The accompanying data on x = current density (mA/cm2) and y = rate of deposition (m/min)μ appeared in a recent study.
x 20 40 60 80
y 0.24 1.20 1.71 2.22
a. Do you agree with the claim by the article’s author that "a linear relationship was obtained from the tin-lead rate of deposition as a function of current density"? (Hint: determine the coefficient of correlation and determination factors)
b. Determine the linear regression equation.
Answers
Answer:
a) \(r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857\)
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
b) \(m=\frac{64.5}{2000}=0.03225\)
Now we can find the means for x and y like this:
\(\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50\)
\(\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425\)
\(b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27\)
So the line would be given by:
\(y=0.3225 x -0.27\)
Step-by-step explanation:
Part a
The correlation coeffcient is given by this formula:
\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}\)
For our case we have this:
n=4 \( \sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501\)
\(r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857\)
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
Part b
\(m=\frac{S_{xy}}{S_{xx}}\)
Where:
\(S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}\)
\(S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}\)
With these we can find the sums:
\(S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000\)
\(S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5\)
And the slope would be:
\(m=\frac{64.5}{2000}=0.03225\)
Now we can find the means for x and y like this:
\(\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50\)
\(\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425\)
And we can find the intercept using this:
\(b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27\)
So the line would be given by:
\(y=0.3225 x -0.27\)
Related Questions
In a fruit salad, there are 12 strawberries, 14 grapes, 6 kiwis, and 4 papayas. Find the ratio of kiwis to the total number of pieces of fruit in the fruit salad. Write the ratio as a fraction in the SIMPLEST FORM.
Answers
Answer:
1:6
this is because 6 kiwis + 30 fruits = 36 fruits. Then you have 6 kiwis and 36 fruits. therefore the ratio is 6:36. when you simplify , it becomes 1:6
Answer:
1:6
Step-by-step explanation:
you start out with 6:36 which simplifies to 1:6
6 represents the number of kiwi and 36 represents the number of total fruits
then you divide both numbers by 6
and end up with 1:6
hope this helps
\(\sqrt{7x+2}\)
Answers
Answer:
\( \sqrt{7x + 2} \\ \)
for answer please see
please mark me brainliest please![[tex]\sqrt{7x+2}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/9TsPjxjGaLZkwhkTuf7L0cIRJjhzxbWI.jpeg)
Bob has 28 shirts to fold.
Let N be the number of shirts he would have left to fold after folding F of them.
Write an equation relating N to F. Then use this equation to find the number of shirts he would have left to fold after folding 26 of them.
Answers
and the answer is 2.
Which angle mesuare is greater
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
You can see angle B is much smaller than angle A because Angle B is an acute angle (smaller than 90°) while angle A isn't.
if f(x)=3x-2 and g(x)=2x+1 find(f-g)(x)
Answers
Answer:
(f-g)(x) = x-3
Step-by-step explanation:
f(x)=3x-2
g(x)=2x+1
(f-g)(x)= 3x-2 - ( 2x+1)
Distribute the minus sign
3x -2 -2x -1
Combine like terms
x-3
order of operation problem who two operations inside parentheses and two ex outside ( using all add, subtract, multiply and divide)
PLEASE SHOW ALL WORK
Answers
Answer:
17 + 123 (4 - 1) + (36 / 18) 52 =
17 + 123 x 3 + 2 x 52 =
17 + 369 + 104 =
17 + 473 =
490
Step-by-step explanation:
hope this helps! i made up everything so i hope its okay!
6. Becca is helping to sell tickets to the spring musical. They sold 135 tickets and collected $799. Each student ticket costs $5 and each adult ticket costs $7. Define the variables, and write a system of equations to find out how many student tickets and adult tickets were sold. Label everything for full credit!
Answers
Answer:
$400 dollars in five dollar tickets then $399 dollars in seven dollar tickets.
so you do $400+$399=799
Step-by-step explanation:
You do $400÷5=80 then you do $395R4÷7=55 Then you do 55+80=$135.
so 55 adult tickets and then 80 student tickets.
