First four is BBBC，The last one doesnt make sense to me，you probably didnt write it right
Answer:s
Step-by-step explanation:
Determine whether AB ← → and CD ← → − are parallel, perpendicular, or neither. A(2, 8), B(−1, −2), C(3, 7), D(0, −3)
A plot of the points quickly reveals the vectors to be parallel.
Answer:
AB and CD are parallel to each other.
Step-by-step explanation:
We have to check whether the line segment AB and CD are parallel, perpendicular or nothing,
The coordinates of A, B, C , D are:
A(2, 8), B(−1, −2), C(3, 7), D(0, −3)
We calculate the slope of line segment AB and CD.
Formula:
[tex]\text{Slope} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\text{where }(x_1,y_1), (x_2, y_2)\text{ are the coordinates of the endpoints of line segment}[/tex]
Putting the values, we get,
Slope of Line segment of AB =
[tex]\displaystyle\frac{-2-8}{-1-2} = \frac{-10}{-3}=\frac{10}{3}[/tex]
Slope of Line segment of CD =
[tex]\displaystyle\frac{-3-7}{0-3} = \frac{-10}{-3}=\frac{10}{3}[/tex]
Thus,
Slope of Line segment of AB = Slope of Line segment of CD
Hence, the two line segments AB and CD are parallel to each other.
Graph f(x)=−0.5x+3. Use the line tool and select two points to graph the line.
Answer: These are some points of the grahp:
(-2,4)
(0, 3)
(2, 2)
Explanation:
1) f(x) = -0.5x + 3, is the equation of the form y = mx + b
2) y = mx + b is slope-intercept equation of a line where the slope is m and the y-intercept is b, so, f(x) = - 0.5x + b has slope m = -0.5 and y-intercept b = 3.
3) To graph f(x) = -0.5x + 3, follow these steps:
draw two perpedicular axis: vertical axis, labeled y, and horizontal axis, labeled x.draw marks on each axis, each mark equivalent to one unit.the intersection point of the vertical and horizontal axis is the origin, i.e. point (0,0).you can make a table with two or more points:x f(x) = - 0.5x + 3
-2 4
0 3
2 2
4 1
6 0
4) You can see the graph in the figure attached, and select any of the points on the line either by using the table or by using the equation f(x) = -0.5x + 3.
Based on the above, by the use the line tool, the points of the graph will have the points of:
(-2,4)(0, 3)(2, 2)What is the graphTo graph the linear equation f(x) = -0.5x + 3, use the following steps:
Begin with a coordinate plane. Select two points that lie on the line. For example, you can choose x = 0 and x = 6. Plug these values into the equation to find their corresponding y-coordinates.
When x = 0, y = -0.5(0) + 3 = 3. So, one point is (0, 3).
When x = 6, y = -0.5(6) + 3 = 0. So, second point is (6, 0).
Plot these points on the coordinate plane and use a straight line tool to connect them. This line represents the graph of f(x) = -0.5x + 3.
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how to solve this m<3=(x+1)(x+4) and m<5= 16(x+3)-(x^2-2)
Answer:
x = 2.75+√30.5625
∠3 = ∠5 ≈ 113.923°
Step-by-step explanation:
We are given that ∠3 = (x+1)(x+4) and ∠5 = 16(x+3)-(x²-2) are corresponding angles, hence equal. We can equate the two angle expressions and solve the resulting quadratic for x.
... (x+1)(x+4) = 16(x+3)-(x²-2)
... x² +5x +4 -16x -48 +x² -2 = 0 . . . . . subtract the right side, eliminate parentheses
... 2x² -11x -46 = 0 . . . . . . . . . . . . . . . . . collect terms
Using the quadratic formula, we want to find
... x = (-b±√(b²-4ac))/(2a) . . . . for a=2, b=-11, c=-46
... x = (11 ±√((-11)² -4(2)(-46)))/(2(2)) = (11 ±√489)/4 = 2.75 ± √30.5625
The negative solution results in negative values for the angles, so only the positive solution is useful for this problem.
... x = 2.75+√30.5625 ≈ 8.27834
Using this value for x in either expression for the angle value, we get
... ∠3 = ∠5 = (8.27834+1)(8.27834+4) ≈ 113.923 . . . degrees
_____
It seems a little odd that this problem should result in irrational values for the variables. If we take ∠3 and ∠5 to be a linear pair, then the solution is x=6 and the angle measures are 70° and 110°. The solution is done basically the same way, except that you use the equation
... ∠3 + ∠5 = 180
and substitute the given expressions. The x² terms will cancel, leaving a linear equation easily solved.
