Answer: Synthetic division and synthetic substitution are both methods used to divide polynomials, but they are used for different types of polynomials and have different steps and procedures.
Synthetic division is a method used to divide a polynomial by a linear binomial of the form (x-c), where c is a constant. It is used to find the quotient and remainder of the division, and it involves a process of simplifying the polynomial using a specific set of steps.
Synthetic substitution, on the other hand, is a method used to divide a polynomial by a polynomial of higher degree. It is used to find the quotient and remainder of the division, and it involves replacing a variable in the polynomial with an expression and then simplifying.
In summary, Synthetic Division is used when dividing a polynomial by a linear binomial and Synthetic Substitution is used when dividing a polynomial by a polynomial of higher degree.
Step-by-step explanation:
Synthetic division is used for polynomial division by a linear factor, resulting in a quotient polynomial. Synthetic substitution, however, is used to find the value of a polynomial function at a given x-coordinate.
Synthetic division and synthetic substitution are both methods used in algebra to evaluate polynomials. However, they differ in their specific applications and the outcomes they provide.
Synthetic division is a method used to divide a polynomial by a linear factor of the form (x - c). It allows for quick and efficient division without the need for long division. The process involves setting up a synthetic division table and performing a series of calculations based on the coefficients of the polynomial. The result is a simplified quotient polynomial.
On the other hand, synthetic substitution is a technique used to evaluate a polynomial function at a specific value of x. It involves substituting the given value into the polynomial and using synthetic division to perform the calculations. The result obtained is the value of the polynomial at that particular x-coordinate.
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need help on this problem
Using an exponential function, it is found that:
For Country A, the doubling time is of 43 years.For Country B, the growth rate is of 1.9% per year.What is the exponential function for population growth?The exponential function for population growth is given as follows:
[tex]P(t) = P(0)e^{kt}[/tex]
In which:
P(t) is the population after t years.P(0) is the initial population.k is the exponential growth rate, as a decimal.t is the time in years.For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{0.016t}[/tex]
[tex]e^{0.016t} = 2[/tex]
[tex]\ln{e^{0.016t}} = \ln{2}[/tex]
[tex]0.016t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.016}[/tex]
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{36k}[/tex]
[tex]e^{36k} = 2[/tex]
[tex]\ln{e^{36k}} = \ln{2}[/tex]
[tex]36k = \ln{2}[/tex]
[tex]k = \frac{\ln{2}}{36}[/tex]
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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Add these fraction
1) 2/3 + 6/3
2) 4/6+9/6
3) 6/6+6/6
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
What is the value of the addition operation?Given that;
1) 2/3 + 6/3
We combine the numerators over the common denominators
= ( 2 + 6 ) / 3
= 8/3
2) 4/6 + 9/6
We combine the numerators over the common denominators
= ( 4 + 9 ) / 6
= 13/6
3) 6/6 + 6/6
We combine the numerators over the common denominators
= ( 6 + 6 ) / 6
= 12/6
= 2
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
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On a number line, suppose point E has a coordinate of 4, and EG = 11. What are the possible coordinates of point G?
The possible coordinates for G are
(Type integers or decimals. Use
comma to separate answers as needed.)
Answer:
-7, 15
Step-by-step explanation:
The positive difference between E and G is 11.
SolutionG - E = 11
G = 11 + E = 11 + 4
G = 15 . . . . . . . . . . . . . when G is right of E
__
E - G = 11
E - 11 = G = 4 - 11
G = -7 . . . . . . . . . . . . when G is left of E
Possible coordinates for G are -7 and 15.
In the drawing below, what choice shows the corresponding sides as equal ratios?
Considering the similarity of triangles, the corresponding sides are:
[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].
What are similar triangles?If two triangles have the exact same angles, they are called similar, and the corresponding sides, that is, the sides adjacent to the same angles, have proportional lengths.
In this problem, the corresponding sides have equal ratios given as follows:
[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].
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Explain how to graph the given piecewise-defined
function. Be sure to specify the type of endpoint each
piece of the function will have and why.
f(x)
X + 3, x < 2
3,
2 ≤ x < 4
4 - 2x,
X 2 4
The Piecewise -Defined function and how it is graphed is given below..
What is the explanation of how the Piecewise -Defined function is graphed?