A recipe calls for 21 scoops of sugar. each scoop is 2.5 oz. how many scoops do you need if each scoop holds 3.5 oz of sugar ?
Answers
Answer:
we need 6 scoops of sugar
5
Select the correct answer.
Which number has a repeating decimal form?
A. 15
OB.
11
25
3
20
C. D.
2
ODIN
Answers
Answer:
C=6.6666666666666666666666666
Answer:
\(D.\frac{2}{6}\)
Step-by-step explanation:
√15 = 3.87298334621
11/25 = 11 ÷ 25 = 0.44
3/20 = 3 ÷ 20 = 0.15
2/6 = 2 ÷ 6 = 0.33333333333
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
Factor the polynomial 6x^2-3x+2
Answers
How can she find the coordinates of the new point without graphing the point?
Answers
#CarryOnLearning
A company makes about 2.5 × 1 0 7 2.5×10 7 tablets in a year. The company spends about $20 to make each tablet. About how much money, in dollars, does the company spend making tablets each year?
Answers
The company spends making tablets each year, you can multiply the number of tablets by the cost per tablet so the company spends about $500 million making tablets each year.
Why is it referred to as money?Its origins lie in the Latin word moneta, which was given to the Roman goddess Juno, at whose temple or close by, or both, the Romans first started minting coins approximately 300 BCE.
We may multiply the quantity of tablets produced by the cost of producing each tablet to see how much money the company spends annually making tablets:
Total cost = Production of tablets x Price per tablet
Number of tablets produced =\(2.5 × 10^7\)
Cost per tablet = $20
Therefore, the total cost = \(2.5 × 10^7 × $20 = $5 × 10^8\)
As a result, the corporation spends over $500 million annually producing tablets.
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Arizona license plates are designed so there
are three letters followed by four digits.
How many different license plates are
possible if letters and digits cannot be
repeated?
A. 175,760,000
B. 47,174,400
C. 78,624,000
D. 115,316,136
Answers
78,624,000 different license plates are possible if letters and digits cannot be repeated.
For the letters:
There are 26 letters in the English alphabet, and we need to choose three of them without repetition.
This can be calculated as a permutation of 26 letters taken 3 at a time:
P(26, 3) = 26! / (26 - 3)!
= 26! / 23!
= 26 x 25 x 24
= 15,600
For the digits:
There are 10 digits (0-9), and we need to choose four of them without repetition.
This can be calculated as a permutation of 10 digits taken 4 at a time:
P(10, 4) = 10! / (10 - 4)! = 10! / 6!
= 10 x 9 x 8 x 7
= 5,040
To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total possibilities = P(26, 3) x P(10, 4)
= 15,600 x 5,040
= 78,624,000
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Colin borrowed 4200 at 8% simple interest to be paid back in 3 years. How much interest will he pay
Answers
Answer:
Answer 1008
Step-by-step explanation:
HELPPPPP
can someone give me the answer for this
Answers
Answer:
x = -1, y = 1
Step-by-step explanation:
2x - 3y = -5
3x + y = -2
2x - 3y = -5
9x + 3y = -6
11x = -11
x = -1
-3 + y = -2
y = 1
x = -1, y = 1
Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.
a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.
Answers
The additional information needed to calculate ORS are the measures of SPR and PSR
The special names of the linesThe lines are given as:
Lines a, b, c and d
The special names of the lines are as follows:
Line a: A secant. This is because the line divides the circle into unequal segmentsLine b: A tangent: This is because the line touches the circle at a point on the circumferenceLine c: A diameter. This is because the line divides the circle into equal segmentsLine d: A secant. This is because the line divides the circle into unequal segmentsThe additional information neededThe angle is given as:
OPS= 139 degrees
Start by calculating SPR using
SPR = 180- 139
SPR = 41 degrees
So, the additional information needed to calculate ORS are the measures of SPR and PSR
How to calculate the lengths RO, RS, RV, and RTThe theorem 65 is not stated.
