Answer:
To the nearest tenth = 10.8cm
Step-by-step explanation:
Using the cosine rule
J² = i² + k² + 2ikcosj
J² = 3.4² + 7.7² + 2(3.4)(7.7) cos 30
J² = 11.56 + 59.29 + 52.36cos30
J² = 11.56 + 59.29 + 52.36(0.8660)
J² = 11.56 + 59.29 + 45.35
J² = 116.2
J=√116.2
J= 10.78 cm
To the nearest tenth = 10.8cm
Answer:
its 5.1
Step-by-step explanation:
\text{S.A.S.}\rightarrow \text{Law of Cosines}
S.A.S.→Law of Cosines
a^2=b^2+c^2-2bc\cos A
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
j^2 = 7.7^2+3.4^2-2(7.7)(3.4)\cos 30
j
2
=7.7
2
+3.4
2
−2(7.7)(3.4)cos30
Plug in values.
j^2 = 59.29+11.56-2(7.7)(3.4)(0.866025)
j
2
=59.29+11.56−2(7.7)(3.4)(0.866025)
Square and find cosine.
j^2 = 59.29+11.56-45.34509
j
2
=59.29+11.56−45.34509
Multiply.
j^2 = 25.50491
j
2
=25.50491
Add.
j=\sqrt{25.50491} \approx5.05 \approx5.1
j=
25.50491
≈5.05≈5.1
Square root and round.
Solving for Unknown Values
Use parallelogram ABCD. What are the values of x and
y?
FERTE
A
4y-3
B
x =
y =
3x-9
42
D
37
C
Answer:x=17 y=10
Step-by-step explanation:
Simplify the expression by combining like terms.
Write the terms in alphabetical order of the
variables.
6x - 6y + 6z + 18x - 11y + 2z
Answer:
24x - 17y + 8z
Step-by-step explanation:
If you spin the spinner 90 times,
how many times should the
number 3 be selected?
Answer:
15
Step-by-step explanation:
1/6 of 90 is 15
The number of times 3 should be selected is 45/2.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that;
Number of spins= 90
Number of selected= 3
Now,
If the spinner has 4 equal sections and one of them has a 3, then the probability of landing on 3 is 1/4.
To find the expected number of times that the spinner lands on 3 in 90 spins, we need to multiply 1/4 by 90.
=1/4 * 90
=45/2
Therefore, by algebra the answer will be 45/2.
More about the Algebra link is given below.
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Events A and B are independent. The probability of A occuring is 2/3. The probability of B occuring is 1/4 what is p(A and B)
Answer: A 1/10
Step-by-step explanation: edge 2021
Which number line shows the solution if 4x - 36 < -12?
One solution was found :
x = 9
what is 4 3/8 - 5 1/2 ?
Answer:-1.125
Step-by-step explanation:
You work for a candy company and the manufacturing manager claims that the production line produces bags of candy with an average of exactly 50 candies per bag. You are skeptical about this and you decide to test the claim by counting the candies in a sample of 25 bags. You discover in your sample that x = 48 and s = 5. Determine whether have enough statistical evidence to reject the level of 0.05. Show your work and give all the necessary numbers required to reach your conclusion. Be sure to indicate all the necessary steps for a hypothesis test. Repeat the p-value.
Answer:
Step-by-step explanation:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H₀: u = 50
H₁: u ≠ 50
Null hypothesis: The production line produce bags of candy has an average of exactly 50 candies per bag.
Alternative hypothesis: The production line produce bags of candy does not have an average of exactly 50 candies per bag.
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.0
Test Statistic
t = (x - u) / SE
t = - 2.0
DF = n - 1
D.F = 24
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 24 degrees of freedom is less than -2.0 or greater than 2.0.
Thus, the P-value = 0.057
Statistic result
Interpret results. Since the P-value (0.057) is greater than the significance level (0.05), we failed to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the production line produce bags of candy with an average of exactly 50 candies per bag.
Jessica has to make a trip of 8925 MI. if she travels 425 miles a day how long will the trip take?
Answer:
21 days.
Step-by-step explanation:
You just divide the total number of miles by miles traveled a day.
8925÷425=21
It will takes 21 days.
