using the digits -9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution in quadrant 2. Tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
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Okay, here we have this:
Considering the provided information and options, we are going to find the requested numbers, so we obtain the following:
So first we will choose two values for x and y that meet the given tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
For our case we will take x=-1 and y=1, then we can write the following two equations:
1x+3y=2 -> 1(-1)+3(1)=2 -> -1+3=2 -> 2=2
y=7x+8 -> 1=7(-1)+8 -> 1=-7+8 -> 1=1
Related Questions
someone please help I don't get it!!
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Answer:
which one
Step-by-step explanation:
don't forget to follow rate like
what is the value of x to the nearest tenth on problem 5
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Answer:
Explanation:
In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).
So, by Pythagorean theorem, we can write the following equation
[tex](x+8)^2=x^2+16^2[/tex]Now, we can expand the left side
[tex]\begin{gathered} x^2+2(8)(x)+8^2=x^2+16^2 \\ x^2+16x+64=x^2+256 \end{gathered}[/tex]Then, subtract x² from both sides
[tex]\begin{gathered} x^2+16x+64-x^2=x^2+256-x^2 \\ 16x+64=256 \end{gathered}[/tex]Subtract 64 from both sides
[tex]\begin{gathered} 16x+64-64=256-64 \\ 16x=192 \end{gathered}[/tex]Finally, divide by 16
[tex]\begin{gathered} \frac{16x}{16}=\frac{192}{16} \\ \\ x=12 \end{gathered}[/tex]Therefore, the value of x is 12
Find the exponential function f(x)=Ca^x whose graph is given below.
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Answer:
f(x) = 2[tex](\frac{1}{3}) ^{x}[/tex]
Step-by-step explanation:
exponential in the form
f(x) = C[tex]a^{x}[/tex]
to find C and a use points from the graph
using (0, 2 ) , then
2 = C[tex]a^{0}[/tex] ( [tex]a^{0}[/tex] = 1 ) , so
C = 2
f(x) = 2[tex]a^{x}[/tex]
using (2, [tex]\frac{2}{9}[/tex] )
[tex]\frac{2}{9}[/tex] = 2a² ( divide both sides by 2 )
[tex]\frac{1}{9}[/tex] = a² ( take square root of both sides )
[tex]\sqrt{\frac{1}{9} }[/tex] = a ⇒ a = [tex]\frac{1}{3}[/tex]
f(x) = 2 [tex](\frac{1}{3}) ^{x}[/tex] ← exponential function
1 2 3 At the beginning of the day the temperature was - 17°C. At noon the thermometer read -2°C What is the total change in degrees Celsius?
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The total change in temperature = temperature at noon minus temperature at the beginning of the day
[tex]=-2^0^{}c-(-17^0c)=-2^0c+17^0c=15^0c[/tex]if f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which of the following
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Answer:
The correct answer is the third option:
[tex]\lim_{x\to4}(\sqrt{x}-2)[/tex]Explanation:
We have the function:
[tex]f(x)=\frac{x-4}{\sqrt{x}-2}[/tex]In the numerator, we have x - 4. We can rewrite it as a difference of squares, since:
[tex]\begin{gathered} x=(\sqrt{x})^2 \\ 4=2^2 \end{gathered}[/tex]Thus:
[tex]x-4=(\sqrt{x}-2)(\sqrt{x}+2)[/tex]Then, the limit:
[tex]\begin{gathered} \lim_{x\to4}(\frac{(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)} \\ \end{gathered}[/tex]We can cancel out the terms, since we are taking limit, this is, numbers that infinitely close to 4, bt never 4. This way we can cancel the terms, and get:
[tex]\lim_{x\to4}(\sqrt{x}+2)[/tex]
