Find the area of a triangle bounded by the y-axis, the line f(x)=9−2/3x, and the line perpendicular to f(x) that passes through the origin. Area =
Answers
Answer:
The area of the triangle is 18.70 sq.units.
Step-by-step explanation:
It is provided that a triangle is bounded by the y-axis, the line [tex]f(x)=y=9-\frac{2}{3}x[/tex].
The slope of the line is: [tex]m_{1}=-\frac{2}{3}[/tex]
A perpendicular line passes through the origin to the line f (x).
The slope of this perpendicular line is:[tex]m_{2}=-\frac{1}{m_{1}}=\frac{3}{2}[/tex]
The equation of perpendicular line passing through origin is:
[tex]y=\frac{3}{2}x[/tex]
Compute the intersecting point between the lines as follows:
[tex]y=9-\frac{2}{3}x\\\\\frac{3}{2}x=9-\frac{2}{3}x\\\\\frac{3}{2}x+\frac{2}{3}x=9\\\\\frac{13}{6}x=9\\\\x=\frac{54}{13}[/tex]
The value of y is:
[tex]y=\frac{3}{2}x=\frac{3}{2}\times\frac{54}{13}=\frac{81}{13}[/tex]
The intersecting point is [tex](\frac{54}{13},\ \frac{81}{13})[/tex].
The y-intercept of the line f (x) is, 9, i.e. the point is (0, 9).
So, the triangle is bounded by the points:
(0, 0), (0, 9) and [tex](\frac{54}{13},\ \frac{81}{13})[/tex]
Consider the diagram attached.
Compute the area of the triangle as follows:
[tex]\text{Area}=\frac{1}{2}\times 9\times \frac{54}{13}=18.69231\approx 18.70[/tex]
Thus, the area of the triangle is 18.70 sq.units.
Related Questions
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
HELP PLEASE
Answers
Answer:
All real numbers greater than or equal to -3
Step-by-step explanation:
First look at graph where the line points to which direction of the graph
And look for any closed or open circles in the graph
Since in the graph has a close circle at (-3,-2) meaning it includes that x-value for its domain.
With the graph going to positive infinity it states that the domain is all real numbers.
So in conclusion it has a domain of all real numbers greater than or equal to -3
What is the value of (Negative one-half)–4?
A) -16
B) Negative StartFraction 1 Over 16 EndFraction
C) StartFraction 1 Over 16 EndFraction
D) 16
Answers
Answer:
It would be 16!!!
The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (-1/2)⁻⁴
Simplify the equation, then we have
⇒ (-1/2)⁻⁴
⇒ (-2)⁴
⇒ -2⁴
⇒ 16
The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.
More about the value of the expression link is given below.
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Simplify 1 ∙ x -x/1 .
Answers
Answer:
0
Step-by-step explanation:
1x=x
-x/1=-x
x-x=0
Answer:
Brainleist !
Step-by-step explanation:
x - x /1
x - x = nothing or 0
Find tan x if sec x = sort 37/6 and sin x <0
Answers
Answer:
tan(x) = -1/6
Step-by-step explanation:
We can use the relation between tan and sec:
[tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]
The tangent of x is -1/6.
The mean of the data set(9,5,y,2,x)is twice the data set (8,x, 4,1,3).What is (y-x)
Answers
Answer:
y - x = 16
Step-by-step explanation:
Explanation:-
Step(i):-
Given data set A is 9,5,y,2,x
Mean of the Data set A
= [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]
= [tex]\frac{16 +x+y}{5}[/tex]
Given data set B is 8, x, 4, 1, 3
Mean of the Data set B
= [tex]\frac{8+ x+4+1+3}{5}[/tex]
Step(ii):-
Mean of the Data set A = 2 X Mean of the Data set B
[tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]
On simplification , we get
16 +x + y = 2( 16 +x)
16 + x + y = 32 + 2 x
16 + x + y - 32 - 2 x = 0
y - x -16 =0
y - x = 16
the sum of the measures of the angles of any triangle is 180 degrees. in triangle ABC, angles A and B have the same measure, of bile the measure of angle C is 72 degrees larger than each of A and B. what are the measures of the three angles?