Answer:21 days
Step-by-step explanation:
Which is greater 16/12 or 9/3
Answer:
[tex] \frac{16}{12} \: \: < \frac{9}{3} [/tex]
9/3 is greater
Step-by-step explanation:
[tex] \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9}{3} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{9 \times 4}{3 \times 4} \\ \frac{16}{12} \: \: \: \: \: \: \: \: \: \: \frac{36}{12} \\ \frac{16}{12} \: < \: \frac{36}{12} \\ \\ so \\ \frac{16}{12} < \frac{9}{3} [/tex]
Answer:
the answer is attached to the picture
Write the slope-Intercept form of the equation for the line
Answer:
Equation : y = -0.9x − 1.5
Step-by-step explanation:
Slope is rise over run, 7 over 8
-7/8 = -0.875, round to nearest tenth
-0.875 = -0.9
y- intercept is the point that crosses the y-axis,
the line crosses the y-axis at -1.5
11(11d+3z+8)for d = 10 and z = 12
Answer: 1,694
Step-by-step explanation: 11(11d + 3z + 8) d = 10 and z = 12
121d + 33z + 88
121(10) + 33(12) + 88
1210 + 396 + 88
1,694
Select all of the following that are quadratic equations. 5 x - 1 = 3 x + 8 5 x - 3 = 0 x2 - 2 x = 4 x + 1 2 x2+ 12 x = 0 x3 - 6 x2 + 8 = 0 9 x2 + 6 x - 3 = 0
Answer:
Answers are below.
Step-by-step explanation:
x2 - 2 x = 4 x + 12
x2+ 12 x = 0
x2 + 8 = 0
9x2 + 6 x - 3 = 0
These are all quadratic equations because they have x2 in all of them.
If this answer is correct, please make me Brainliest!
Answer:
x^2 - 2x = 4x + 1
2x^2 + 12x = 0
9x^2 + 6x - 3 = 0.
Step-by-step explanation:
A quadratic equation will contain a term with an exponent of 2 as the highest exponent.
Write the slope-intercept form of the equation for the line
Answer:
y=3x-1
Step-by-step explanation:
start at (-1,-4) and go up 6 and over 2, thats your slope or m.
the y intercept is -1
Answer: y=3x-1
Step-by-step explanation:
(1,2) and (-1,-4) are on the so we could use then to find the slope.
2-(-4)=6
1-(-1)= 2
6/2=3
We know the y-intercept is -1 because the line passes through (0,-1) which is on the y axis. And the y-intercept is when x is 0.
so the equation will be y = 3x -1
y = 6x - 4
y = -x + 3
Answer:
(1, 2)
Step-by-step explanation:
Subtract the second equation from the first:
(y) -(y) = (6x -4) -(-x +3)
0 = 7x -7 . . . . . simplify
0 = x - 1 . . . . . . divide by 7
1 = x . . . . . . . . . add 1
y = -1 +3 = 2 . . . substitute into the second equation
The solution is (x, y) = (1, 2).
the ratio of savings to expenditure is 2:8 find the savings if the expenditure is 24,000
Answer:
the savings is 6000
Step-by-step explanation:
We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.
They tell us to find the savings when the cost is 24,000, so we are left with:
24000 * 2/8 = 6000
which means that when 24000 are spent the savings is 6000
Use matrix algebra to show that if A is invertible and D satisfies ADequalsI, then Upper D equals Upper A Superscript negative 1. Choose the correct answer below. A. Left-multiply each side of the equation ADequalsI by Upper A Superscript negative 1 to obtain Upper A Superscript negative 1ADequalsUpper A Superscript negative 1I, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1. B. Add Upper A Superscript negative 1 to both sides of the equation ADequalsI to obtain Upper A Superscript negative 1plusADequalsUpper A Superscript negative 1plusI, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1.
Answer:
D=A^-1
Step-by-step explanation:
Given that A is invertible and matrix D satisfies AD=I
Where I is an identity matrix
D is the inverse of A
Multiply both sides of AD=I by A^-1
A^-1(.AD) =A^-1 I
A^-1 .A=I
Therefore D=A^-1
All equations are identies, but not all identies are equations
True or False
ANSWER: It is false that All equations are identities, but not all identities are equations, as all identities are equations, but only some equations are identities.
HOPE THIS HELP
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
(A) Approximately normal with mean $206,274 and standard deviation $3,788
(B) Approximately normal with mean $206,274 and standard deviation $37,881
(C) Approximately normal with mean $206,274 and standard deviation $520
(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788
(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881
Answer:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Right skewed
Mean $206,274
Standard deviation $37,881.
Sample:
By the Central Limit Theorem, approximately normal.
Mean $206,274
Standard deviation [tex]s = \frac{37881}{\sqrt{100}} = 3788.1[/tex]
So the correct answer is:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem.
Given :
There were 5,317 previously owned homes sold in a western city in the year 2000.The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. Simple random samples of size 100.According to the central limit theorem the approximately normal mean is $206274.