Kyla is filling a water bucket that holds 5 and 1/4 gallons using a container that holds 3/4 of a gallon per container (a) Create a division problem that finds how many containers Kyla will need to use. Evaluate this quotient(b) Check your answer to (a) by using a product. Show your work
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Given a water bucket that holds
[tex]5\frac{1}{4}gallons[/tex]A container with the measurement below was used to fill the water bucket
[tex]\frac{3}{4}\text{gallon}[/tex](a) The division problem that shows how many containers are needed to fill the water bucket is
[tex]\frac{5\frac{1}{4}}{\frac{3}{4}}[/tex]The quotient is as solved below:
[tex]5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}[/tex][tex]\begin{gathered} \frac{5\frac{1}{4}}{\frac{3}{4}}=\frac{\frac{21}{4}}{\frac{3}{4}} \\ \frac{21}{4}\frac{\square}{\square}\frac{3}{4} \\ =\frac{21}{4}\times\frac{4}{3} \end{gathered}[/tex][tex]\frac{7\times1}{1\times1}=7[/tex]Hence, the quotient is 7 Containers
(b) Checking the answer using a product as shown below
[tex]\begin{gathered} 7\times\frac{3}{4}=5\frac{1}{4} \\ \frac{7\times3}{4}=\frac{21}{4} \end{gathered}[/tex][tex]\frac{21}{4}=5\frac{1}{4}[/tex]Hence, the product of 7 and 3/4 gallons container will fill 5 1/4 water bucket
lax and tip word pr You might need: 3 Calcu The sales tax in your city is 4.4%. and an item costs $3 before tax. How much tax would you pay on that item?
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Tax = $0.13(nearest hundredth)
-2( 4 - 6h ) +9-8 - 12h + 9-12h + 1Explain the error in the work.
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The error is in the distribution property application, in the way the signs are multiplied.
We will look at it in detail:
[tex]\begin{gathered} -2(4-6h)+9 \\ \lbrack(-2)(4)+(-2)(-6h)\rbrack+9 \\ (-8+12h)+9 \\ 12h+1 \end{gathered}[/tex]When (-2) is multiplied by (-12h) it should end with a positive sign, as (-a)*(-b)=a*b
I need help on this, I need it answered in steps
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Let's solve the given logarithmic expression:
[tex]\text{ log}_4(64)\text{ = m}[/tex]We get,
[tex]\text{ log}_4(64)\text{ = m}[/tex][tex]\mathrm{Factor\: the\: number\colon\: }\: 64=4^3[/tex][tex]=\log _4\mleft(4^3\mright)[/tex][tex]\mathrm{Apply\: log\: rule}\colon\quad \log _a\mleft(a^x\mright)=x[/tex][tex]\log _4\mleft(4^3\mright)\text{ = 3 = m}[/tex]Therefore, m = 3.
PQR is a right triangle. If PQ=8, what is PR?
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Sine formula
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hypotenuse}}[/tex]Considering angle Q = 60°, the opposite side is PR, and the hypotenuse is PQ = 8. Substituting this information into the formula, we get:
[tex]\begin{gathered} \sin (m\angle Q)=\frac{PR}{PQ} \\ \sin (60\degree)=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}\cdot8=PR \\ 4\sqrt[]{3}=PR \end{gathered}[/tex]What rule describes the translation that was applied to triangle JKM to create triangle J’K’M’, Initial directions with the pic below.
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Given a point (x, y), let's evaluate the transformations:
- Translation 6 units to the right.
Means moving the point 6 units in the horizontal direction; to the right.
The new point will be (x + 6, y).
- Translation 2 units down.
Means moving the point 2 units down; in the vertical direction.
The new point will be (x + 6, y - 2).
Answer: (x + 6, y - 2).
Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.9 ft13 ft6 ft
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The area of the triangle is 27 square feet
Explanation:The area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]Where b and h are the base and height of the triangle respectively
[tex]\begin{gathered} A=\frac{1}{2}(9\times6) \\ \\ =27ft^2 \end{gathered}[/tex]Lynn got a $50 gift card to an online music store she uses the gift cards to buy an album for 9.99 she also wants to use the gift card to buy some songs. Each song cost 1.29. What equality is described the situation where n is the number of songs like monster by
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ANSWER
B. 9.99 + 1.29n ≤ 50
EXPLANATION
The total amount of money she spends at the store has to be at most, the value of the gift card $50. This is the cost of the album, 9.99, and then 1.29 for each song. If the total number of songs is 'n', then for n songs, she'll spend 1.29n. In total she spends: 9.99 + 1.29n at the store. The equation is
[tex]9.99+1.29n\le50[/tex]In the image below, line ris perpendicular to both lines p and q. Lines p and p and r. are parallel to one another. Transversal s goes through lines p 28° s What is the value of x? A 62 OB. 72 O C 152 OD. 162 Sign out INTL 2
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In this problem we have that
m by supplementary angles
so
mmtherefore
the answer is
x=52 degreesPart 2
the transformations that produce triangle ABC are
1) A dilation from the with scale factor of 2
2) A reflection across the x-axis
3) A translation of
I need help with this practice problem, I am struggling to solve It’s from my trigonometry prep guide
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Answer:
Corey stepped 59.71 ft away
Explanation:
The situation is sketched in the following diagram.
The distance from the foot of the tree is y and x for angles 41 and 68 degrees respectively.
Therefore, the distance Corey has to step away is y - x.
Now, from trigonometry, we know that
[tex]\tan (68^o)=\frac{\text{opposite}}{\text{adjacent}}[/tex][tex]\Rightarrow\tan (68^o)=\frac{\text{8}0}{\text{x}}[/tex]We solve for x and get
[tex]\begin{gathered} \Rightarrow x\tan (68^o)=80 \\ \Rightarrow x=\frac{80}{\tan (68^o)} \end{gathered}[/tex]since tan (68) = 2.475.., the above becomes
[tex]x=\frac{80}{2.75\ldots}=32.32[/tex]Now, for angle 41 we have
[tex]\tan (41^o)=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan (41^o)=\frac{80}{y}[/tex]solving for y gives
[tex]y=\frac{80}{\tan (41^o)}[/tex]since tan(41) = 0.869..., the above becomes
[tex]y=\frac{80}{0.869\ldots}[/tex][tex]\Rightarrow y=92.0295\ldots[/tex]Therefore, the distance Corey has to step away from the tree to get a better view is (rounded to the nearest hundredth)
[tex]y-x=92.0295-32.322[/tex][tex]\boxed{y-x=59.71.}[/tex]Rewrite the area formula with the info given from the problem then find the value of x , then how many feet of fencing should me Korber buy ?
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Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:
[tex]A=\frac{1}{2}x^2[/tex]Now, let's use the given area and solve it for x:
[tex]\begin{gathered} 4232=\frac{1}{2}x^2\\ \\ x^2=8464\\ \\ x=92\text{ ft} \end{gathered}[/tex]Since the "path" already has fence, the amount of fence needed is 2x:
[tex]2x=2\cdot92=184\text{ ft}[/tex]15% of 80 is 60% of what number?
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Let x be the required number.
[tex]15\text{ \% of 80 =}60\text{ \% of x}[/tex][tex]15\text{ \% }\times\text{ 80 =}60\text{ \% }\times\text{ x}[/tex][tex]\frac{15}{100}\text{ }\times\text{ 80 =}\frac{60}{100}\text{ }\times\text{ x}[/tex]
Using the cross-product method, we get
[tex]\frac{15\times80}{100}\times\frac{100}{60}=x[/tex][tex]x=20[/tex]Hence 15% of 80 is 60% of 20.
The answer is 20.
In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75.Algebraically determine the rate of growth to thenearest percent.
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The Solution.
In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25
Similarly.
In 2015, t = 49 years , (that is, 1966 to 2015), and y = $8.75
The rate of growth to the nearest percent is
[tex]\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100[/tex][tex]\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \$1.25},t_1=0 \end{gathered}[/tex]Substituting into the formula above, we get
[tex]\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100[/tex][tex]\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}[/tex]Hence, the correct answer is 15%
Given: the function f defined by f(x) = 3x^2. Which statement is true?
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The given function is
[tex]f(x)=3x^2[/tex]If we evaluate the function when x = 0, we get
[tex]f(0)=3(0)^2=3\cdot0=0[/tex]Hence, the first option is correct.1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables fill in the missing cells on table and make sure to reduce your fraction.
