Answer:
A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. β = 0.0122
C. β = 0.0000
Step-by-step explanation:
Given that:
Mean = 100
standard deviation = 2
sample size = 9
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu = 100}[/tex]
[tex]\mathtt{H_1: \mu \neq 100}[/tex]
A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .
Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]
∴
[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]
[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]
when [tex]\mu = 100[/tex]
[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]
[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]
[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]
From the standard normal distribution tables
[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]
[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]
[tex]\mathbf{\alpha = 0.0244 }[/tex]
Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]
B. Find beta for the case where the true mean heat evolved is 103.
The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]
Thus;
β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )
∴
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 103[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]
[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]
From standard normal distribution table
β = 0.0122 - 0.0000
β = 0.0122
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]
Given that [tex]\mu = 105[/tex]
[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]
[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]
[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]
[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]
From standard normal distribution table
β = 0.0000 - 0.0000
β = 0.0000
The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.
Please help. I’ll mark you as brainliest if correct
Answer:
(a)
dependent
(b)
x = -3t - 12
y = -5t - 16
z = t
Step-by-step explanation:
2x - 3y - 9z = 24 Eq. 1
x + 3z = -12 Eq. 2
-3x + y - 4z = 20 Eq. 3
2x - 3y - 9z = 24
(+) -9x + 3y - 12x = 60 3 * Eq. 3
--------------------------------
-7x -21z = 84 Eq. 4
7x + 21z = -84 7 * Eq. 2
(+) -7x - 21z = 84 Eq. 4
-----------------------------
0 = 0
(a) The system is dependent.
(b)
z = t
x + 3z = -12 Eq. 2
x + 3t = -12
x = -3t - 12
2x - 3y - 9z = 24 Eq. 1
2(-3t - 12) - 3y - 9t = 24
-6t - 24 - 3y - 9t = 24
-3y - 15t = 48
-y - 5t = 16
-y = 5t + 16
y = -5t - 16
x = -3t - 12
y = -5t - 16
z = t
help please i need this now step by step
Answer:
40 mi ^2
Step-by-step explanation:
SA = 2(lw+wh+lh) where l is the length, w is the width, h is the height
SA = 2( 2*2 + 2*4 * 2*4)
= 2( 4+8+8)
= 2(20)
= 40 mi ^2
The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter
Let breadth be x
Length=2x[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto 72=2x(x)[/tex]
[tex]\\ \sf\longmapsto 2x^2=72[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]
[tex]\\ \sf\longmapsto x^2=36[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
Length=6×2=12inBreadth=6in[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]
[tex]\\ \sf\longmapsto Perimeter=36in[/tex]
Find the common ratio for the following sequence. Type a numerical answer in the space provided. If necessary, use the
/ key to represent a fraction bar. Do not type spaces in your answer.
2,-2, 2, -2, ...
Answer:
-1
Step-by-step explanation:
the common ratio in this geometric series is -1
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
Which graph shows the polar coordinates (-3,-) plotted
Examining and Interpreting a Statistical Report
To help make his case to potential investors in his invention, Martin found a poll conducted by Gallup, a well-known research organization. Take some time to read the report, and then answer the questions to analyze the merits and limitations of this survey.
Part A
The poll report includes a table titled, “Americans Using Cash Now Versus Five Years Ago, by Age.” The age intervals are not equal. Why do you think the Gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results?
The Gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results due to they wanted to identify the habits about the use of cash in the different stages of a person's life, differentiated by ranges of unequal age.
Application of statistics in the collection of information.
Although the most common case when preparing a frequency table is to develop equal ranges that allow the behavior of the respondents to be identified every certain number of possible values.
Example:
0.1 - 10 10.1 - 20 20.1 - 30
On some occasions, irregular or uneven ranges are used that refer to a specific market stage or niche.