Answers
Answer:
A=36
B=36
C=108
Step-by-step explanation:
A =B
2A+C=180
C is greater than A
2A+(A+72) =180
SIMPLIFY
3A +72=180
-72 ON BOTH SIDES
3A=108
DIVIDE BY 3
A=36
SO
B=36
36 TIMES 2 IS 72
180-72=108
SO
C=108
hope this helps
Answer:
Angle C= 108
Angles A and B=36
Step-by-step explanation:
180-72=108
108-72= 36
Check
36+36=72
72+108=180
A researcher conducts two studies. Study 1 uses a one-way between-subjects ANOVA. and Study 2 uses a within-subjects ANOVA. If the number of groups and participants per group are the same in each study, then in which study was the total number of participants larger? Explain.
Answers
Answer:
One way between subjects ANOVA
Step-by-step explanation:
In the between groups ANOVA, different people tests each conditions corresponding to the variables in the study while for the within groups ANOVA, the same person tests for all conditions corresponding to the variables. This way the total number of participants will be larger in the between subjects ANOVA group.
(a) There are $n$ chairs in a row. Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
(b) There are 10 chairs in a circle, labelled from 1 to 10. Find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent.
(c) There are $n$ chairs in a circle, labelled from 1 to $n.$ Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
Answers
Answer:
(A) P (n,k) = n!/(n-k)! divided by 2
(B) C (n,3) = n!/(12)(n-3)!
(C) C (n,k) = n!/(n-k)!(k!)
Step-by-step explanation:
Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.
We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.
For (B), n=10
C (n,3) = n!/(n-3)!(3!) divided by 2
3! = 3×2×1 = 6
The expression divided by 2 means it will be multiplied by 1/2
Hence 6×2 = 12
And we arrive at
C (n,3) =n!/(12)(n-3)!
Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2 filled an avaerage of 76.1 cans per minute with a standard deviation of 4.1 cans per minute.
Required:
a. If the counts are made each minute for 60 consecutiveminutes, what assumption necessary to the validity of a hypothesistest may be violated?
b. Assuming that all necessary assumptions are met, perform a hypothesis test. Can you conclude that machine 2 is faster than machine 1?
Answers
Answer:
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than machine one
Step-by-step explanation:
Step(i):-
Given sample size n₁ = n₂ = 60 minutes
The average of first sample 'x⁻₁ = 73.8
The standard deviation of the first sample 'S₁ ' = 5.2 cans per minute
The average of second sample 'x⁻₂ = 76.1
The standard deviation of the second sample 'S₂ ' = 4.1 cans per minute
step(ii):-
Null Hypothesis : H₀: 'x⁻₁ = 'x⁻₂
Alternative Hypothesis : H₁ : 'x⁻₁ > 'x⁻₂
Test statistic
[tex]t = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S^{2} _{1} }{n_{1} } +\frac{S^{2} _{2} }{n_{2} } } }[/tex]
[tex]t = \frac{73.8 - 76.1 }{\sqrt{\frac{(5.2)^{2} }{60 } +\frac{(4.1)^{2} }{60 } } }[/tex]
t = - 2.6932
|t| = | - 2.6932 | = 2.6932
Step(iii):-
Degrees of freedom
ν = n₁ + n₂ -2 = 60 +60 -2 = 118
t₀.₀₅ = 1.9803
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Final answer:-
Null hypothesis is rejected at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than the average of machine one
A garden bed contains 8 tomato plants, 4 squash plants and 8 bell pepper plants. What percentage of the plants are tomato plants
Answers
Answer:
33.33%
Step-by-step explanation:
Add them together 8 plus 8 plus 8 which is 24 there are 8 tp so its 8/24 which is equal to 1/3 so the percent is
1 adult and 6 children went swimming. How much did they pay together
Answers
Answer:
[tex]x+6y[/tex] where x is the cost of one adult ticket and y is the cost of one child ticket.
Step-by-step explanation:
This is an incomplete question since we would need to know the cost of the adult ticket and the cost of the children ticket.
However, let's say that the price is x dollars per adult and y dollars per child.
Now, we need to find out how much one adult and 6 children paid.
Thus, we would have to multiply the cost per adult by the number of adults and the cost per child per number of children and then sum up these two results.
Writing this in an algebraic way we would have:
[tex]1(x)+6y\\x+6y[/tex]
Thus, 1 adult and 6 children would have paid x + 6y dollars where x is the cost of the adult ticket and y is the cost of the children ticket.
(For example, if an adult ticket is 6 dollars and a child ticket is 4 dollars we would have that they paid 6 + 6(4) = 6 + 24 = 30 dollars)
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
Answers
Hey there! I'm happy to help!
The only thing we have to do is solve our inequality to find the answer!
