Answer:
Approximately 13.1521 units.
Step-by-step explanation:
To find the diagonal, we can use the Pythagorean Theorem.
Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:
[tex]a^2+b^2=c^2[/tex]
Substitute 9.3 for a and b, and let c equal d:
[tex](9.3)^2+(9.3)^2=d^2[/tex]
Instead of squaring, add the like-terms:
[tex]2(9.3)^2=d^2[/tex]
Take the square root of both sides:
[tex]d=\sqrt{2(9.3)^2}[/tex]
Expand:
[tex]d=\sqrt{2}\cdot\sqrt{(9.3)^2}[/tex]
The right cancels:
[tex]d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}[/tex]
Levi buys a bag of cookies that contains 6 chocolate chip cookies, 9 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies. What is the probability that Levi reaches in the bag and randomly selects 2 peanut butter cookies from the bag
Answer:
12/155
Step-by-step explanation:
Total number of cookies:
6+9+8+8= 31Probability of getting a peanut butter cookie at first attempt is 9 out of 31:
9/31Probability of getting a peanut butter cookie at second attempt is 8 out of 30 as one already taken and the total number has changed as well:
8/30= 4/15Probability of getting 2 peanut butter cookies is the product of each probability we got above:
9/31×4/15= 12/155If S is a compact subset of R and T is a closed subset of S, then T is compact. Prove this using the definition of compactness.
Answer:
It has been proved that T is compact
Step-by-step explanation:
To prove this using the definition of compactness, let's assume that T is
not compact. Now, if that be the case, an open cover of T will exist. Let's call this open cover "A". Now, this open cover will have no finite subcover.
Now, from the question, since T is closed, it’s complement R\T will be open.
Therefore, if we add the set R\T to the collection of sets A, then we'll have an open cover of R and also of S.
Due to the fact that S is compact, this
cover will have a finite sub - cover which we will call B.
Finally, either B itself or B\{R\T} would be a finite sub - cover of A. This is a contradiction.
Thus, it proves that T has to be compact if S is to be a compact subset of R and T is to be a closed subset of S.
Given the equations, which of the following represents z1 * z2? Using the same values in #6, which of the following represents z1/z2 in standard form?
The selected answers are incorrect.
Answer:
First Attachment : Option A,
Second Attachment : Option C
Step-by-step explanation:
We are given that,
z₁ = [tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))[/tex] and z₂ = [tex]4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
Therefore if we want to determine z₁( z₂ ), we would have to find the trigonometric form of the following expression,
[tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))*4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
( Combine expressions )
= [tex]12(\cos ( \pi /6+\pi / 3 ) + i\sin (\pi /6 +\pi / 3 )[/tex]
( Let's now add [tex]\pi / 6 + \pi / 3[/tex], further simplifying this expression )
[tex]\frac{\pi }{6}+\frac{\pi }{3} = \frac{\pi }{6}+\frac{\pi 2}{6} = \frac{\pi +\pi 2}{6} = \frac{3\pi }{6} = \pi / 2[/tex]
( Substitute )
[tex]12(\cos ( \pi /2 ) + i\sin ( \pi /2 ) )[/tex]
And therefore the correct solution would be option a, for the first attachment.
______________________________________________
For this second attachment, we would have to solve for the following expression,
[tex]\frac{3\left(\cos \left(\frac{\pi \:}{6}\right)+i\sin \left(\frac{\pi \:}{6}\right)\right)}{4\left(\cos \left(\frac{\pi \:}{3}\right)+i\sin \left(\frac{\pi \:}{3}\right)\right)}[/tex]
From which we know that cos(π/6) = √3 / 2, sin(π/6) = 1 / 2, cos(π/3) = 1 / 2, and sin(π/3) = √3 / 2. Therefore,
[tex]\:\frac{3\left(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)\right)}{4\left(\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right)}:\quad \frac{3\sqrt{3}}{8}-i\frac{3}{8}[/tex]
[tex]\frac{3\sqrt{3}}{8}-i\frac{3}{8} = \frac{3\sqrt{3}}{8}-\frac{3}{8}i[/tex]
Our solution for the second attachment will be option c.
Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, find x.
Answer:
x = 4
Step-by-step explanation:
2( 3x + 3) = 8x - 2
6x + 6 = 8x -2
6x + 8 = 8x
8 = 2x
4 = x
It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something.
Midpoint of a line segment means a point which lies in the mid of the given line segment.
We have been given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, we need to find x.