In part A of the exercise, you can clearly identify the three stages of adult life that could change your money-use habits:
23 - 34: Group that could be called "young adults", possibly made up of university students, and people who recently started their work stage. 35 - 54: Group of "middle-aged people", made up of people who have been working and managing their finances for a long time, even those who are even close to retirement. 55 or more: People of the "third age" or close to said category, made up of pre-pensioners and pensioners or people who are no longer active in employment.
As you can see, each of these groups present great differences that, from the point of view of a person interested in investing in their invention, a poll report like this is more attractive to select the niche of potential investors based on the work stage of said person.
By this reason, The Gallup organization chose the age intervals due to their money-habits, depending on the stage of his/her life.
If you want to see another example about poll reports, you can use the next link: https://brainly.com/question/15223266?referrer=searchResults
What is 12 1/2% as a fraction
3/25
1/8
6/25
1/4
9514 1404 393
Answer:
1/8
Step-by-step explanation:
The percent symbol % can be thought of as being fully equivalent to /100.
12 1/2% = (12 1/2)/100 = (25/2)/100 = 25/200 = 1/8
_____
Additional comment
It can be useful to memorize the decimal equivalents of the reciprocals of the numbers up to 12.
1/12 = 0.0833...(repeating 3)
1/11 = 0.0909...(repeating 09)
1/10 = 0.1
1/9 = 0.111...(repeating 1)
1/8 = 0.125
1/7 = 0.142857...(repeating the same 6 digits)
1/6 = 0.1666...(repeating 6)
1/5 = 0.2
1/4 = 0.25
1/3 = 0.333...(repeating 3)
1/2 = 0.5
Of course, any of these is expressed as a percentage by multiplying by 100%. 1/8 = 12.5%, 1/6 = 16.6...% (repeating 6)
WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWERLenora wants to buy granola bars for her hiking trip. Eight bars cost $2.40. She wants to buy 12 bars. How much will 12 bars cost?
Answer:
$3.60
Step-by-step explanation:
2.40/8=.30
$.30 per bar
.3 x 12= $3.60
Answer:
$3.60
Step-by-step explanation:
Proportions
8 bars ⇔ $2.4
12 bars ⇔ $W
W = 12*2.4/8
W = $3.6
Simplify the product. 7(–9)
Answer:
have a great day
god is great
The midterm exam will have a total of 108 marks and there are twice as many 05 marks questions than 02 marks questions. Each question is worth either 02 marks or 05 marks”. Find out how many questions of each value there are in the online test?
Answer: 9 (2 mark question) and 18 (5 marks questions)
Step-by-step explanation:
Given: Total mark = 108
Let the 2 marks questions be x
Therefore 5 mark question = 2x
ATQ
⇒5(2x)+2(x) = 108
⇒10x+2x =108
⇒12x = 108
⇒x = 108/12
⇒x = 9
Total two mark questions are 9 and 5 mark questions are 18.
please click thanks and mark brainliest if you like :)
$17,818 is invested, part at 11% and the rest at 6%. If the interest earned from the amount invested at 11% exceeds the interest earned from the amount invested at 6% by $490.33, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.
a is inversely proportional to (b - 4).
If a = 8 and b = 22, express a in terms of b.
Answer:
Step-by-step explanation:
a is expressed in terms of b as a = 144/(b - 4).
If A is inversely proportional to (b - 4), we can express this relationship using the formula:
A = k/(b - 4),
where k is the constant of proportionality.
To determine the value of k, we can use the given information when a = 8 and b = 22:
8 = k/(22 - 4).
Simplifying the equation:
8 = k/18.
To isolate k, we multiply both sides of the equation by 18:
8 * 18 = k.
k = 144.
Now that we know the value of k, we can rewrite the equation in terms of b:
A = 144/(b - 4).
Therefore, a is expressed in terms of b as a = 144/(b - 4).
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If the areas of the given pairs of shapes are equal, find the value of x.