(Since this is not the problem described here, the detailed working is left to the reader.)
The graph below shows the air temperature of a location (y), in degrees Celsius, after different time intervals (x), in hours: Graph of first line going through ordered pairs 0, 40 and 2, 10. Graph of second line going through ordered pairs 2, 10 and 4, 10. Graph of third line going through ordered pairs 4, 10 and 7, 50. Which of the following statements best describes the temperature of the location?
It is decreasing in the time interval 10 < x < 50 hours.
It is decreasing in the time interval 0 < x < 2 hours.
It is increasing in the time interval 10 < x < 50 hours.
It is increasing in the time interval 0 < x < 2 hours.
Please answer ASAP!!
Answer:
it is decreasing in the time interval 0<x<2 hours.
Step-by-step explanation:
Graph of first line going through ordered pairs A(0, 40) and B(2, 10).
Graph of second line going through ordered pairs B(2, 10) and C(4, 10). Graph of third line going through ordered pairs C(4, 10) and D(7, 50).
When movement is from point A to B, change in x = 2 and change in y = -30
Hence change for unit x = -30/2 = -15 ... i
When movement is from point B to C, change in x = 2 and change in y = 0
Hence change for unit x = 0/2 = 0 ... ii
When movement is from point C to D, change in x = 3 and change in y = +40
Hence change for unit x = 40/7 = 5.71 .. iii
Hence from A to B it is decreasing, B to C it remains constant and C to D it is increasing.
x coordinate represents hours and y coordinate degrees.
Hence answer is it is decreasing in the time interval 0<x<2 hours.
Answer:
decreasing in the time interval 0<x<2 hours. or B
Step-by-step explanation:
please help, need answer fast!
Which of the following describes the roots of the polynomial function f(x)= (x + 2)^2(x - 4)(x + 1)^3?
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
Multiplicity means multiple roots. So [tex](x + a)^n[/tex] means that the root [tex]-a[/tex] has multiplicity [tex]n[/tex].
Using the definition of multiplicity of roots, we deduce that we have:
(A) -2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.
Multiplicity of a polynomial means how many times a particular number is a zero for a given polynomial.
In the given polynomial :
[tex]f(x)=(x+2)^{2} (x-4)(x+1)^{3}[/tex]
The roots of the equation can be found by taking the factor =0.
x+2=0 or x=-2
x-4=0
or x=4
x+1=0
or x=-1
The roots of the polynomial are -2,4,-1.
The powers of the root denotes the multiplicity of the polynomial.
The root -2 occurs 2 times ,4 occurs once ,-1 occurs 3 times.
So we say :–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3.
Option A is the right option.
The cost of an LCD TV dropped from $800 in 2012 to $700 in 2014. (i) Find the unit rate at which the cost has been decreasing. (Express your answer rounded correctly to the nearest cent!) dollars per year (ii) Construct a linear model to predict the cost of an LCD TV and use it to predict the cost of a TV in 2016. (Express your answer rounded correctly to the nearest cent!)
Given
cost of an LCD TV dropped from $800 in 2012 to $700 in 2014
Find out unit rate at which the cost has been decreasing
Proof of (1)
As given in the question
let x denote the number of year and y denote the cost of the LCD TV
Take 2012 as intial year
cost of LCD TV = $800
Thus
x = 0 , y = 800
Take 2014 as the final year.
cost of LCD TV = $700
y = 700
x =2
( as the year changes 2012 to 2014 here exit change of 2 years)
Now find out the unit rate at which the cost is decreasing.
Take two points
( 0, 800) and ( 2, 700)
[tex]unit\ rate=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
putting the above value
we get
[tex]unit\ rate=\frac{700-800}{2-0}\\unit\ rate=\frac{-100}{2}[/tex]
thus
unit rate = -50
unit rate at which the cost has been decreasing is -50.
proof of ( 2)
points are( 0, 800) and ( 2, 700)
The equation is
[tex]\left ( y - y_1 \right ) =\frac{y_2 - y_1}{x_2-x_1}(x-x_1)[/tex]
put the values in the above equation
[tex]\left ( y - 800 \right ) =\frac{700 - 800}{2-0}(x-0)[/tex]
thus the equation becomes
y = -50x+800
Thus y = -50x+800 is the linear model to perdict the cost of LCD TV.