30+15x ≥ 90
We subtract 30 from both sides.
15x ≥ 60
Finally, we divide both sides by four.
x ≥ 4
Therefore, Deepak can only accept jobs that last 4 or more hours.
I hope that this helps! Have a wonderful day!
The solution for the inequality is x≥4. Therefore, option A is the correct answer.
Given that, Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The inequality for the given situation is 30+15x≥90
Subtract 30 on the both the sides of an inequality, which is
30+15x-30≥90-30
⇒ 15x≥60
Divide 15 on the both the sides of an inequality, that is
15x/15≥60/15
⇒ x≥4
The solution for the inequality is x≥4. Therefore, option A is the correct answer.
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Please help :( : Solve the equation 3x + 5y = 15 for y
Answers
Answer:
y = -3/5 x +3
Step-by-step explanation:
3x + 5y = 15
Subtract 3x from each side
-3x+3x + 5y = -3x+15
5y = -3x+15
Divide each side by 5
5y/5 = -3x/5 +15/5
y = -3/5 x +3
Which operation is the default operation in algebra?
Answers
Step-by-step explanation:
in mathematics, a basic algebra corporation is there any one of the traditional operation of arithmetic, which are addition, subtraction, multiply, division, rising to an integer power, and taking root (fractional power ).
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2018, but statisticians might be more interested in the processes behind exit polling and the rellabllity of thelr results.
When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents.
Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a random telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed
(a) What type of sampling methods are used in selecting people for exit polls?
a. Simple Random Sampling
b. Cluster Sampling
c. Stratified Sampling
d. Convenience Sampling
e. Systematic Sampling
(b) Why do the polllng companles randomly select the preclncts to vislt?
a. Randomly selecting precincts to assign pollsters ensures that the companies can conclude a cause and effect relationship between the voters' beliefs and their voting pattern
b. There are too many precincts to manually select, so they are forced to randomly select them
c. Randomly selecting precincts increases the likelihood that the people polled represent the population well.
Answers
Answer:
A) cluster sampling ( b ) and systematic sampling ( e )
B ) Randomly selecting precincts increases the likelihood that the people polled represent the population well. ( c )
Step-by-step explanation:
Cluster sampling is a type of sampling plan used when there is an internally heterogeneous groups can be found inside a population that is supposed to be mutually homogeneous . while systematic sampling is a type of probability sampling that involves the selection of samples from a larger population at random but using a specific interval. to get the systematic sample the larger population is divided by the sample size.
from the information available in the report it is very evident that not all voters can be captured at once hence cluster sampling and systematic sampling would be employed .
B) the company will randomly select precinct to increase the likelihood of the sample size representing the entire population very well
x=(y+2)^2 solve the equation
Answers
Answer:
x= y^2+4y+4
Step-by-step explanation:
x= (y+2)(y+2)
x= y^2+2y+2y+4
x= y^2+4y+4
Answer:
X = y^2 + 4y + 4
Y= (√X) -2
Step-by-step explanation:
X = (Y+2)^2
X = (Y+2)(Y+2)
X = Y^2 + 4y + 4
X = (Y+2)^2
√X = √(Y+2)^2 (taking the root of both sides cancels the exponent)
√X = Y+2
-2 -2
(√X) - 2 = Y
or
Y = (√X) - 2
If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the bottom left corner of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.
Answers
Answer:
the first one
Step-by-step explanation:
I just took it on edge.
Answer:
It is B just took the unit quiz
Step-by-step explanation:
Chris is constructing a diagram for a deck he is restructuring in his backyard. The deck will be in the shape of a square, and he
has labeled a side length with the equation below, where x represents the original deck area.
side length = V1 + 12
Answers
Answer:
Increase the area of the deck by 12 square feet.
Step-by-step explanation:
The area of the deck increased by 12 square feet.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, Chris is constructing a diagram for a deck he is restructuring in his backyard.
The deck will be in the shape of a square, and he has labeled a side length with the equation below, where x represents the original deck area. Side length = V1 + 12
Increase the area of the deck by 12 square feet.
Therefore, the area of the deck increased by 12 square feet.
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9.2 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.