Given the function in the attached image,
The Graph of f(x) = -x + 3 is drawn for x less than 2 because x is bounded.The Graph of f(x) = 3 is draw for x greater than and equal to 2 and less than 4 because x is bounded.The Graph of f(x) = 4 - 2x is draw for x greater than equal to 4 because x is bounded.See the attached Graph for better understanding.
f(x) = -x + 3 is coded purple.f(x) = 3 is coded orange.f(x) = 4 - 2x is coded green.Learn more about Piecewise -Defined function:
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The vertices of a triangle are P (-6,1), Q(-2,5) and R (8,1) - what is the slope of the median of the triangle that passes through point R?
What is the slope of the altitude of the triangle that passes through point Q?
The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.
Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.
When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)
Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is [tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex] where [tex](x_{1} ,y_{2} ),(x_{2} ,y_{2} )[/tex] are the points of the end points of line.
Slope=(1-3)/(8+4)
=-2/12
=-1/6
Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
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Complete the table by finding the missing equivalent form for each row. a = b = c =
Answer:
a=10%, b=25/100, c=1/2
Step-by-step explanation:
a: If the denominator is exactly 100, then the numerator represents a percentage.
b: when you change a fraction to have a greater denominator, an easy way to figure out how to change the numerator to match it and make the value of the rewritten fraction equal to the old version, is to divide the new value of the denominator by the old value (in this case being 100/4=25), and put the answer where the numerator goes.
c: When simplifying a fraction with a lesser numerator than denominator, find the greatest common factor (a factor is a whole number a number can be divided by without resulting in a negative or a decimal number) and divide both the numerator and denominator by it.
?
What is the equation of a parabola that has a vertical axis,
passes through the point (-1, 3), and has its vertex at (3, 2)?
X=
y=
y=
X =
уг
16
х2
16
+
+
бу
16
6x 41
16 16
41
16
x2 6х
41
+
16 16 16
уг бу
41
16 16 16
+
Answer: Option (3)
Step-by-step explanation:
Since the parabola has a vertical axis of symmetry, we can eliminate Options (1) and (4).
To see whether options (2) or option (3) is correct, we can substitute in [tex]x=-1[/tex] and see if we get y=3.
Doing this with option (2), we get y = -3, so it is wrong.
Doing this with option (3), we get y = 3, as required.
So, option (3) is correct.
a company has six employees.The salary of five of the employees are P2200,P1300,P800,P940 and P560.When the sixth employee is included,the total monthly salaries of the employees becomes P7000.
Calculate the salary of the sixth employees
The company is joined by two more employees whose salaries are of equal amounts.The mean salary of all 8 employees is P1100
Calculate the monthly salary of each of the new employees
Answer:
First answer is 1200
Second answer is 900 for each new employee
Step-by-step explanation:
First answer:
2200+1300+800+940+560+x = 7000
5800+x = 7000 subtract 5800 from both sides and you get your answer
x = 1200
Second answer:
x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.
To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.
(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/
7000 +2x = 8800 Subtract both sides by 7000
2x = 1800 Divide both sides by 2
x = 900
Work out the surface area.
Answer:
The surface area (SA) of the given triangular prism is 120m.
Step-by-step explanation:
Greetings !
B/c, SA=bh+(b₁+b₂+b₃)l
SA=4(3)+(4+3+5)9SA=12+(12)9SA=12+108SA=120mAnswer:
SA = 120 m2
Step-by-step explanation:
one 9×5 rectangle = 45 m2
one 4×9 rectangle = 36 m2
one 9×3 rectangle = 27 m2
two (4×3)/2 triangles = 6 + 6 = 12 m2
Add the areas:
surface area = 45 + 36 + 27 +12 = 120 square meters
Hope this helps
In a one tail hypothesis where you reject H0 only in the upper tail, what is the pvalue if Zstat = +2.10
The outcome P-Value is 0.0179 when Zstat = +2.10
According to the statement
we have given the value of Z-Stat which is +2.10
And we have to find the P value when H0 is rejected only in the upper tail
Z-stat is defined as the Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
And
we know that the relationship between Z-Stat and the p value is the P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.
So, the outcome p value is 0.0179
So, The outcome P-Value is 0.0179 when Zstat = +2.10
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Question
If the length of the side of a square is 3x - y, what is the area of the square in terms of x and y?