Now, to determine the approximately normal standard deviation, use the below formula:
[tex]s =\dfrac{\sigma }{\sqrt{n} }[/tex] ---- (1)
where 's' is the approximately normal standard deviation, 'n' is the sample size, and [tex]\sigma[/tex] is the standard deviation.
Now, put the known values in the equation (1).
[tex]s = \dfrac{37881}{\sqrt{100} }[/tex]
s = 3788.1
[tex]\rm s \approx 3788[/tex]
So, the correct option is A).
For more information, refer to the link given below:
https://brainly.com/question/18403552
A copy machine makes 24 copies per minute. How many copies does it make in 3 minutes and 45 seconds?
copies
Х
?
Answer:
90 copies
Step-by-step explanation:
24*3= 72
1/2*24= 12 for 30 seconds
1/2*6= 6 for 15 seconds
45/15=3
72+18= 90
The new Elk Grove radio station KFIN, features the top 60 songs for that week. The #1 song is played 60 times, the #2 song is played 59 times, the #3 song is played 58 times, and so on until the #60 song is played once. Each song takes 3 minutes to play.
The station also has 24 ten-minute news breaks each day, and the rest of the time is sold for advertising. If the station charges $100 for every 30 seconds of advertising, how much money do they take in each week?
Answer:
Step-by-step explanation:
The number of times that each song is played is reducing in arithmetic progression. We would determine the total number of time for plating all the songs in a week by applying the formula for determining the sum of the n terms in an arithmetic sequence. It is expressed as
Sn = n/2(2a + (n - 1)d
Where
d represents the common difference
n represents the number of terms
a represents the first term of the sequence
Sn represents the sum of n terms if the sequence.
From the information given,
a = 60
n = 60
d = - 1
Sn = 60/2(2 × 60 + (60 - 1)-1)
Sn = 30(120 - 59)
Sn = 1830 times
The 60 songs are played for 1830 times in a week. If each song takes 3 minutes to play, then the total time taken to play the songs for 1830 times in a week is
3 × 1830 = 5490 minutes
7 days = 1 week
24 hours = 1 day
60 minutes = 1 hour
The number of minutes in a week is
7 × 24 × 60 = 10080 minutes
The station also has 24 ten-minute news breaks each day. The number of minutes of break for each day is
24 × 10 = 240 minutes
The amount of break time in a week is
240 × 7 = 1680 minutes
If the remaining minutes is meant for advertising, then the number if minutes available for advertising is
10080 - (5490 + 1680) = 2910 minutes
1 minute = 60 seconds
2910 minutes = 2910 × 60 = 174600 seconds
If the station charges $100 for every 30 seconds of advertising, then the amount that they take in each week(for 174600 seconds) is
(174600 × 100)/30 = $5820000
In a lottery​ game, the jackpot is won by selecting five different whole numbers from 1 through 37 and getting the same five numbers​ (in any​ order) that are later drawn. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below:a. What is the probability of winning a jackpot in this​ game? ​P(winning a jackpot in this ​game)= ________b. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. What is the probability of winning this​ game? ​P(winning the Pick 55​game)= ______________c. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit? ​
Answer:
The probability of winning a jackpot is [tex]P = 0.000003[/tex]
The probability of winning the pick 5 game is [tex]P_a = 0.00001[/tex]
The earning of the lottery organisation if the game were to be runed for no profit is [tex]x =[/tex]$10 000
Step-by-step explanation:
From the question
The sample size is n= 37
The number of selection is [tex]r = 5[/tex]
Now the number of way by which these five selection can be made is mathematically represented as
[tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]
Now substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]
[tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]
Now the probability of winning a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as
[tex]P = \frac{1}{333333.3}[/tex]
[tex]P = 0.000003[/tex]
Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as
[tex]k = 10^5[/tex]
Now the probability of winning the game is
[tex]P_a = \frac{1}{10^5}[/tex]
[tex]P_a = 0.00001[/tex]
We are told that for a $1 ticket that the pick 5 game returns $50 , 000
Generally the expected value is mathematically represented as
[tex]E(X) = x * P(X =x )[/tex]
In this question the expected value is $1
So
[tex]1 = x * 0.00001[/tex]
So [tex]x = \frac{1}{0.00001}[/tex]
[tex]x =[/tex]$10 000
A sprinkler swings back and fourth between A and B in such a way that <1 is congruent to <2. <1 and <3 are complementary, and <2 and <4 are complementary. If m<1=47.5 degrees, find m<2, m<3, and m<4
Answer:
Congruent
Step-by-step explanation:
Answer:
I think is congruent, but I m not sure
Madison drew Triangle D E F. In her triangle, Measure of angle D is represented as x degrees. The measure of Angle E is half the measure of Angle D. The measure of Angle F is 2 degrees less than twice Measure of angle D. What is Measure of angle F?