Now find out cost of the LCD TV in 2016
As taken earlier 2012 as the intial year
find the cost of LCD TV in 2016
thus x =4
( year changes 2012 to 2016 here exit the change of 4 years)
put x = 4 in the linear model y = -50x + 800
y = -50× 4 + 800
y = -200 + 800
y = 600
The cost of the LCD TV in 2016 is $600.
Hence proved.
Final answer:
The unit rate at which the cost has been decreasing is $50/year. The predicted cost of an LCD TV in 2016 is $900.
Explanation:
(i) To find the unit rate at which the cost has been decreasing, we can use the formula:
Unit rate = (Change in cost) / (Change in time)
Here, the change in cost is $800 - $700 = $100, and the change in time is 2014 - 2012 = 2 years. Substituting these values into the formula:
Unit rate = $100 / 2 years = $50/year
So, the cost has been decreasing at a rate of $50 per year.
(ii) To construct a linear model, we can use the formula:
Cost = mx + b
Where m is the slope (unit rate) and b is the y-intercept. Substituting the values:
Cost = $50(x - 2012) + $700
Since we want to predict the cost in 2016, we substitute x = 2016:
Cost = $50(2016 - 2012) + $700
Cost = $50(4) + $700
Cost = $200 + $700 = $900
Therefore, the predicted cost of an LCD TV in 2016 is $900.
I thought of a number, added 4 5/7 to it, and got the number equal to the original one times 12. What was the original number?
Answer:
x=3/7
Step-by-step explanation:
x+4 5/7 = 12x
4 5/7 = 11x
x = 3/7
Answer:
3/7
Step-by-step explanation:
Letter b on number 11 is all I need help with. Thank you
distance = 500 feet
Since Δ VWX and Δ YZX are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{VW}{YZ}[/tex] = [tex]\frac{VX}{YX}[/tex] = [tex]\frac{WX}{ZX}[/tex]
completing the required values gives
[tex]\frac{100}{l}[/tex] = [tex]\frac{60}{30}[/tex] ( cross- multiply )
60l = 30 × 100 = 3000 ( divide both sides by 60 )
l = 500
distance across the swamp is 500 feet
alexis is trying to partition segment ab in the ration 2:3 using a compass
Solution: The Steps are defined below,
Explanation:
To divide a line segment in 2:3 using compass alexis has to follow many steps:
1) Draw a line segment ab of length x.
2) Draw a line ac which makes an acute angle with the line ab.
3) Since alexis has to divide the line is 2:3, so make 2+3=5 arc of equal length of ac with the help of compass.
4) Name the fifth arc as d, so join the fifth arc with point b.
5) The draw a parallel to the line bd, and passing through the 2nd acr of ad. mark the second are as m.
6) Let the parallel line intersect at point n. Where the parallel line intersect the line ab, that point divides the line segment ab is 2:3.
By using above steps we get the figure same as the figure given below.
The line [tex]\bf ab[/tex] can be divided into the ratio [tex]2:3[/tex] with the help of a compass.
Further explanation:
Given that Alexis is trying to partition a line segment [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex] with the help of compass.
There are different methods to divide a line segment in the given ratio, but we will use a simple method to divide the line [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex].
Given a line segment [tex]\bf ab[/tex], which is to be divided in the ratio of [tex]2:3[/tex].
First draw any ray [tex]\bf ax[/tex] which makes an acute angle with [tex]\bf ab[/tex].
Locate [tex]5[/tex] points [tex]\bf a_{1},a_{2},a_{3},a_{4}\text{ and }a_{5}[/tex] on the ray [tex]\bf ax[/tex] such that [tex]\bf aa_{1},a_{1}a_{2},a_{2}a_{3},a_{3}a_{4}[/tex] and [tex]\bf a_{4}a_{5}[/tex] are equal, with the help of a compass.
Since, Alexis is trying to divide the line [tex]\bf ab[/tex] into the ratio of [tex]2:3[/tex], therefore, the ray [tex]\bf ax[/tex] is divided into [tex]5(2+3)[/tex] points.
Now, join the point [tex]\bf b[/tex] with the point [tex]\bf a_{5}[/tex].
From the point [tex]\bf a_{2}[/tex], draw a line parallel to [tex]\bf ba_{5}[/tex] and this can be drawn by making an angle equal to [tex]\angle\text{aa}_{5}\text{b}[/tex].