Answer:
X= 8cm
Step-by-step explanation:
area of the square = s×s = 16×16 = 256cm
area of the rectangle = l×b = 32×x = 32x
Given , area of triangle = area of square
32x = 256
x= 256/32
x= 8cm
Answer:
[tex]x = 8cm[/tex]
Step-by-step explanation:
we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e
the area of the square equal to the area of the rectangletherefore,
[tex] \displaystyle \rm A _{square } = A _{rect}[/tex]
recall the formula of the area of square and rectangle so,
[tex] \displaystyle {s}^{2} = lw[/tex]
now assign variables
[tex]s \implies16cm[/tex][tex]l \implies32cm[/tex][tex]w \implies x[/tex]thus substitute:
[tex] \displaystyle 32cmx = {16cm}^{2} [/tex]
simplify square:
[tex] \displaystyle 32cmx = 256cm^2[/tex]
divide both sides by 32:
[tex] \displaystyle \boxed{x = 8cm}[/tex]
and we're done!
a ball is thrown upward with an initial height of 3 feet with an initial upward velocity 37 ft/s the balls heigh in feet after t second is given by h=3=+37t-16t^2
Answer:
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Step-by-step explanation:
Given
[tex]h=3+37t-16t^2[/tex]
Required
Find all values of t when height is 23 feet
To solve this, we simply substitute 23 for h
[tex]23=3+37t-16t^2[/tex]
Collect like terms
[tex]16t^2 - 37t - 3 + 23=0[/tex]
[tex]16t^2 - 37t +20=0[/tex]
Solve t using quadratic formula;
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 16, b =-37 and c = 20
[tex]t = \frac{-(-37)\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{1369 - 1280}}{32}[/tex]
[tex]t = \frac{37\±\sqrt{89}}{32}[/tex]
[tex]t = \frac{37\±9.43}{32}[/tex]
[tex]t = \frac{37+9.43}{32}[/tex] or [tex]t = \frac{37-9.43}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)
Answer:
93 is the exam score needed in order to get the A grade in Mrs Simpson’s test
Step-by-step explanation:
Let x be the score that gives an A grade
Mathematically from the z-score formula, we know that;
z-score = x-mean/SD
From the question, x = ? , mean = 80 and SD = 15
Thus;
z-score = x-80/15
But in this question, we have the probability but we do not have the z-score
So we need the z-score that is equivalent to 20%
20% is same as 0.2
Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84
Thus, mathematically;
0.84 = x-80/15
x-80 = 15(0.84)
x-80 = 12.6
x = 80 + 12.6
x = 92.6 which is approximately 93
Find out the Time Zone for UAE and its neighboring countries. Express them as positive or negative rational numbers with reference to Greenwich Mean Time. Note down the time of few of your daily activities such as breakfast, school time, lunch time, etc. Compare the same time with GMT.anyone please answer this.
Answer:
UAE is in the Gulf Standard Time zone.
It is GMT + 4
Breakfast: 7 am; GMT 3 am
School time 8 am: GMT 4 am
Lunch time: 12:30 pm; GMT 8:30 am
Step-by-step explanation:
UAE is in the Gulf Standard Time zone.
It is GMT + 4
Breakfast: 7 am; GMT 3 am
School time 8 am: GMT 4 am
Lunch time: 12:30 pm; GMT 8:30 am
NEED IT ASAP
Tony is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $45 fee for disposing of his old tires. If Tony has determined that he will spend less than $559.80 total, then what is the price range he can spend on the tire set?
Select one:
a. Less than $468
b. At least 472
c. $468 or more
d. Less than 473
Answer:
A
Step-by-step explanation:
Let:
Total price be T
And price of tire set be x
T<559.80 ---(1)
T=x +(10% of x)+ 45. ——(2)
T=x+(1/10)x+45
T=(11/10)x+45
Substitute T into equ. 1
T<559.80
(11/10)x +45<559.80
(11/10)x < 514.80
11x < 5148
x < 468
A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answer:
a
Step-by-step explanation:
answer is a on edg
What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
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Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. Reset Submit
Answer:
f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.