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Horizontal addition
Row 1 a + 12 + b +6 =37
[tex]\begin{gathered} a+12+b+6=37 \\ a+b+18=37 \\ a+b=37-18 \\ a+b=19 \end{gathered}[/tex]Row 2
[tex]\begin{gathered} 8+c+16+11=d \\ c+35=d \end{gathered}[/tex]Row 3
[tex]\begin{gathered} 17+5+e+18=f \\ 40+e=f \end{gathered}[/tex]Row 4
[tex]\begin{gathered} g+34+45+h=143 \\ g+h+79=143 \\ g+h=143-79 \\ g+h=64 \end{gathered}[/tex]Now Let us add the columns
Column 1
[tex]a+8+17=g[/tex]Column 2
[tex]\begin{gathered} 12+c+5=34 \\ c+17=34 \\ c=34-17 \\ c=17 \end{gathered}[/tex]Column 4
[tex]\begin{gathered} 6+11+18=h \\ h=35 \end{gathered}[/tex]Column 2
[tex]\begin{gathered} b+16+e=45 \\ b+e=45-16 \\ b+e=29 \end{gathered}[/tex]Hence, Video games under 10-12 is c=17, gotten from column 2
Vertical total under 16-18 is h=35 gotten from column 4
Hence, the horizontal total of the video game is 52
Since h is gotten, we can solve for 7 to 9 vertical total
[tex]\begin{gathered} g+h=64 \\ g=64-h \\ g=64-35 \\ g=29 \end{gathered}[/tex]Hence, the 7 to 9 vertical total is 29
[tex]\begin{gathered} a+25=g \\ a=g-25 \\ a=29-25 \\ a=4 \end{gathered}[/tex]Hence, Darts under 7 to 9 is 4
Darts under 13 to 15 is b
[tex]\begin{gathered} a+b=19 \\ b=19-a \\ b=19-4 \\ b=15 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 15
Basket ball under 13 to 15 is e
[tex]\begin{gathered} b+e=29 \\ e=29-b \\ e=29-15 \\ e=14 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 14
Video Games Horizontal total is d,
[tex]\begin{gathered} c+35=d \\ 17+35=d \\ d=52 \end{gathered}[/tex]Hence, the Horizontal total of the Video game is 52
Basketball horizontal total is f
40+e=f
[tex]\begin{gathered} 40+e=f \\ 40+14=f \\ 54=f \end{gathered}[/tex]Hence, the horizontal total of the Video game is 54.
Hence, the above table fill the empty space
im on a bit of a time crunch so please hurry :)
Answers
Answer
39 child tickets were sold that day
Step-by-step explanation
Variables
• x: child tickets sold
,• y: adult tickets sold
Given that four times as many adult tickets as child tickets were sold, then:
[tex]y=4x[/tex]If 1 child ticket cost $5.70, then x child tickets will cost 5.7x dollars.
If 1 adult ticket cost $9.20, then y adult tickets will cost 9.2y dollars.
Given that the theater sold tickets for $1657.50, then:
[tex]5.7x+9.2y=1657.5[/tex]Substituting the first equation into the second one and solving for x:
[tex]\begin{gathered} 5.7x+9.2(4x)=1,657.5 \\ 5.7x+36.8x=1,657.5 \\ 42.5x=1,657.5 \\ \frac{42.5x}{42.5}=\frac{1,657.5}{42.5} \\ x=39 \end{gathered}[/tex]hello I am stuck on this problem in need of help please thank you
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First let's do a quick table to help us, when we have S = 0 we cannot make any cookies, then N = 0. When we have one cup of sugar S = 1 we can make 30 cookies, then N = 30. For S = 2, which means, 2 cups of sugar we can make 60 cookies, and so on, then we can do a table like
Then we can see that the relation between N and S is 30, because N = 30.S, for each unit of S that we put we get 30 more cookies, then the equation is
[tex]N=30S[/tex]And if we want to solve it for S
[tex]S=\frac{N}{30}[/tex]Looking at the graph we can see that S is in the y-axis, therefore we are going to use the equation where we have S on the left side, which means, solved for S. Then we are going to plot the equation:
[tex]S=\frac{N}{30}[/tex]This equation is a line, a very simple graph! you can plot two points and then draw a line, for example, use the point (30,1) and (60,2), if we plot these points we get
Now we draw a line that connects these two points, and we have the graph!