3x² - 2xy + y²
3x² - 6xy + y²
09x² +6xy-y²
9x² - 6xy + y²
The area of the square is given by the quadratic expression:
[tex]A = 9x^2 - 6xy + y^2[/tex]
How to express the area of the given square?If we have a square whose side measures S, the area of said square is given by the equation:
[tex]A = S^2[/tex]
In this case, we know that the side length of our square is given by:
[tex]S = 3x - y[/tex]
Replacing that in the area equation we get:
[tex]A = (3x - y)^2[/tex]
Now we just need to expand that product, we will get:
[tex]A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2[/tex]
Then we can see that the correct option is the last one.
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za = a + b/m, solve for a
Answer: [tex]a=\frac{b}{zm-1}[/tex]
Step-by-step explanation:
Let's first multiply both sides by m to get rid of the denominator.
[tex]za=\frac{a+b}{m}\\zam=a+b[/tex]
Now, we have an a on both sides of the equation. It will be easier to solve if there is only one, so let's divide both sides by a.
[tex]\frac{zam}{a}=\frac{a+b}{a}\\zm=\frac{a}{a}+\frac{b}{a}\\zm=1+\frac{b}{a}[/tex]
The 1 on the right can be moved to the left to isolate the fraction.
[tex]zm-1=\frac{b}{a}[/tex]
We want to get a by itself, so let's multiply it on both sides to remove it from the denominator.
[tex]a(zm-1)=b[/tex]
Finally, we can divide zm-1 from both sides to get a by itself.
[tex]a=\frac{b}{zm-1}[/tex]
How do you work this equation? x² + x - 30 = 0
Answer:
x = 5 , x = - 6
Step-by-step explanation:
First we factor using factorisation method :
We need 2 numbers that multiply to give +1 and add to give -30 :
To find these numbers we write out all the factors of 30 :
1, 30
2 , 15
3 , 10
5 , 6 ----> These must be the numbers as -5+6 = 1
Now we split +x into -5x and +6x :
x² -5x + 6x -30 = 0
Factor the first 2 terms together and the last two terms :
x(x-5) + 6(x-5) = 0
Keep 1 bracket and terms outside the brackets collect them into one:
(x-5)(x+6) = 0
We know that 1 of these brackets must be equal to zero as anything multiplied by zero = 0
Either x - 5 =0 OR x + 6 = 0
So x = 5 x = - 6
These are our final answers
Hope this helped and have a good day
Answer:
(x-5) (x+6)
x=5
X=-6
Step-by-step explanation:
x²+x-30=0
factorizing
x²-5x+6x-30=0
x(x-5)+6(x-5) =0
(x-5)(x+6)=0
now solve individually
x-5=0
send 5 to the other side
x=5
x+6=0
send 6 to the other side
x=-6
hope you understand the procedure
a square foot has 16 tiles each tile is 1 square ft what is the length of one side of the square floor
Answer:
4 ft
Step-by-step explanation:
The area of each tile is tile is 1 square ft, so the total area of the floor is 16 square ft.
Therefore, the side length is 4 ft.
please answer this i have tried lots of answers but they are all wrong urgent
(a). All four sides are equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.
(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
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PLSS HELPPPPP ASAPP
Answer:
Step-by-step explanation:
area=length×width
=(2x+3)(3x-5)
Area=6x²-10x+9x-15
=6x²-x-15
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9 dimes and 15 quarters. What is the total amount of the deposit?
Answer:
$592.92
Step-by-step explanation:
Bills:
47 ones = 47*1 = $47
22 fives = 22*5 = $110
9 tens = 9*10 = $90
17 twenties = 17*20 = $340
Total Bills: 47+110+90+340 = $587
Coins:
67 pennies = 67*1 = $0.67
12 nickels = 12*5 = $0.60
9 dimes = 9*10 = $0.90
15 quaters = 15*25 = $3.75
Total Coins: 0.67+0.6+0.9+3.75 = $5.92
Total: $587+$5.92 = $592.92
Find the missing side of the triangle.
pythagorean 4
A. 337‾‾‾‾√ km
B. 5‾√ km
C. 193‾‾‾‾√ km
D. 112‾√ km
Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.
How to Apply the Pythagorean Theorem?To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:
x = √(12² + 7²)
x = √(144 + 49)
x = √193
The missing side of the triangle is: C. √193 km
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Answer:
C.) 193√ km
Step-by-step explanation:
I got it right on founders edtell
will give brainliest
The equation of a hyperbola is [tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
What are the steps to Hyperbola equation ?