So, the question cannot be answered
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Find the difference,
(20m+ 3) - (7m - 5)
A. 27m - 2
B. 13m +8
C. 27m +8
D. 13m - 2
SUBMU
Answers
Answer:
B 13m+8
Step-by-step explanation:
(20m+3) - (7m-5)
20m+3-7m+5
13m+8
Ana uses 58 beads to make a necklace. She plans to sell 36 necklaces at each craft fair she goes to this summer. She plans to go to 4 craft fairs this summer. What is the total number of beads that Ana will use to make the necklaces she plans to sell at the 4 craft fairs?
Answers
Answer:
8064Step-by-step explanation:
56 beads for each necklace,36 necklaces at each craft,4 craft fairsTotal number of beads:
56*36*4 = 8064what is
1 1/4 + 2/14
Answers
Answer:
1.39285714286
Step-by-step explanation:
\(1\frac{1}{3} + 2\frac{1}{4} = \frac{3*1+1}{3} + \frac{4*2+1}{4} = \frac{4}{3} + \frac{9}{4} = \frac{4*4}{3*4} + \frac{9*3}{4*3} = \frac{16}{12} + \frac{27}{12} = \frac{16+27}{12}=\frac{23}{12} = 1\frac{11}{12}\)
What is the overall average number of hours per month of social media use for the countries listed? How does this average compare to your own social media use?
Answers
Internet users worldwide spent an average of 147 minutes per day on social media as of 2022, up from 145 minutes the year before.
Currently, the Philippines is the nation where people spend the most time on social media each day, with an average of three hours and 53 minutes each day. In contrast, Americans only spent two hours, and three minutes every day on social media.
The collection, description, analysis, and drawing of conclusions from numerical data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Calculus, specifically differential and integral calculus, as well as linear algebra and probability theory, are key components of the mathematical ideas that underpin statistics.
Hence, People typically use social media for 147 minutes every day, or two hours and 27 minutes.
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what is 36 divided by 6 equals blank sold 36000 divided by 6 equals
Answers
Step-by-step explanation:
The correct calculations show that 36 divided by 6 equals 6, and 36000 divided by 6 equals 6000.
When we divide 36 by 6, the quotient is 6. Therefore, 36 divided by 6 equals 6.
Similarly, when we divide 36000 by 6, the quotient is 6000. Therefore, 36000 divided by 6 equals 6000.
To calculate these divisions, we divide the dividend (36 and 36000) by the divisor (6) to find the quotient.
In the case of 36 divided by 6, we have 36 ÷ 6 = 6.
For 36000 divided by 6, we have 36000 ÷ 6 = 6000.
Hence, the correct calculations show that 36 divided by 6 equals 6, and 36000 divided by 6 equals 6000.
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Solves problems 1, and 2.
I WILL CROWN THEE BRAINLIEST IF YOU ANSWER CORRECTLY
Answers
Answer: 6 nickels 19 dimes
Step-by-step explanation: none
y + 3x = 5; x= -2, 0, 3
Solve the equation for y. Then find the value of y for each value of x.
Answers
Answer:
y= -3x +5, y= 11, y= 5, y= -4.
Step-by-step explanation:
Well first you want to just find the equation of y like you said and subtract 3x from each side to get y by itself which gives you y= -3x +5. Then you plug in each x value for x separate times of course and solve each time to get your different values for y. I think this is what you're looking for if not I'm sorry.
From the top of a lighthouse 82 m tall, a guard sees two ships at sea.
The angle of depression to the closer ship is 53° and to the further ship is 39°.
How far are the ships apart from each other to the nearest metre?
Answers
The distance between the two ship based on the angle of depression is 42 meters.
The distance of each ship can be calculated thus:
TanX = opposite / Adjacent
The first ship:
Tan53 = distance/ 82
distance= 108.82 meters
The second ship:
Tan39 = distance/ 82
distance= 66.40 meters
The Difference between the ships are :
108.82 - 66.40 = 42.42 metersTherefore, the distance between the two ships is 42 meters.