Marcus is playing dodge ball with hisfriends. He catches 2 out of every 5 ballsthrown in his direction. If he catches14 balls, how many balls were thrownat him?balls
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Step 1
Given;
[tex]\begin{gathered} \text{Marcus is playing dodge ball with his friends.} \\ He\text{ catches 2 out of every 5 balls thrown in his direction.} \end{gathered}[/tex]Required; To find out how many balls are thrown at him if he catches 14 balls.
Step 2
There are two approaches to determine the number of balls thrown at Marcus
Approach 1
[tex]\begin{gathered} \text{Marcus catches 2 balls for every 5 balls thrown in his direction.} \\ we\text{ can draw up a table and add up 2 balls caught and 5 balls } \\ \text{thrown respectively until we arrive at 14 balls caught.} \end{gathered}[/tex]Draw the table;
we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.
Answer=35 balls
Approach 2
[tex]\begin{gathered} We\text{ will use the ratio} \\ \frac{2\text{ balls caught}}{14\text{ balls caught}}=\frac{5\text{ balls thrown }}{x\text{ balls thrown}} \\ \text{cross multiply} \\ 2x=5(14) \\ \text{simplify} \\ 2x=70 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{70}{2} \\ x=35\text{ balls thrown} \end{gathered}[/tex]Hence, 35 balls were thrown at Marcus
Can you help me with number 11? Thank you I am having trouble with it.
Answers
N 11
Remember that
The law of sines
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]In this problem
[tex]\frac{14.9}{\sin X^o}=\frac{25.5}{\sin 71^o}[/tex]Solve for x
sinX=(14.9*sin71)/25.5
Alexa read a total of 54 books over 9 months. If Alexa has read 120 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
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If the relation between the book read by Alexa and the number of months she takes to read them is directly proportional, then, if x is the number of months she took to read 120 books, you can write:
[tex]\frac{x}{120}=\frac{9}{54}[/tex]By solving for x and simplifying, you obtain:
[tex]\begin{gathered} x=\frac{9}{54}\cdot120 \\ x=20 \end{gathered}[/tex]Hence, Alexa read 120 books in 20 months
D − 37 = 40D =Check your solution.− 37 = 40
Answers
We have to solve this equation:
[tex]D-37=40[/tex]We can solve it for D by adding 37 on both sides of the equation as this won't change the equality:
[tex]\begin{gathered} D-37+37=40+37 \\ D=77 \end{gathered}[/tex]Answer: D = 77
Use the point highlighted in the graph below to write the equation in point slope form for the line provided.
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Making the equation of the graph using the Point-Slope Form:
[tex]\text{ y - y}_1=m(x-x_1)[/tex]Since slope was not given, let's compute first for the slope (m) using this formula,
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1_{}}[/tex]From the graph, we have one set of coordinates given: (2, 3)
However, we cannot solve the slope with one point alone, thus let's find another point that's along the line and easier to find. From the graph, we get (0,4).
Let's now compute for the slope (m).
[tex](x_1,y_1)=(0,4);(x_{2,}y_2)=(2,3)_{}[/tex][tex]\text{ m = }\frac{3\text{ - 4}}{2\text{ - 0}}\text{ = }\frac{-1}{2}[/tex]Let's now make the equation using the Point-Slope Form using (2,3) as (x1,y2),
[tex]\text{ y - y}_1=m(x-x_1)[/tex][tex]\text{ y - 3 = (}\frac{-1}{2})(x-\text{ 2)}[/tex][tex]\text{ y - 3 + 3 = -}\frac{1}{2}x\text{ + }\frac{2}{2}\text{ + 3}[/tex][tex]\text{ y = }\frac{-1}{2}x\text{ + 1 + 3 = }\frac{-1}{2}x\text{ + 4}[/tex]Thus, the equation of the line is,
[tex]\text{ y = }\frac{-1}{2}x\text{ + 4}[/tex]aThecity of Huntsville, TX has approximately 25,000 registered voters. There are two candidates forcity council in an upcoming election: Brown and Solano. The day before the election, a telephone pollof 550 randomly selected registered voters was conducted. 243 said they'd vote for Brown, 253 saidthey'd vote for Solano, and 54 were undecided.give the simple statistic for the proportion of voters surveyed
Answers
The surveyors are really interested in all registered boters in Huntsville, therefore the first answer is F.