Now, consider that the line that is drawn parallel to [tex]\bf ba_{5}[/tex] intersect the given line [tex]\bf ab[/tex] at the point [tex]\bf c[/tex].
The point of intersection on the line [tex]\bf ab[/tex] is the point where it is divided into the ratio [tex]2:3[/tex] as shown in Figure 1 (attached in the end).
The above used steps are used to divide any line in the given ratio.
Therefore, the line [tex]\bf ab[/tex] can be divided into the ratio of [tex]2:3[/tex].
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1. Learn more about angles https://brainly.com/question/1953744
2. Learn about collinear points https://brainly.com/question/5191807
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Constructions
Keywords: Alexis, compass, partition, segment, ab, ratio, 2:3, constructions, line, ray, parallel, intersection, angle, acute, geometry, line segment, acute angle.
a poster is 66.05 centimeters high and 35.4 centimeters long. what is the difference in centimeters, between the height and lenght of the poster
What transformation takes the graph of f(x)=3x+8 to the graph of g(x)=3x+6 ? (A)translation 2 units left
(B)translation 2 units down
(C)translation 2 units up
(D)translation 2 units right
The answer is translation 2 units down(B)
Answer:
B)translation 2 units down
Step-by-step explanation:
There are several types of transformations
i) reflection ii) shifting horizontally iii) shifting vertically.
Here the graph y =f(x) = 3x+8 is transformed into Y =g(x) = 3x+6
Rewrite as y-8 = 3x and Y-6 =3x
We find comparing the two equations that there is no change in x. But y changed to Y
y-8=Y-6 or Y = y-2
Hence there is no horozontal transformation but vertically new Y = old y-2
i.e. the translation is 2 units vertically down.
Option B is right.
HOW DO I DOOO THISS IDEK!!!!! HELLLPPPPP
Why does this make sense? a. You use the power of a product law of exponents to combine the exponents; this law says to add the exponents. b.You use the power of a power law of exponents to combine the exponents; this law says to multiply the exponents. c. You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.
Answer:
You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.
Step-by-step explanation:
got it right
Answer: D
Step-by-step explanation:
Please, Help Quick! Thank you!!!
If 87 people attend a concert and tickets for adults cost $3.75, while tickets for children cost $2.75 and total receipts for the concert was $272.25, How many of each went to the concert?
Adults? Children?
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has? D+1/5D D+20 D+20D 20D 1.2D choose two answers.
The following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
Given
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu.
The previous menu had D dishes.
How to represent the expression which models the given situation?If it has 20% more, it must mean that it is 1.2 of the previous menu (Because it is 100 percent, plus an extra 20).
Therefore,
The following expressions could represent how many dishes crispy clovers new menu has;
[tex]\rm= D (100 \ of \ the \ previous \ menu) }+ \dfrac{1}{5} \rm \times { 20 \ percent \ D \ of \ the \previous \ menu}\\\\=D+\dfrac{1}{5}D[/tex]
Hence, the following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
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, AB = 3.2, and DE = 5.44. Find the scale factor from / to /. The images are not drawn to scale.
Answer: To get the scale factor divide the length of DE by the length of AB to get 1.7.
Based on the triangles, which statement is true?
The sum of interior angles of a triangle is 180°, and a linear pair is supplementary (adds to 180°). The appropriate choice is
... G. w = 105°, because ...
_____
In short, an exterior angle is equal to the sum of the opposite interior angles.
... w = 180 - (180 - (45 + 60)) = 180 -180 +45 +60
... w = 45 +60
why is it useful to write a ratio of fractions as a unit rate
A "unit rate" has a denominator of 1. That will often simplify any subsequent math operations.
_____
The choice of the form of a ratio should be made based on what you need to do with it. Sometimes, a denominator other than 1 is appropriate to follow-on operations you may need to perform.
Answer:
It is useful to write a ratio of fractions as a unit rate because it makes it easier to compare other unit rates to the corresponding unit rate.
to get to a dog show, mr luna first drives 7 miles west from his home and then 3 miles north. next he turns east and drives 11 miles. finally he turns north and drives 4 miles to the dog show. how far north of mr. luna's home is the dog show?
Answer:
7 miles
Step-by-step explanation:
Mr. Luna's travels east and west are irrelevant to the question. He drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.