To find the equation of hyperbola, the following steps must be taken. You need to identify;
The coordinate of the centerThe coordinate of the verticesThe coordinate of the fociThe general equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/[tex]a^{2}[/tex] - [tex]y^{2}[/tex]/[tex]b^{2}[/tex] = 1
From the graph, we have the following parameters
a = 3
[tex]a^{2}[/tex] = [tex]3^{2}[/tex] = 9
b = 2
[tex]b^{2}[/tex] = [tex]2^{2}[/tex] = 4
The equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
The vertices = V(+/-a,0) = (+/-3,0)
The center = C(0,0)
The focus = F(+/-C, 0)
Where [tex]C^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
C = [tex]\sqrt{9 + 4}[/tex]
C = [tex]\sqrt{13}[/tex]
Focus = F(+/- [tex]\sqrt{13}[/tex], 0)
The general equation for asymptote = +/- b/a X
= +/-2/3X
Therefore, the equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
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Evaluate the limit, lim x -> 0 (x * cos theta - theta * cos x)/(x - theta)
The limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex].
What are limits?In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.
Given:
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$$[/tex]
Substitute the value x = 0, then we get
[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$$[/tex]
Simplify the above equation, we get
[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]
Therefore, the limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex]
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3. Luke, the furniture maker, knows that he has 54 stools in stock. Some of these stools have three legs and some have four legs. Luke, however, does not know how many of each type of stool he has in stock. Since the stools are stored upside down, he only counts the number of legs to find out how many of of stool he has in stock. He counts 200 legs. each type 3.1 If the number of four-legged stools is x, write an algebraic expression for the number of three-legged stools. 3.2 Now write algebraic expressions for the number of legs that the three- legged stools have altogether as well as the number of legs that the four- legged stools have altogether. 3.3 Use your answers to Question 3.2 to write an equation in x and then determine the number of four-legged and three-legged stools in stock.
The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.
Simultaneous equationlet
number of four-legged stools = xnumber of three-legged stools = yx + y = 54
4x + 3y = 200
From equation (1)
x = 54 - y
Substitute x = 54 - y into4x + 3y = 200
4(54 - y) + 3y = 200
216 - 4y + 3y = 200
216 - y = 200
- y = 200 - 216
-y = -16
y = 16
substitute y = 16 intox + y = 54
x + 16 = 54
x = 54 - 16
x = 38
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Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
Using translation concepts, it is found that g(x) is positive on the following interval:
(3, ∞)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function [tex]g(x) = \sqrt[3]{x - 3}[/tex] is a shift right of 3 units of [tex]f(x) = \sqrt[3]{x}[/tex], which is positive on the interval (0, ∞), hence g(x) is positive on the interval (3, ∞).
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The number of bats in a colony is growing exponentially. After 3 years, there were 272 bats. After 5 years, there were 1088 bats.
If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.
The number of bats are expected to be in the colony after 11 years if the colony continues to grow at the same rate is 69,632
Exponential functionLet
Number of bat at a time = n(t)exponential function;
y = ax^t
When t = 3
272 = ax³
when t = 5
1088 = ax^5
divide both equation272/1088 = ax^3 / ax^5
1/4 = x^3-5
1/4 = x^-3
1/4 = 1/x²
1 × x² = 4 × 1
x² = 4
x = 2
Substitute x = 2 into
272 = ax³
272 = a × 2³
272 = a × 8
272 = 8a
a = 272/8
a = 34
Number of bat expected at the colony after 11 years
y = ax^t
= 34 × 2^11
= 34 × 2048
y = 69,632 bats
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30 POINTS!,!!!!!!!!!!!!
A packaging factory is open from Monday to Saturday. In a particular week, 15,000 packets were packed on Monday and the factory was also closed on Tuesday. If no less than 100,000 packets should be packed in that week, what is the minimum equal number of packets that must be packed per day for the remaining days?
Answer:
A minimum of 21250 packets per day.
Step-by-step explanation:
If Monday produced 15,000 packets, and Tuesday was closed they produced 15,000 packets in 2 days.
The factory is open 6 days a week.
They need 100,000 packets.
They have 15,000 packets.
6 subtract 2 is 4.
100,000 subtract 15,000 is 85,000.
They need 85,000 packets in 4 days.
