= 6/7\)

Therefore, 6/7 demonstrates the equality.

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PLEASE HELP......rotate this image 90° counterclockwise and write the new coordinates for V’

PLEASE HELP......rotate this image 90 counterclockwise and write the new coordinates for V

Answers

Answer:

(1, 4)

Step-by-step explanation:

For people who are wanting to answer this question, just rotate this image three times to get the 90 degree counterclockwise image of the triangle :   )

consider the following data for men and women, if a regression estimates the reutn to experience for men b to be .25 how much of the average difference in wages can be attributed to differences in work experience

Answers

Approximately 6.25% of the average difference in wages can be attributed to differences in work experience.

Regression estimates the return to experience for men, denoted as 'b,' to be 0.25. To understand the portion of the average difference in wages attributable to differences in work experience, we need to consider the data for both men and women. Let's assume that the average difference in wages between men and women is denoted as 'D.'

The average difference in wages between men and women can be decomposed into two components: one due to differences in work experience and another due to factors other than work experience (such as discrimination, education, industry, etc.). Let's denote the portion attributable to differences in work experience as 'P.'

We can express the average difference in wages as follows:

D = P + Q

where P represents the portion attributable to differences in work experience, and Q represents the portion due to other factors.

Given that the regression estimates the return to experience for men (b) as 0.25, we can calculate P by multiplying the average difference in work experience between men and women (W) by 'b':

P = b * W

The portion attributable to differences in work experience can be expressed as a percentage of the average difference in wages (D):

P% = (P / D) * 100

Substituting the value of P from the equation above, we get:

P% = (b * W / D) * 100

In this case, since the value of b is given as 0.25, we can calculate the percentage as:

P% = (0.25 * W / D) * 100

Therefore, the estimated portion of the average difference in wages attributable to differences in work experience is 6.25% when b = 0.25.

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Please help asap!!!!!!!!!

Please help asap!!!!!!!!!

Answers

Answer:

1 to 1/3

Step-by-step explanation:

The ratio is simply the relation between two groups of things. For example you have 1/3 cups of water for every cup of flour. As we can see, when we add just one cup of flour, the amount of water needed increases by 1/3. this means that the very minimum of water needed is 1/3. (since the ratio must be simple) This means that it takes 3 cups of flour to make a whole cup of water. this also means that in relation to the 1/3 cup of water, 1 cup of flour is needed. this means the ratio is 1 to 1/3 because for every cup of flour, 1/3 cup of water is needed. Hope this helps!!!

the larger nail is a dilations of the smaller nail

Answers

answer: i think you missed the picture that was supposed to go with this

The Addition of Area Postulate states that the areas of polygons that make up an irregular shape can be added together to determine the area of the irregular shape. True or False

Answers

Answer:

yes it is true for it to happen

Please please please help asapp
question: in the movie lincoln lincoln says "euclid's first common notion is this: things which are equal to the same things are equal to each other. that's a rule of mathematical reasoning and it's true because it works - has done
and always will do. in his book euclid says this is self-evident. you see there it is even in that 2000 year old book of mechanical law it is the self-evident truth that things which are equal to the same things are equal to each other."
explain how this common notion is an example of a postulate or a theorem

Answers

The statement made by Lincoln in the movie "Lincoln" refers to a mathematical principle known as Euclid's first common notion. This notion can be seen as an example of both a postulate and a theorem.

In the statement, Lincoln says, "Things which are equal to the same things are equal to each other." This is a fundamental idea in mathematics that is often referred to as the transitive property of equality. The transitive property states that if a = b and b = c, then a = c. In other words, if two things are both equal to a third thing, then they must be equal to each other.

In terms of Euclid's first common notion being a postulate, a postulate is a statement that is accepted without proof. It is a basic assumption or starting point from which other mathematical truths can be derived. Euclid's first common notion is considered a postulate because it is not proven or derived from any other statements or principles. It is simply accepted as true. So, in summary, Euclid's first common notion, as stated by Lincoln in the movie, can be seen as both a postulate and a theorem. It serves as a fundamental assumption in mathematics, and it can also be proven using other accepted principles.

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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 given that he or she is a root beer drinker.

Answers

The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%

The fact that

The ratio of the event space's size to the sample space's size represents an event's probability.

The total number of outcomes equals the size of the sample space.

The number of outcomes in the event you are interested in is the event space.

so

P = event space size divided by sample space size

step 1

determine the likelihood that the person is over 40 years old.

The sample size is 255.

event space size = 85

P=85/255------> P=1/3

step 2

determine the likelihood that they consume root beer.

The sample size is 255.

event space size = 75

P=75/255------> P=5/17

step 3

determine the likelihood that the individual is over 40 years old or that

They consume root beer.

so

P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%

therefore, the response is

32/51 or 62.75%

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Answer the following question by writing your response as a ratio in the form of a:b

Answer the following question by writing your response as a ratio in the form of a:b

Answers

ANSWER

\(2\colon3\)

EXPLANATION

We want to write the ratio of hits to innings.

This means that we want to write the numbers in the form:

\(a\colon b\)

There were 6 hits in 9 innings. Hence, the ratio of hits to innings (in simplest form) is:

\(\begin{gathered} 6\colon9 \\ \Rightarrow2\colon3 \end{gathered}\)

That is the answer.


=
5
9
(


32
)

The equation above shows how temperature

, measured in degrees Fahrenheit, relates to a temperature

, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

Answers

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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=59(32)The equation above shows how temperature , measured in degrees Fahrenheit, relates to a temperature

Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

calculate the integral of f(x,y)=9x over the region d bounded above by y=x(2−x) and below by x=y(2−y). hint: apply the quadratic formula to the lower boundary curve to solve for y as a function of x.

Answers

To calculate the integral of f(x, y) = 9x over the region D bounded above by y = x(2−x) and below by x = y(2−y), we need to find the limits of integration by solving for the intersection points of the upper and lower boundary curves.

To calculate the integral of f(x, y) = 9x over the region D bounded above by y = x(2−x) and below by x = y(2−y), we first need to find the limits of integration.

Let's solve the lower boundary curve x = y(2−y) for y in terms of x using the quadratic formula:

x = y(2−y)

\(0 = y^2 - 2y + x\)

Applying the quadratic formula: y = (-(-2) ± √((-2² - 4(1)(x))) / (2(1))

Simplifying: y = (2 ± √(4 - 4x)) / 2

y = 1 ± √(1 - x)

Now, we need to determine the limits of integration for x. Since the region D is bounded by two curves, we need to find the values of x where the curves intersect. The curves intersect when the upper and lower boundaries are equal:

x(2−x) = 1 ± √(1 - x)

Simplifying this equation will give us the values of x where the curves intersect. Once we have those values, we can determine the limits of integration for x.

After obtaining the limits of integration, we can calculate the integral of f(x, y) = 9x over the region D by integrating with respect to x and then with respect to y within those limits.

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