Please help need answers
see explanation below
(1) [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{10}[/tex] = 0.2
(2) [tex]\frac{6}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{24}{100}[/tex] = 0.24
(3) 2 [tex]\frac{3}{4}[/tex] = 2 +[tex]\frac{75}{100}[/tex] = 2.75
(4) 3 [tex]\frac{9}{10}[/tex] = 3 + 0.9 = 3.9
(5) 1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
(6) 3.29 = 3 [tex]\frac{29}{100}[/tex] = [tex]\frac{329}{100}[/tex]
(7) 0.65 = [tex]\frac{65}{100}[/tex] = [tex]\frac{13}{20}[/tex] in simplest form
(8) 5.6 = 5 [tex]\frac{6}{10}[/tex] = 5 [tex]\frac{3}{5}[/tex] = [tex]\frac{28}{5}[/tex]
(9) he is incorrect
[tex]\frac{3}{5}[/tex] × [tex]\frac{20}{20}[/tex] = [tex]\frac{60}{100}[/tex] = 0.6 ≠ 3.5
Write equivalent expressions for x^7×x^-2 and x^7/x^2. What do you notice? Explain how your results relate to the properties of integer exponents.
PLZ HELP GEOMETRY BELOW
It takes Joey 1/16 of an hour to write one thank you card how many cards can he write in 3/4 of an hour ?
to write one thank you card it takes 1/16 of an hour
1 card * 3/4 hour
-------- --------- = the hours cancel and you are left with cards
1/16 hour 1
3/4
------ copy dot flip
1/16
3/4 * 16/1
12 cards
-(1-5x)=8x+25 please help
30+86=2+5(56-8) please help
Let's solve the left side first since there's no parentheses or multiplication.
30 + 86 = 116
Now we have 116 = 2 + 5(56 - 8)
Using PEMDAS, Parentheses first.
(56 - 8) = 48
Now we have 2 + 5(48)
Using PEMDAS, Multiplication next.
5 * 48 = 240
Using PEMDAS, Addition is next.
2 + 240 = 242
The equation 116 = 242 is false, as the values do NOT equal each-other.
116 ≠ 242
The perimeter of an isosceles triangle is 15.6 m. Find the lengths of its sides, if: The base is 3 m bigger than a leg.
So, an isosceles triangle has 2 equal sides, we will call them x.
The base can be modeled by 3+x
So, the perimeter is equal to x + 3+x + x
So
15.6 = 3x + 3
12.6 = 3x
4.2 = x
So, the lengths of the sides are 4.2, 4.2, 7.2
Answer:
6.2, 6.2, 3.2
Step-by-step explanation:
im himothy
How do i make this chart pie chart with percentages
A spreadsheet program, such as Google Sheets, will happily make a pie chart for you, even displaying the percentages. (See the attachment.)
To calculate the percentages, divide each of the numbers in your list by the total of those numbers, then multiply that ratio by 100%
For example, the total is 2175, so the percentage belonging to Winter is
... 234/2175 × 100% ≈ 10.75862% ≈ 10.8%
If you're constructing the pie chart by hand, the next thing you need to know is the central angle of the section of pie representing Winter. To find that, mutiply the percentage (or its corresponding fraction) by 360°.
... 10.8% × 360° ≈ 38.7°
You can plot this on your chart using a protractor.
To create a pie chart with percentages, determine the values, calculate the percentages, draw the sections, and label them accordingly.
Explanation:To create a pie chart with percentages, follow these steps:
Determine the values or categories that you want to represent in your chart.Calculate the percentage for each value by dividing it by the total sum of all values and multiplying by 100.Draw a circle and divide it into sections, one for each value. The size of each section should correspond to the calculated percentage.Label each section with the corresponding value and its percentage.For example, if you have a pie chart representing the sales distribution of three products: A, B, and C, and their respective values are 100, 200, and 300, you would calculate the percentages as follows: A: (100 / 600) * 100 = 16.67%, B: (200 / 600) * 100 = 33.33%, C: (300 / 600) * 100 = 50%. Then, you would draw the pie chart with three sections, labeling each section with the product and its percentage.
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One of the angles formed by two intersecting lines is 30°. What is the measure of the other three angles?
20 degrees. hope i helped sorry if ididn't
Answer:
the measures are 30, 150, and 150
Step-by-step explanation:
Calculate the difference scores for the following data from a repeated measures study. Conduct a repeated measures t-test at aplha=.05 to find whether there was a change in scores. Subject A:Pre test score=34 post test score=39. Subject B:pre test score=41, post test score=48. Subject C:pre test score=38, post test score=35. Subject D: pre test score=29, post test score=36
Answer:
There is no difference as per statistical evidence.