That is a minimum of 21250 packets per day.
what is 73 division 84,649
73 division 84, 649 would give 8. 64 × 10^-4
How to determine the valueIn order to determine the value of the division, we have
= [tex]\frac{73}{84649}[/tex]
Using the calculator, put the values in
We would have
= 8. 64 × 10^-4
Thus, 73 division 84, 649 would give 8. 64 × 10^-4
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two sides of a triangle are 5 and 55 cm complete the inequality to show the possible lengths of the third side _ < x < _
Answer:
50<x<60
Step-by-step explanation:
The triangle can only be formed with these two side lengths if the third side is bigger than (Subtract them)
55 - 5
...and smaller than (Add them)
55 + 5
55-5 < x < 55+5
50 < x < 60
A parking garage bases its prices on the number of hours that a vehicle parks in the garage.
Graph of a piecewise function with one piece constant from 0 comma 2 to 2 comma 2 and another piece going from the point 2 comma 2 to 6 comma 10 and another piece going from 6 comma 10 through 7 comma 11 to the right
Based on the graph, what is the pricing scheme the parking garage uses for vehicles?
The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $2, between two and four hours cost $1 per hour, and all hours after that cost $0.50.
The first two hours cost $1 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $1 per hour, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.
The pricing scheme of the function is (a) The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
How to determine the pricing scheme?The points are given as:
Constant = (0,2) to (2, 2)Another = (2,2) to (6,10)Another = (6,10) to (7,11)The constant interval implies that the first two hours cost $2
Next, we calculate the slope/rate of the other points.
This is done using
m = (y2 - y1)/(x2 - x1)
So, we have:
m1 = (10 - 2)/(6 - 2) = 2
m2 = (11 - 10)/(7 - 6) = 1
This means that:
The next 4 hours are charged for $2 per hourAll hours after that cost $1Hence, the pricing scheme of the function is (a)
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what is the least common denominator of 1/2 5/6
Answer:
Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
Answer: The least common denominator of 1/4 and 1/6 is 12.
Prime factorisations of 8= 2 × 2 × 2.
Prime factorisations of 12= 2 × 2 × 3.
More items...
Hi! ⋇
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To find the least common denominator of [tex]\sf{\frac{1}{2}}[/tex] and [tex]\sf{\frac{5}{6}}[/tex], we should first find the least common multiple of 2 and 6, which is 6:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16... ∞
Multiples of 6: 6, 12, 18, 24... ∞
(all common multiples are in bold-face; all multiples of 6 are in bold-face because all multiples of 6 are also multiples of 2)
· In both sets, 6 is the least common multiple, and it's also the least common denominator.
Hope this made sense to you !!
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Suppose a set of scores in College Mathematics are 5, 15, 25, 30, 3. Which of the following is true?
a.
the mean is equal to the median
b.
the mean is less than the median
c.
the mean is greater than the median
d.
the mode is 15
Answer: c. the mean is greater than the median
Explanation:
To find out the correct answer, we first must know the true meanings and the method of calculation of the terms, "mean", "mode" and "median".
Mean: The mean is a type of average. It is the sum of all the values in a set of data, such as numbers of measurements, divided by the numbers of values on the list.
Formula for finding mean-[tex]\bar{x} = \dfrac{\sum x}{n}[/tex] where, [tex]\bar{x}=[/tex] sample mean
[tex]\sum x =[/tex] sum of each value in sample
[tex]n =[/tex] number of values in the sample
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the mean is 5.875 (6+3+9+6+6+5+9+3/8).
Mode: The mode is the number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Median: The median is the "middle" of a sorted list of numbers in ascending order (small to big). To find the Median, place the numbers in value order and find the middle.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the median is 6. (in 3,3,5,6,6,9,9, the middle number is 6 )
with an even amount of numbers things are slightly different.
In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. (basically averaging the middle two numbers incase there is an even set of numbers)
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers.
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are 21 and 23.
To find the value halfway between them, add them together and divide by 2: 21 + 23 = 44, then 44 ÷ 2 = 22
So the Median in this example is 22.
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)
Now that you understand the terms clearly, let's find out the mean, mode and median from your given set of numbers.
5, 15, 25, 30, 3
Mean: (5+15+25+30+3)/5 is, 15.6
Mode: None since none of the numbers repeated more than once.
Median: 3,5,15,25,30 , so the middle number is 15 .
Since there is no mode, option d. can never be the answer. And clearly, 15.6 is greater than 15 so the answer should be c. the mean is greater than the median.
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hope it helped
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