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".
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
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.
1.Write 32 1/2 in radical form
Answer:
√32
Step-by-step explanation:
(b) Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs. Identify the types of programs you want to study (e.g., sitcoms, sports events, movies, news, children's programs, etc.). How large should the sample be for a specified margin of error
Answer:
The correct option is b.
Step-by-step explanation:
The complete question is:
Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs. Identify the types of programs you want to study (e.g., sitcoms, sports events, movies, news, children's programs, etc.). How large should the sample be for a specified margin of error.
(a) It depends only on the specified margin of error.
(b) It depends on not only the specified margin of error, but also on the confidence level.
(c) It depends only on the confidence level.
Solution:
The (1 - α) % confidence interval for population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}[/tex]
Then the sample size formula is:
[tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]
The sample size is dependent upon the confidence level (1 - α) %, the standard deviation and the desired margin of error.
Thus, the correct option is b.
The size of the sample 'n' depends on not only the specified margin of error, but also on the confidence level.
Given :
Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs.
The following steps can be used in order to determine the size of the sample be for a specified margin of error:
Step 1 - The formula of the confidence interval is given below:
[tex]\rm CI =\bar{x}+z_{\alpha /2}\times \dfrac{\sigma }{\sqrt{n} }[/tex]
Step 2 - Now, for this interval, the formula of margin of error is given below:
[tex]\rm MOE = z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
Step 3 - Solve the above expression for sample size 'n'.
[tex]\rm n = \left(\dfrac{z_{\alpha /2}\times \sigma}{MOE}\right)^2[/tex]
From the above steps, it can be concluded that the correct option is B) It depends on not only the specified margin of error, but also on the confidence level.
For more information, refer to the link given below:
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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= 12/155A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C
Answer:
A
Step-by-step explanation:
The height is always perpinducular to the base. The height here is perpendicular to line segment A.
Answer:
A
Step-by-step explanation:
(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.
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.
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.
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Please answer this correctly without making mistakes
Answer: 7 mi
Step-by-step explanation: since the distance from bluepoint to Manchester is 12 9/10 mi and you know that bluepoint to Silverstone is 5 9/10 subtract that and you get 7 mi as your answer
Answer:
7 miles
Step-by-step explanation:
Hey there!
Well given BM and BS, we need to subtract them.
12 9 /10 - 5 9/10
9/10 - 9/10 = 0
12 - 5 = 7
Silvergrove to Manchester is 7 miles.
Hope this helps :)
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.
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....
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
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.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases, how much would your cash back be?
Answer:
$16.43.
Step-by-step explanation:
At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.
At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.
9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.
Hope this helps!
The amount of cashback that you earned will be $16.42.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.
The total cashback is calculated as,
⇒ 0.02 x $485.72 + 0.01 x $671.28
⇒ $9.71 + $6.71
⇒ $16.42
More about the percentage link is given below.
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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°
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
x = 4: 3x3 - 2x2 +10
Answer:
170
Step-by-step explanation:
3(4)³ - 2(4)² + 10
192 - 32 + 10 = 170
True or False: If the data for an observation on either the dependent variable or one of the independent variables are missing at random, then the size of the random sample available from the population must be reduced, which reduces the estimator's precision and introduces a bias.
Answer:
true
Step-by-step explanation:
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
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
What number should replace the question mark?
Answer:
1 Cruz it makes sense I hope this helps tho
Graphs are everywhere in the news, but just because a graph is in print does not mean that it is trustworthy. Review the graph and determine why it is misleading or inaccurate.
Answer:
Kindly check explanation
Step-by-step explanation:
Taking a careful look at the graph above, the graph depicts that there is sizeable growth or increase in the rate of interest between 2008 to 2012. However, the actual increase in the rate of interest between 2008 - 2012 is (3.152% - 3.141%) = 0.011%. This change is very small compared to what is portrayed by the pictorial representation of the bar graph. This could be due to the scaling of the vertical axis which didn't start from 0, thereby exaggerating the increase in the actual rate of interest. It will thus mislead observers into thinking the increase is huge.
3) Write the operation used to obtain the types of solutions.
Sum:
Difference:
Product:
Quotient:
Answer:
the Sum
hope this helps
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)
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
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
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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