Since they are only doing a sample of people with phones the real population is all registered voters with telephones, therefore the second answer is C.
The sample for this survey is the 550 voter surveyed.
To find the proportion of people who said they vote for brown we divide the number of this people by the total of people surveyed:
[tex]\frac{243}{550}=0.4418[/tex]Therefore the proportion was 0.4418
Now finish solving the equation. What is the value of m?-(m - 6) = 3m + 14-m + 6 = 3m + 14-m + 6 - 3m = 3m + 14 - 3m-4m + 6 = 14m=
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The USDA collects and distributes a wide variety of data about agriculture in the United States. One statistic reported each year is the number of milk cows (in thousands) in each state. A random sample of 10 states is selected, with the number of milk cows reported in both 2011 and 2015.
State 2011 2015 Difference
North Dakota 19 16 -3
California 1769 1778 9
Nevada 29 29 0
Ohio 268 267 -1
New Hampshire 14 14 0
Colorado 128 146 18
Minnesota 468 460 -8
Oklahoma 53 39 -14
Utah 93 96 3
Washington 260 277 17
mean 310.1 312.2 2.1
sd 532.857 535.367 10.159
An agricultural researcher wants to conduct a paired difference test to determine if the mean number of milk cows (in thousands) in the US changed between 2011 and 2015.
Round all calculated values to 4 decimal places as appropriate.
1. Which hypotheses should be used to conduct the test?
A. H0:μdiff=0 vs. Ha:μdiff≠0
B. H0:μdiff<2.1 vs. Ha:μdiff>2.1
C. H0:μdiff=0 vs. Ha:μdiff<0
D. H0:μdiff=0 vs. Ha:μdiff>0
2. Assume the conditions for the hypothesis test are met and find the test statistic and the p-value.
test statistic =
p-value =
3. Based on the p value we have
?
evidence that the null model is not a good fit for our observed data.
4. Construct a 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015.
Answers
1. The hypothesis tested are given as follows: A. H0:μdiff=0 vs. Ha:μdiff≠0.
2.
The test statistic is of: t = 0.65.The p-value is of: 0.26603. Based on the p-value, we do not have enough evidence that the null model is not a good fit for our observed data.
4. The 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015 is of (-8.34, 12.54).
What are hypothesis tested?At the null hypothesis, it is tested if there has not been change, that is, if the mean is of zero, hence:
H0:μdiff=0
At the alternative hypothesis, it is tested if there has been change, hence:
Ha: μdiff≠0
Considering a two-tailed test, as we are testing if the mean is different of a value, with 10 - 1 = 9 df, and a significance level of 1 - 0.99 = 0.01, the critical value is of:
|t| = 3.25.
What is the test statistic?The test statistic for the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters in this problem are given as follows:
[tex]\overline{x} = 2.1, s = 10.159, n = 10, \mu = 0[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{2.1 - 0}{\frac{10.159}{\sqrt{10}}}[/tex]
t = 0.65.
What are the p-value and the conclusion?Considering a two-tailed test, with t = 0.65 and 10 - 1 = 9 df, the p-value is of:
0.2660.
What is the confidence interval?The confidence interval is given as the estimate plus/minus the multiplication of the critical value and the standard error.
Hence the lower bound of the interval is of:
2.1 - 3.25x10.159/sqrt(10) = -8.34.
The upper bound of the interval is of:
2.1 + 3.25x10.159/sqrt(10) = 12.54.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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