Step-by-step explanation:
The set of all polynomials is closed under addition, subtraction, and multiplication, because performing any of these operations on a pair of polynomials will give a polynomial result.
__
Comment on the question
The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.
Answer:
f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.
Step-by-step explanation:
Its correct trust
consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation
Answer:
Explained below.
Step-by-step explanation:
Enter the data in an Excel sheet.
(a)
Go to Insert → Chart → Scatter.
Select the first type of Scatter chart.
The scatter plot is attached below.
(b)
The scatter plot with the line of best fit is attached below.
The line of best fit is:
[tex]y=-0.8046x+103.56[/tex]
(c)
Compute the value of x for y = 30 as follows:
[tex]y=-0.8046x+103.56[/tex]
[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]
Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.
(d)
The Pearson's Correlation Coefficient is:
[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]
[tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]
Thus, the Pearson's Correlation Coefficient is -0.71.
(e)
A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.
The correlation between Advanced Mathematics and English results is -0.71.
This implies that there is a strong negative correlation.
If c o v (x comma space y )space equals space 1260, s subscript x squared equals 1600, and s subscript y squared equals 1225 , then the coefficient of determination is:
Complete Question
The complete question is shown on the first uploaded image
Answer:
The coefficient is [tex]r =0.81[/tex]
Step-by-step explanation:
From the question we are told that
[tex]cov(x, y )= 1260[/tex]
[tex]s_x^2 = 1600[/tex]
[tex]s_y^2 = 1225[/tex]
Generally the coefficient of determination is mathematically represented as
[tex]r = [ \frac{cov(x,y)}{ \sqrt{s_x^2} * \sqrt{s_y^2} } ]^2[/tex]
substituting values
[tex]r = [ \frac{ 1260}{ \sqrt{1600} * \sqrt{1225} } ]^2[/tex]
[tex]r =0.81[/tex]
Which option is correct and how would one solve for it?
Answer:
102
Step-by-step explanation:
We have the sum for k = 1 to 4 of 3 ^ ( k-1) * ( k-1)
k =1 3 ^ (1-1) * ( 1-1) = 3^0 * 0 = 0
k =2 3 ^ (2-1) * ( 2-1) = 3^1 * 1 = 3
k =3 3 ^ (3-1) * ( 3-1) = 3^2 * 2 = 9*2 = 18
k =4 3 ^ (4-1) * ( 4-1) = 3^3 * 3 = 27 *3 = 81
Add these together
0+3+18+81 =102
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▹ Answer
102
▹ Step-by-Step Explanation
Convert the notation into a sum and substitute values from 1-4:
(3¹⁻¹ *(1 - 1)) + (3²⁻¹ * (2 - 1)) + (3³⁻¹ * (3 - 1)) + (3⁴⁻¹ * (4 - 1))
0 + 3 + 18 + 81
= 102
Hope this helps!
CloutAnswers ❁
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What is the value of n
Answer:
9 + 18 = 27
27 + n + 1
= n = 27 - 1 = 26.
n = 26
9 + 18 + 26 + n + 7 =
53 + n + 7
53 + 7 + n
60 + n = 360
n = 360 - 60 = 300
so, n 300
so = 9, 18, 300, 26
y''+y'=3 hihihihihhihihihihihihih
Answer:
Maaf Saya Tidak Tahu
Step-by-step explanation:
Maaf Maaf
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
Learn more:
https://brainly.com/question/13078415
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x→9 x − 9 x2 − 81
Without resorting to L'Hopitâl's rule,
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}[/tex]
With the rule, we get the same result:
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}[/tex]
5/2 + 6g = 11/4 solve it
Answer:
g = [tex]\frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]
Multiply through by 4 to clear the fractions
10 + 24g = 11 ( subtract 10 from both sides )
24g = 1 ( divide both sides by 24 )
g = [tex]\frac{1}{24}[/tex]
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57