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An ellipse is defined by 3x2 +2y2 =k and the length of its major axis is 6. What is the value of k?
Answers
Given:
The equation of the ellipse is
\(3x^2+2y^2=k\)
The length of its major axis is 6.
To find:
The value of k.
Solution:
The standard form of an ellipse is
\(\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1\)
Where, a>b and 3a is the length of major axis.
We have,
\(3x^2+2y^2=k\)
Divide both sides by k.
\(\dfrac{3x^2+2y^2}{k}=\dfrac{k}{k}\)
\(\dfrac{x^2}{\frac{k}{3}}+\dfrac{y^2}{\frac{k}{2}}=1\)
\(\dfrac{x^2}{(\sqrt{\frac{k}{3}})^2}+\dfrac{y^2}{(\sqrt{\frac{k}{2}})^2}=1\)
Here, \(\sqrt{\frac{k}{2}}>\sqrt{\frac{k}{3}}\).
So, the length of the major axis is
\(2\sqrt{\dfrac{k}{2}}=6\)
\(\sqrt{\dfrac{k}{2}}=3\)
\(\dfrac{k}{2}=9\)
\(k=18\)
Therefore, the value of k is 18.
Triangle DEF and triangle GHI are similar right triangles.
Based on this information, which statements are true? (Select all that apply.)
A.
The slope of the hypotenuse of triangle DEF is greater than the slope of the hypotenuse of triangle GHI.
B.
The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI.
C.
The slope of the hypotenuse of triangle DEF is less than the slope of the hypotenuse of triangle GHI
D.
The relationship between the slope of the hypotenuse of triangle DEF and the slope of the hypotenuse of triangle GHI cannot be determined
E.
The slope of the hypotenuse of triangle GHI is similar to the slope of the hypotenuse of triangle DEF.
F.
The slope of the hypotenuse of triangle GHI is congruent to the slope of the hypotenuse of triangle DEF.
Answers
The statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI is true .
The slope of a line passing through two points A(x₁,y₁) and B(x₂,y₂) is calculated using the formula
slope = (y₂-y₁)/(x₂-x₁)
In the question ,
given that ΔDEF and ΔGHI are similar ,
and hypotnuse of ΔDEF is DF and hypotnuse of ΔGHI is GI ,
we can see that the coordinates of D = (-9,6) , F = (-6,4) and
coordinates of G = (-3,2) and I = (6,-4)
Using slope formula for line DF
we get ,
slope = (4-6)/(-6 - (-9))
= -2/(-6+9)
= -2/3 ...(i)
Using slope formula for line GI
we get ,
slope = (-4-2)/(6 - (-3))
= -6/(6+3)
= -6/9
In simpler form
= -2/3 ...(ii)
From equation (i) and equation (ii) , we can see that slope of hypotnuse of both the triangles are equal .
Therefore , only statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI , is true .
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Priya and Hadley, fans of this player, calculate the expected value of X is E(X) = 0.80. Priya says, "The probability that this player makes a free-throw is 0.80, on average." Hadley says, "This player will make 0.80 free-throws in his next set of 2." Whose statement is correct based on the expected value? Choose 1 answer: B Only Priya's Only Hadley's Both statements are correct. Neither statement is correct.
Answers
Only Priya's statement is correct based on the expected value. The expected value of X represents the average or mean number of successful free-throws that the player makes. Therefore, it is correct to say that the probability of making a free-throw is 0.80 on average. Hadley's statement about the next set of 2 free-throws is incorrect because the expected value does not tell us exactly how many free-throws the player will make in a given set, but rather what the average or expected number of successful free-throws will be over a series of trials.
Can you help me in this question?
Answers
Answer: I think its B
Step-by-step explanation: My friend answered it.
The woods behind Wendy’s house were 8 miles wide and have an area of 24 mi.² what is the length of the woods 
Answers
Answer:
48 miles
Step-by-step explanation:
i think thats it.
Answer: 4.
Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.
Hope this helps!