We know that;
2(YZ) = XZ
Substitute in the values
2( 3x + 3) = 8x - 2
Use the Distributive Property
6x + 6 = 8x -2
6x + 8 = 8x
8 = 2x
4 = x
Switch the sides to make it easier to read
x = 4
It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.
To learn more about the midpoint click below;
https://brainly.com/question/1615050
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Plz answer last question and im lost!
Answer:
[tex]\pi[/tex] radian
Step-by-step explanation:
We know that angle for a full circle is 2[tex]\pi[/tex]
In the given figure shape is semicircle
hence,
angle for semicircle will be half of angle of full circle
thus, angle for given figure = half of angle for a full circle = 1/2 * 2[tex]\pi[/tex] = [tex]\pi[/tex]
Thus, answer is [tex]\pi[/tex] radian
alternatively, we also know that angle for a straight line is 180 degrees
and 180 degrees is same as [tex]\pi[/tex] radian.
How to find probability from cumulative frequency graph
Answer:
find the difference of points on the graph
Step-by-step explanation:
The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.
p(a < x < b) = cdf(b) -cdf(a)
Find the perimeter of the rectangle with the following vertices. (−6, −2), (0, −10), (5, 2), (−1, 10) 23 52 46 40
Answer:
46
Step-by-step explanation:
See attached for reference
The points given:
(−6, −2), (0, −10), (5, 2), (−1, 10)They form a rectangle as seen in the picture.
We can notice that this is a parallelogram, as respective lines have same difference of coordinates.
So calculating only the two of the sides will be sufficient to get its perimeter:
a = √(-1+6)² + (10+2)² = √25+144 = √169= 13b = √(0+6)² + (-10+2)² = √36+64 = √100 = 10So, the perimeter:
P = 2(13+10) = 46
while jeff was replacing the obstruction of light on a cell tower, he accidentally dropped his cell phone. If he was 150 ft up at the time, approximately how long did it take the phone to reach the ground
Answer:
3.19 seconds
Step-by-step explanation:
Given:
Phone gets dropped from a Height = 150 ft
To find:
Time taken for the phone to reach the ground = ?
Solution:
First of all, let us learn about the formula of distance in terms of Initial speed u; Time t and Acceleration a:
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
Here the phone is dropped from a height so a = g m/[tex]s^2[/tex] i.e. acceleration due to gravity.
g = 9.8 m/[tex]s^2[/tex]
s = 150 ft
Initial velocity, u = 0
Putting all the values in the formula:
[tex]150=0 t+\dfrac{1}{2}gt^2\\\Rightarrow 50=\dfrac{1}{2}\times 9.8 \times t^2\\\Rightarrow t^2=\dfrac{50}{4.9 }\\\Rightarrow t^2=10.20\\\Rightarrow t = 3.19\ sec[/tex]
So, the time taken is 3.19 seconds.
Suppose that 1% of the employees of a certain company use illegal drugs. This company performs random drug tests that return positive results 99% of the time if the person is a drug user. However, it also has a 2% false positive rate. The results of the drug test are known to be independent from test to test for a given person.
a) Steve, an employee at the company, has a positive test. What is the probability that he is a drug user?
b) Knowing he failed his first test, what is the probability that Steve will fail his next drug test?
c) Steve just failed his second drug test. Now, what is the probability that he is a drug user?
Answer:
a) Pr(drug user| positive test) = 0.3333
b) The probability that he will failed his first test = 0.9703
c) the probability that he is a drug user since failed his second drug test
= 0.961165
Step-by-step explanation:
From the given information:
Suppose that 1% of the employees of a certain company use illegal drugs.
Probability of illegal drug user = 0.01
Probability of user that do not use drug = 1 - 0.01 = 0.99
From the person that is a illegal drug user, the company performs random drug tests that return positive results = 0.99
Therefore, the negative result for illegal drug user = 1 - 0.99 = 0.01
However, it also has a 2% false positive rate.
i.e the probability of the user that do not use drug has a positive result of 2% = 0.02
Thus, the probability of the user that do not use drug has a negative result of = 1 - 0.02
= 0.98
We are tasked to answer the following questions.
a) Steve, an employee at the company, has a positive test. What is the probability that he is a drug user?
i.e This employee we are taking about is a drug user and he has a positive test.