Answers
Answer:
765,795 = 96%
Step-by-step explanation:
confidence interval = 0.04
The Za/2 theorem = 1/2 = 0.04/2 = 0.02= /x = 720z
If ; 0.02 = 2.05 then the interval is 780-2.05 x 40/√30 x 780+2.05 x 30/√30 = 765,795 = 96%
We see 40/ √30 which is found in equation of finding the sample mean at point /x = 720z
σ 40/ n√30 = 7.3029674334 and is simply a fraction of /x 720z
By normal distribution we find
The 96% confidence interval for the population mean of all bulbs = 765,795
As 765, x 1.04 = 795 = 765, 795
To find Sampling mean.
The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
Confidence Level z*-value
80% 1.28
90% 1.645 (by convention)
95% 1.96
96% 2.05
98% 2.33
99% 2.58
What’s the correct answer for this question?
Answers
Answer:
3724 in^3
Step-by-step explanation:
19 times 14 times 14 = 3724
Answer:
3724 inches ³
Step-by-step explanation:
Volume of cooler = whl
Where w is width, h is height and l is length
V = (19)(14)(14)
V = 3724 inches³
2x2 + 3x ANSWER TO THIS
Answers
Answer:
x(2x+3)
Step-by-step explanation:
Im guessing 2x2 is 2x^2
2x^2 + 3x = 0
x(2x+3)
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
Answers
Examine the details of the chi‑square test and conclude in context. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence in the study among those drinking cranberry juice daily. The conditions for inference are not met. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence among those abstaining from both drinks. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence among those drinking Lactobacillus drink. There is good evidence (cite P-value) that, in the population of women just treated for a UTI, women drinking cranberry juice daily have fewer UTI recurrences, on average. Question Source: Baldi 4e - The Practice Of Statistics
Answers
Answer:
Step-by-step explanation:
We will examine and outline the details of this chi-square test and then conclude in context.
(A) A population of women have just been treated for a urinary tract infection.
(B) Since the chi-square test is done for categorical variables, we will pick out the variable involved here.
That variable is: "UTI Recurrence"
Hence, we are looking at the recurrence of a urinary tract infection, among samples of the population of women who have recently been treated of it.
(C) There are three samples from this population and they are distinguished thus:
SAMPLE 1: Those drinking cranberry juice daily
SAMPLE 2: Those taking lactobacillus drink
SAMPLE 3: Those abstaining from both drinks (the placebo sample)
(D) The result of the test gave good evidence that SAMPLE 1 has the lowest value of the categorical variable involved; as compared to the values from SAMPLE 2 and SAMPLE 3.
In other words, on the average (average here is equal to mode or frequency of occurrence of the variable), the lowest number of UTI recurrences stems from Sample 1, as compared to the numbers of UTI recurrences in the other two samples
The correlation between height and weight among men age 18-74 in the U.S. is about 0.40. Say whether each conclusion below follows from the data; explain your answer. a) Taller men tend to be heavier. b) The correlation between weight and height for men age 18-74 is about 0.40. c) Heavier men tend to be taller. d) If someone eats more and puts on 10 pounds, he is likely to get somewhat taller.
Answers
Answer:
Options a, b, c are correct.
Step-by-step explanation:
First let's see the equation that governs the statement, which is the following:
[tex]r = \frac{cov (x, y)}{\sqrt{var(x) var (y)} }[/tex]
Therefore, reading options a, b, c are correct.
Since from the formula we have the correlation coefficient of two variables x and y and here it shows us the correlation between x, y and y, x is the same.
This means that the 0.4 correlation implies a moderate but positive relationship between the two variables.
that is, the highest or lowest value of one variable implies a highest or lowest value of the other variable, respectively.
Plz help. Dora calculated the mean absolute deviation for the data set 35, 16, 23, 42, and 19. Her work is shown below. Step 1: Find the mean. mean = StartFraction 35 + 16 + 23 + 42 + 19 Over 5 EndFraction = 27 Step 2: Find each absolute deviation. 8, 11, 4, 15, 8 Step 3: Find the mean absolute deviation. M A D = StartFraction 8 + 11 + 4 + 15 Over 5 EndFraction = 9.5 What is Dora’s error?
A. Dora should have divided by 4 when finding the mean
B. Dora found the absolute deviation of 35 incorrectly
C. Dora used only four numbers in finding the mean
D. Dora used only four numbers in finding the mean absolute deviation
Answers
Answer:
step 3 is wrong
Step-by-step explanation:
i know it because i did the unit test review
Answer:
D
ヾ(•ω•`)o
Step-by-step explanation:
Star Corporation purchased from its stockholders 5,000 shares of its own previously issued stock for $250,000. It later resold 2,000 shares for $53 per share, then 2,000 more shares for $48 per share, and finally 1,000 shares for $43 per share.