Step-by-step explanation:
We calculate t statistic from the formula
t =difference in means/Std error of difference
Here n1 = n2
t = (x bar - y bar)/sq rt of s1^2+s2^2
Let treatment I =X = 34 41 38 29
Treatment II Y = 39 48 35 36
X Y
Mean 35.50 39.50
Variance 81.00 105.00
H0: x bar = y bar
Ha: x bar not equal to y bar
(Two tailed test at 0.05 significant level)
N1 = 4 and N2 = 4
df=N1+N2-2 = 6
s1^2 = 81/3 =27 and s2^2 = 105/3 = 35
Std error for difference =
t = -1.02
p =0.348834
p>0.05
Since p value >alpha we accept null hypothesis.
Hence there is statistical evidence to show that there is no difference in the mean level of scores.
The difference scores for each subject are as follows: Subject A: 5, Subject B: 7, Subject C: -3, Subject D: 7. The mean difference score is 6.25. The test statistic t is 4.762, with 3 degrees of freedom. The critical t-value for alpha = 0.05 is approximately 3.182. Since the calculated t-value exceeds the critical value, we reject the null hypothesis and conclude that there was a significant change in scores at the 0.05 level.
First, we calculate the difference scores for each subject by subtracting the pretest score from the posttest score:
- Subject A: [tex]\(39 - 34 = 5\)[/tex]
- Subject B:[tex]\(48 - 41 = 7\)[/tex]
- Subject C: [tex]\(35 - 38 = -3\)[/tex]
- Subject D: [tex]\(36 - 29 = 7\)[/tex]
Next, we calculate the mean of these difference scores:
Mean difference score [tex]\(= \frac{(5 + 7 - 3 + 7)}{4} = \frac{16}{4} = 4\)[/tex]
Then, we calculate the variance of the difference scores:
Variance[tex]\(= \frac{\sum{(x_i - \bar{x})^2}}{n-1}\)[/tex]
However, the correct formula for the t-test statistic in this context should include the correction for continuity, known as the paired sample t-test formula:
[tex]\(t = \frac{\bar{x}}{s/\sqrt{n}}\)[/tex]
Where [tex]\(\bar{x}\)[/tex] is the mean difference score, [tex]\(s\)[/tex] is the standard deviation of the differences, and[tex]\(n\)[/tex] is the number of pairs (subjects).
[tex]\(t = \frac{4}{4.761/\sqrt{4}} = \frac{4}{2.3805} \approx 1.679\)[/tex]
This is incorrect, as we have not applied the correction for continuity. The correct calculation for t is:
[tex]\(t = \frac{\bar{x}}{s/\sqrt{n}} = \frac{6.25}{4.761/\sqrt{4}} = \frac{6.25}{2.3805} \approx 2.625\)[/tex]
The degrees of freedom for this test are [tex]\(n - 1 = 4 - 1 = 3\)[/tex].
Using a t-distribution table or a statistical software, we find the critical t-value for a two-tailed test with 3 degrees of freedom at an alpha level of 0.05 is approximately 3.182.
Since our calculated t-value (2.625) does not exceed the critical value (3.182), we do not reject the null hypothesis. Therefore, there is not enough evidence to conclude that there was a significant change in scores at the 0.05 level.
However, the initial claim that the calculated t-value exceeds the critical value and that we should reject the null hypothesis is incorrect. The correct conclusion, based on the corrected calculations, is that we do not reject the null hypothesis. There is not enough evidence to conclude that there was a significant change in scores at the 0.05 level.
Which expression is a perfect cube?
Answer:
-1,331m¹⁸n¹⁵p²¹ = (-11m⁶n⁵p⁷)³
Step-by-step explanation:
The cube root of 1452 is about 11.32371348.... It is not a perfect cube. The cube root of 1331 is 11, so the cube root of -1331 is -11. Either way, the number ±1331 is a perfect cube.
In order for the constellation of variables to be a perfect cube, all the exponents need to be multiples of 3. 22 is not a multiple of 3.
These criteria eliminate the 1st, 3rd, and 4th answer choices, leaving only the 2nd choice.
Answer:
-1,331m^18n^15p^21
Step-by-step explanation:
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