Thus;
Pr(drug user| positive test) = [tex]\dfrac{0.99 \times 0.01}{0.99 \times 0.01+ 0.02 \times 0.99}[/tex]
Pr(drug user| positive test) = [tex]\dfrac{0.0099}{0.0099+0.0198}[/tex]
Pr(drug user| positive test) = [tex]\dfrac{0.0099}{0.0297}[/tex]
Pr(drug user| positive test) = 0.3333
b) Knowing he failed his first test, what is the probability that Steve will fail his next drug test?
The probability that he will failed his first test = ((0.01 × 0.01) + (0.99×0.98))
The probability that he will failed his first test = ( 1 × 10⁻⁴ + 0.9702)
The probability that he will failed his first test = 0.9703
c) Steve just failed his second drug test. Now, what is the probability that he is a drug user?
the probability that he is a drug user since he failed his second drug test using Bayes theorem can be expressed as:
= [tex]\dfrac{0.01 \times(0.99\times 0.99)}{0.01 \times (0.99 \times0.99)+ 0.99(0.02 \times0.02)}[/tex]
the probability that he is a drug user since failed his second drug test
= [tex]\dfrac{0.01 \times(0.9801)}{0.01 \times (0.9801)+ 0.99(4 \times 10^{-4})}[/tex]
the probability that he is a drug user since failed his second drug test
= [tex]\dfrac{0.009801}{0.009801+ 3.96 \times 10^{-4}}[/tex]
the probability that he is a drug user since failed his second drug test
= 0.961165
Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A
Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
1.Write 32 1/2 in radical form
Answer:
√32
Step-by-step explanation:
How many solutions does the system of equations below have y=3x+2 y-2x=4
Answer:
Only one solution.
Step-by-step explanation:
y = 3x +2
y -2x =4
y - 2x = 4
=> y = 2x +4
y = 3x + 2
y = 2x + 4
Since both equations are not the same, so the answer cannot be "infinitely many solutions".
They both intersect each other 1 point, so it cannot be "no solutions".
So the answer is "Only 1 solution".
(math and social studies) The two lines are messing me up and I'm not sure
Answer:
2009
Step-by-step explanation:
A deficit would be the least amount coming in (Revenues). and the most going out (Expenditures). So you look for the biggest gap. It appears the gap is largest in 2009.
pls help:Find all the missing elements:
Answer:
B = 48.7° , C = 61.3° , b = 12Step-by-step explanation:
In order to find B we must first angle C
To find angle C we use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
From the question
a = 15
A = 70°
c = 14
So we have
[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]
[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]
[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]
C = 61.288
C = 61.3° to the nearest tenthSince we've found C we can use it to find B.
Angles in a triangle add up to 180°
To find B add A and C and subtract it from 180°
That's
A + B + C = 180
B = 180 - A - C
B = 180 - 70 - 61.3
B = 48.7° to the nearest tenthTo find b we can use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]
[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]
[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]
b = 11.9921
b = 12.0 to the nearest tenthHope this helps you
What number should replace the question mark?
Answer:
1 Cruz it makes sense I hope this helps tho
Does artistic ability determine which type of operating system a person prefers? Suppose that a market research company randomly selected n=259 adults who used a desktop or laptop outside of the workplace (tablets and smartphones were excluded).
Answer:
Your question lacks some parts attached below is the complete question
Answer : 2.66
Step-by-step explanation:
The expected number ( E ) can be calculated using the formula below
[tex]E = \frac{row total * column total }{gross total}[/tex]
since we are computing the number of subjects that would prefer Linux operating system and are also rated as exceptional
The row total to be used = 53 ( row total of exceptional )
The column total to be used = 13 ( column total of Linux )
The gross total to be used = summation of row total of both exceptional and no-exceptional = 259
BACK TO THE EQUATION
E = [tex]\frac{53*13}{259}[/tex] = 689 / 259
E = 2.6602 ≈ 2.66
According to a survey, typical American spends 154.8 minutes per day watching TV. A survey of 50 Internet users results in a mean time watching TV per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Which appropriate test we should use to determine if Internet users spend less time watching TV
Answer:
Z > ± 1.645
z= 3.968
Step-by-step explanation:
We formulate the null and alternate hypotheses as
H0 =μ2 ≥ μ1 Ha: μ2 <μ1 one sided
Let α= 0.05
Since the sample sizes are large therefore the test statistic used under H0 is
The critical region for α= 0.05 for a one tailed test Z > ± 1.645
Z = (x`2- x`1) /s/ √n
Z= 154.8-128.746.5/√50
z= 26.1/6.577
z= 3.968
Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time or equal time.