A) 36 degrees
B)56 degrees
C)102 degrees
D)147 degrees
Answer:
102 degrees.
Step-By-Step Explanation:
We know that D is x and E is 1/2x and Angle F is 2 less than angle D.
So if we use the sum of 180 and solve for x, we will find angle D.
This is the equation: x+.5x+2x-2=180
solve: 3.5x -2 = 180
+2 +2
3.5x=182
/3.5x /3.5x
X = 52
2(52)-2 = 102 degrees
Thus the answer is 102 degrees
hope this helped:)
Answer:
102º
Step-by-step explanation:
1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several times, and the values are: 0.082601, 0.082621, 0.082589, 0.082617, 0.082598. Please use student’s t to find the confidence interval at the 95% confidence level. 2) If one wants the confidence interval to be two thirds of the previous one, how many times should a student repeat? (Assuming the standard deviation is the same as the previous one)?
Answer:
1) [tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
b) [tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
Step-by-step explanation:
Information given
0.082601, 0.082621, 0.082589, 0.082617, 0.082598
We can calculate the sample mean and deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=0.0826052[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=0.000013424 represent the sample standard deviation
n=5 represent the sample size
Part 1
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=5-1=4[/tex]
The Confidence level is 0.95 or 95%, and the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value would be using the t distribution with 4 degrees of freedom: [tex]t_{\alpha/2}=2.776[/tex]
Now we have everything in order to replace into formula (1):
[tex]0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588[/tex]
[tex]0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219[/tex]
Part 2
The original margin of error is given by:
[tex] ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653[/tex]
And we want 2/3 of the margin of error so then would be: [tex] 2/3 ME = 0.00001111[/tex]
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (2)
Replacing we got:
[tex]n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12[/tex]
So the answer for this case would be n=12 rounded up to the nearest integer
What would you do to find the area of 5/8 of a circle?
Answer:
5/8 * pi r^2
Step-by-step explanation:
First , you find the full area of the circle
A = pi r^2
Then multiply by the fraction that you want to find
5/8 * pi r^2
Your friend deposits $6000 in an investment account that earns 7.3% annual interest. Find the balance after 18 years when the interest is compounded quarterly.
Answer: $22,063.2
Step-by-step explanation:
quarterly means that 4 times per year this interest, the balance can be find by the equation:
A = P*(1 + r/4)^(4*t)
Where P is the initial value, r is the rate of increase (7.3% in this case, but remember that you must use the decimal form; 0.073) and t is the number of years:
so we have:
B = $6,000*( (1 + 0.073/4)^(4*18) = $22,063.2
Two angles of a triangle measure 78 and 24
Answer: 78
Step-by-step explanation: Remember every triangle ads up to a total of 180 degrees. You just have to make sure that it adds up to 180
Is the point (7,0) located on the x axis
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Yes. As the y value is 0, this point would be on the x axis
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What is 100 times 10
Answer:
Central graph
Step-by-step explanation:
When a function has a negative rate of change, it means that as the x value increases, the y value decreases. The only graph that does this continuously is the central one. Hope this helps!
The calculated product of the numbers is 1000
The graph with a negative rate to be (c)
How to calculate the product of the numbersFrom the question, we have the following parameters that can be used in our computation:
100 times 10
When represented as an equation, we have
100 times 10 = 100 * 10
Evaluate the products
So, we have the following result
100 times 10 = 1000
Next, we interpret the graph
From the graphs, we have the graph with a negative rate to be (c)
Using the above as a guide, we have the following:
the result is 19/125
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n Hamilton County, Ohio the mean number of days needed to sell a home is days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of homes in a nearby country showed a sample mean of days with a sample standard deviation of days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of days in the nearby county. Round your answer to four decimal places.
Answer:
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Test statistic t=-1.8974
P-value = 0.0326
Step-by-step explanation:
The question is incomplete:
"In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places."
This is a hypothesis test for the population mean.
The claim is that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=86\\\\H_a:\mu< 86[/tex]
The significance level is 0.05.
The sample has a size n=40.
The sample mean is M=80.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{40}}=3.1623[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{80-86}{3.1623}=\dfrac{-6}{3.1623}=-1.8974[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=40-1=39[/tex]
This test is a left-tailed test, with 39 degrees of freedom and t=-1.8974, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.8974)=0.0326[/tex]
As the P-value (0.0326) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.