In 2017, Star Corporation had the following treasury stock transactions.
Mar. 1 Purchased 5,000 shares at $8 per share.
June 1 Sold 1,000 shares at $12 per share.
Sept. 1 Sold 2,000 shares at $10 per share.
Dec. 1 Sold 1,000 shares at $7 per share.
Instructions
As you know that treasury stocks play a significant role in lowering the public ownership. Considering your understanding, journalize the treasury stock transactions and find the total amount of Paid-in Capital from Treasury Stock at December 31, 2017. What are some other circumstances under which company can go for the purchase of treasury stock? Provide your valuable opinion.
Answers
Answer:
Step-by-step explanation:
The objective here is to create a journal entry for the Star corporation treasure stock transaction, then find the total amount of Paid-in Capital from Treasury Stock at December 31, 2017.
Journal Entries:
Date Description $ $
Mar 1 Treasury Stock 40,000
Cash 40,000
June 1 Cash(1,000*12) 12,000
Treasury Stock(1,000*8) 8,000
Paid in Capital(12-8)*1,000 4,000
Sept 1 Cash(1,000*10) 10,000
Treasury Stock (1,000*8) 8,000
Paid in Capital (12-10)*1,000 2,000
Dec 1 Cash (1,000*7) 7,000
Paid in Capital (8-7)*1,000 1,000
Treasury Stock (1,000*8) 8,000
The Beginning Balance:
Treasury Stock Price = 250,000 / 5,000
= $50
Paid in Capital = [2,000×(53-50) + 2,000×(48-50) + 1,000×(43-50)]
= [(2,000×3) + (2,000×-2) + (1,000×-7)]
= 6,000 - 4,000 - 7,000
= -5,000
During the year transactions = 4,000+2,000-1,000
= $5,000
The total amount paid in Capital = Beginning Balance + During the year transactions
= -5,000 + 5,000
= 0
Some other circumstances under which company can go for the purchase of treasury stock includes:
A situation where by they resells the stock in the bid to increase funds for future investment.
The company can go for the purchase of treasury stock in order to empower the financial ratios and have full control interest in the company
It can also aid as a means of increasing the price of the share when it is underpriced in the market.
if log3(x+1) - log3x=2, then x = ?
Answers
Answer:
x= 1/8
Step-by-step explanation:
Your friend believes that he has found a route to work that would make your commute faster than what it currently is under similar conditions. Suppose that data were collected for a random set of 7 days, where each difference is calculated by subtracting the time taken on the current route from the time taken on the new route. Assume that the populations are normally distributed. Your friend uses the alternative hypothesis Ha:μd<0. Suppose the test statistic t is computed as t≈−3.201, which has 6 degrees of freedom. What range contains the p-value?
Answers
Answer:
The range of p-values
0.01 < p < 0.025
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 7
Assume that the populations are normally distributed
Null Hypothesis :H₀:μd=0.
Alternative Hypothesis:H₁:μd<0.
Degrees of freedom
ν = n-1 =7-1 =6
given the test statistic t = - 3.201
we will use single tailed test in t-distribution table
The test statistic t= 3.201 is lies between the critical values is 0.01 and 0.025
The range of p-values
0.01 < p < 0.025 (check t- distribution table single tailed test)
Final answer:-
The range of p-values
0.01 < p < 0.025
A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 10% significance level.
x = 20, n = 36, sigma = 9, H0: mu = 25, H amu : < 25.
Answers
Answer:
[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-3.33)=0.000434[/tex]
For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.
Step-by-step explanation:
Information given
[tex]\bar X=20[/tex] represent the sample mean
[tex]\sigma=9[/tex] represent the population deviation
[tex]n=36[/tex] sample size
[tex]\mu_o =25[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
tzwould represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test the hypothesis that the true mean is lower than 25 and the system of hypothesis are:
Null hypothesis:[tex]\mu \geq 25[/tex]
Alternative hypothesis:[tex]\mu < 25[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given:
[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-3.33)=0.000434[/tex]
For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.
what is the value of this expression plssssss 8z-3 when z =7
Answers
Answer:
53
Step-by-step explanation:
8•7 is 56
56 - 3 is 53
Answer:
53
Step-by-step explanation:
z = 7
8z is the same as saying 8×z
8×7-3 (do multiplication first)
56-3 = 53