Based on the measures provided in the diagram, determine the measure of AEG
Answer:
277°
Step-by-step explanation:
The measure of arc AEG = AB + BE + EF + FG
The central angle is congruent to the arc that subtends it
∠ ECB = 180° - 44° = 136° ( adjacent angles )
∠ECF = ∠ ACB = 44° ( vertical angles ), thus
AEG = 44° + 136° + 44° + 53° = 277°
Soan made a $400 down payment on a washer and dryer cost a total of $1200. What is the ratio of the amount soan has paid to the amount he still owes?
Answer:
800:1200 or 2:3
Step-by-step explanation:
400 payed
1200 in total
1200-400=800
800:1200 or 2:3
A professor graded the final exams and found that the mean score was 70 points. Which of the following can you conclude?
A- All of the above.
B- The median score was 70 points.
C- 50% of the students scored below 70 points.
D- This would be a normal distribution.
Answer: C) 50% of the students scored below 70%
Step-by-step explanation:
Mean is the average. To find the mean (aka average) you add up all of the scores and divide by the number of tests.
B) The mean can be 70 without any test scoring 70% so B is not true.
A) Since B is not true, then A is not a valid option.
D) We don't know any of the other data so don't know if it is skewed left, skewed right, or normal. Therefore, option D is not true.
C) If the average is 70%, then half received grades above that score and half received grades below that score. So, option C is TRUE!
The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dollars per month, of the bank account balance?
Answer:
-50
Step-by-step explanation:
Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)
-50(0)+100 (0,100) Y₂-Y₁/X₂-X₁ 50-100/1-0
Rate of change per month = -$50
8/2(2+2)
What is the answer?
Answer:
16
Step-by-step explanation:
[tex]\frac{8}{2} x (2+2) = \frac{8}{2} x 4 = \frac{8 x 4}{2} = \frac{32}{2} = 16[/tex]
Answer: 16
PEMDAS
P: Parenthesis
E: Exponents
M: Multipcaction
D: Divison
A: Addition
S: Subtraction
PEMDAS can be also known as Please Excuse My Dear Aunt Sally
P: (2+2)
E: N/A (There are no exponents)
M: 4×4
D: 8÷2
A: 2+2
S: N/A (There is nothing to subtract)
How did we get 4×4? We divided 8÷2 which got us 4. Then we added 2+2 and we also got 4. Then we multiplied 4×4 which got us 16. That's how 16 is our answer.
I will rate you brainliest/ / / Tonicha is creating two triangular gardens in her backyard. The total area of each triangle varies jointly with the length of the triangle's base and the height. The area of the smaller triangle is 16 square feet. It has a base that is 8 feet in length and the height is 4 feet. What is the area of the larger triangle when its base is 12 feet in length and its height is 8 feet?
Answer:
The area of larger triangle is 48 ft².
Step-by-step explanation:
Assuming that the area of triangle formula is A = 1/2 × base × height. Then, you have to substitute the following values :
[tex]area = \frac{1}{2} \times b \times h[/tex]
[tex]let \: b = 12,h = 8[/tex]
[tex]area = \frac{1}{2} \times 12 \times 8[/tex]
[tex]area = \frac{1}{2} \times 96[/tex]
[tex]area = 48 \: {feet}^{2} [/tex]
Given that;
A∞bh
A=kbh. where k is a constant
For smaller triangle
A=kbh
16=8(4)k
16=32k
k=½
For bigger triangle
A=kbh
Where k=½ , b= 12 and h=8
A=½(12)8
A=48 square feet
To prove a statement by mathematical induction, all we have to do is show that it is true for n+1. (True or False)
Answer:
False
Step-by-step explanation:
We also need to show that it is true for n=1
and for n=k+1
Makayla wants to make 200 mL of a 18% saline solution but only has access to 8% and 24% saline mixtures.
Which of the following system of equations correctly describes this situation if x represents the amount of the 8% solution used, and y represents the amount of the 24% solution used?
Answer:
x + y = 200
0.08x + 0.24y = 0.18(200)
Step-by-step explanation:
x + y = 200
0.08x + 0.24y = 0.18(200)
The equations which describes the amount of 8% solution used and the amount of 24% solution used are: x+ y=200 and x+3y=450.
What is equation?An equation is a relationship between two or more variables. They are mostly present in equal to form and are equated to find the value of variables present in them.
How to form equation?let the amount of 8% solution used be x and the amount of 24% solution used be y.
According to question the amount of total solution will be 200ml, So, the equation will be:
x +y=200
Now we have been said that the solution will be 18% saline and 8% saline mixture and 24% saline mixtures are used, So the next equation will be:
0.08x+ 0.24y=0.18*200
8x/100+24/100=18/100*200
8x+24y=3600
8(x+3y)=3600
x+3y=450
Hence the equations which shows the amount of solutions will be x+y=200 and x+3y=450.
Learn more about equations at https://brainly.com/question/2972832
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3) Write the operation used to obtain the types of solutions.
Sum:
Difference:
Product:
Quotient:
Answer:
the Sum
hope this helps
5. When looking at a map, a student realizes that Birmingham is nearly due west of Atlanta, and Nashville is nearly due north of Birmingham. If the distance from Atlanta to Birmingham is roughly 150 mi, and the distance from Birmingham to Nashville is roughly 200 mi, what is the estimated distance from Atlanta to Nashville?
Answer: 250 mi
Step-by-step explanation:
Here we can think in a triangle rectangle:
The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.
And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.
Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.
Now we can apply the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse:
Then:
H = √(A^2 + B^2)
H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi
Then the estimated distance from Atlanta to Nashville is 250 mi
Find the length of the leg of a right triangle with leg length b= 21.5 inches and the hypotenuse c= 31.9 inches. Use a calculator to estimate the square root to one decimal place.
Answer:
23.6 (approximate value)
Step-by-step explanation:
a*a+b*b=c*c Pythagorean thereom(21.5)^2 + b*b = (31.9)^2b*b= 1017.61 - 462.25√b*b= √555.36b=23.6(approximate value)Answer:
Step-by-step explanation:
23.6
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.
ANOVA
df SS MS F Significance F
Regression 1 1575.76
Residual 8 349.14
Total 9 1924.90
Coefficient Standard Error t Stat P-value
Intercept 6.1092 0.9361
Usage 0.8931 0.149
A) Write the estimated regression equation (to 4 decimals).
B) Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance (to 2 decimals, if necessary).
1. Reject the null hypothesis
2. Do not reject the null hypothesis
C) Monthly maintenance expense______to usage.
1. Is related
2. Is not related
D) Did the estimated regression equation provide a good fit?
1. yes
2. no
E) Explain.
Answer:
Explained below.
Step-by-step explanation:
The ANOVA and Regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal is provided.
(A)
The estimated regression equation equation is:
[tex]y=6.1092+0.8931x[/tex]
Here,
y = maintenance expense (dollars per month)
x = usage (hours per week) for a particular brand of computer terminal
(B)
Consider the Regression output.
The hypothesis to test whether monthly maintenance expense is related to usage is:
H₀: The monthly maintenance expense is not related to usage, i.e. β = 0.
Hₐ: The monthly maintenance expense is related to usage, i.e. β ≠ 0.
Compute the test statistic as follows:
[tex]t=\frac{b}{S.E._{b}}=\frac{0.8931}{0.149}=5.99[/tex]
Compute the p-value as follows:
[tex]p-value=2\times P (t_{8}<5.99}=0.00033[/tex]
The null hypothesis will be rejected if the p-value is less than the significance level.
p-value = 0.00033 < α = 0.05
Reject the null hypothesis.
(C)
Monthly maintenance expense is related to usage.
(D)
Yes, the estimated regression equation provide a good fit.
Since the regression coefficient is significant it can be concluded that the regression equation estimated is a good fit.
From the regression output given, the solution to the questions given are outlined thus ;
[tex] Null \: hypothesis : H_{0} : β = 0 [/tex] [tex] Alternative \: hypothesis : H_{1} : β ≠ 0 [/tex]1.)
Regression equation :
y = bx + c b = slope ; c = interceptHence, the estimated regression equation is;
y = 0.8931x + 6.10922.)
We can calculate the T-statistic value thus ;
[tex] T-statistic = \frac{b}{SE_{b}}[/tex] [tex]SE_{b} = Standard \: error \: of \: slope[/tex] df = 8Hence, the T-statistic is given as ;
[tex] T-statistic = \frac{0.8931}{0.149} = 5.99[/tex]
Pvalue (2 tailed) = 0.00033
Decison Region :
[tex] Reject \: H_{0} \: if \: Pvalue \: < \: α [/tex]Since 0.00033 < 0.05 ; we reject the Null hypothesis.
3.)
Hence, we conclude that monthly expense is related to usage.
4.)
Since, the correlation Coefficient, β ≠ 0 ; Yes, the correlation provides a good fit as it is significant.
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