Answer:
S7 = 175S17 = 2465Sn = 1/2(n³ +n)Step-by-step explanation:
The progression of sums is ...
1, 5, 15, 34, 65, ...
So, first differences are ...
4, 10, 19, 31
Second differences are ...
6, 9, 12, ...
Third differences are constant:
3, 3, ...
This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...
Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))
And this simplifies a little bit to ...
Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)
In simpler form, we have ...
Sn = 1/2(n³ +n)
Then the two terms we're interested in are ...
S7 = (1/2)(7³ +7) = 175
S17 = (1/2)(17³ +17) = 2465
Each term Sₙ consists of the sum of a triangular number of terms, which are given by
[tex]T_n = \displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
The triangular numbers are given recursively for n ≥ 1 by
[tex]T_n = T_{n-1} + n[/tex]
starting with T₀ = 0.
For example,
• S₁ = 1 and
[tex]\displaystyle S_1 = \sum_{k=T_0+1}^{T_1} k = \sum_{k=1}^1 k = 1[/tex]
• S₂ = 2 + 3 and
[tex]\displaystyle S_2 = \sum_{k=T_1+1}^{T_2} k = \sum_{k=2}^3 k = 2 + 3[/tex]
• S₃ = 4 + 5 + 6 and
[tex]\displaystyle S_3 = \sum_{k=T_2+1}^{T_3} k = \sum_{k=4}^6 k = 4 + 5 + 6[/tex]
Then the n-th term of the sequence we're considering is
[tex]S_n = \displaystyle \sum_{k=T_{n-1}+1}^{T_n} k = \sum_{k=T_{n-1}+1}^{T_{n-1}+n} k[/tex]
Expanding this sum, we have
[tex]S_n = \left(T_{n-1}+1\right) + \left(T_{n-1}+2\right) + \left(T_{n-1}+3\right) + \cdots + \left(T_{n-1}+n\right)[/tex]
There are n terms on the right side, and hence n copies of [tex]T_{n-1}[/tex], and the rest of the terms make up the next triangular number [tex]T_n[/tex] :
[tex]S_n = nT_{n-1} + 1 + 2 + 3 + \cdots + n[/tex]
[tex]S_n = nT_{n-1} + \displaystyle \sum_{k=1}^n k[/tex]
[tex]S_n = nT_{n-1} + T_n[/tex]
We have a closed form for [tex]T_n[/tex], so we end up with
[tex]S_n = n \cdot \dfrac{(n-1)n}2 + \dfrac{n(n+1)}2 \implies \boxed{S_n=\dfrac{n^3+n}2}[/tex]
From here it's easy to find S₇ and S₁₇.
[tex]S_7 = \dfrac{7^3+7}2 \implies \boxed{S_7 = 175}[/tex]
[tex]S_{17} = \dfrac{17^3+17}2 \implies \boxed{S_{17} = 2465}[/tex]
HELP!!
is {(-3,-6),(-2,-1),(-1,-0),(0,3),(1,15)} a function??
It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.
The domain is {-3,-2,-1,0,1} which is the set of all x inputs.
The range is {-6, -1, 0, 3, 15} which is the set of y outputs.
Tom and Rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points. They let XXX represent the sum in a given turn, and they find the expected value of XXX is E(X)=17.5E(X)=17.5E, left parenthesis, X, right parenthesis, equals, 17, point, 5 points. Tom says, "A player will most likely get 17.517.517, point, 5 points in any given roll." Rosie says, "Over 100100100 turns, we can expect a total of about 175175175 points." Whose statement is correct based on the expected value?
Answer: neither statement is correct
Step-by-step explanation:
on Khan Academy
The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .
What is expected value?Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept.
According to the question
Tom and Rosie are designing a game.
In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn.
let X represent the sum in a given turn
the expected value of X is E(X)=17.5
As
expected value is also called mean value
i.e
highest value of sum = 6+6+6+6+6
= 30
Lowest value of sum = 1+1+1+1+1
= 5
Therefore,
Mean = [tex]\frac{30+5}{2}[/tex]
= 17.5
Now,
Tom says, "A player will most likely get 17.5
This statement is correct as per expected value which is mean value and it is 17.5 .
Rosie says, "Over 100 turns, we can expect a total of about 175
This statement is incorrect as per expected value as
expected value = 17.5
when 100 turn will happen it will
17.5 * 100
= 1750
Hence, The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .
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The cost C in dollars of producing a certain item is represented by the equation C = n/2+ 20. where n
represents the number of items produced. The revenue R, in dollars, from selling n items is represented by
the equation R=2n+ 5. For what value of n are the cost and revenue equal?
O 5
O 10
O 15
0 20
Considering the definition of equation, for a value of n of 10 the cost and revenue are equal.
What is equationA first degree equation is a mathematical equality with one or more unknowns.
Solving an equation consists of finding the value that the unknown must take so that equality is fulfilled.
The steps to solve an equation are as follows:
Group similar terms. That is, proceed to pass the terms containing variables from one side of the expression and the constants from the other side of the expression.Finally, the unknown is solved.Value of nThe cost C in dollars of producing a certain item is represented by the equation C = [tex]\frac{n}{2}[/tex]+ 20, where n represents the number of items produced.
The revenue R, in dollars, from selling n items is represented by the equation R=2n+ 5.
The cost and revenue are equal. Then:
[tex]\frac{n}{2}[/tex]+ 20= 2n+ 5
Solving:
When a term passes to the other side of equality, its sign changes (if it is positive it becomes negative and vice versa):
20 -5= 2n - [tex]\frac{n}{2}[/tex]
15= [tex]\frac{3}{2}n[/tex]
The X is cleared. Since the term in front of it is multiplying, it goes to the other side of the equation by dividing.
15 ÷[tex]\frac{3}{2}[/tex]= n
10= n
Finally, for a value of n of 10 the cost and revenue are equal.
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Help help math math math
Answer:
[tex]slope = \frac{20 - 16}{5 - 3} [/tex]
[tex] = \frac{4}{2} [/tex]
[tex] = 2 \: is \: the \: answer[/tex]
The slope of the equation is 2.
What is the slope of an equation?The slope of an equation shows a gradient line that measures the steepness of the line.
It can be expressed by using the formula:
[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]
[tex]\mathbf{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
From the parameters given;
The change in y distance from y2 to y1 The change in x distance from x2 to x1[tex]\mathbf{slope = \dfrac{20-16}{5-3}}[/tex]
[tex]\mathbf{slope = \dfrac{4}{2}}[/tex]
slope = 2
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If a plane travels 900kms in 3 hours what is its rate of speed expressed as a unit rate
Answer:
300kms
Step-by-step explanation:
900÷300 is 300. so then i think it would be 300kms
if your leg get cut off, where would you feel the pain if you got no leg. hehehe
Answer:
lol in your head , literally
Step-by-step explanation:
After one of your limbs is amputated, you may feel as if the limb is still there. This is called phantom sensation. You may feel: Pain in your limb even though it is physically not there.
Answer:
The nerve in your leg.
Explanation:
It's not your leg that will hurt but the nerve in your leg that'll hurt. So wherever the leg is cut, the nerves must be cut as well, but another thing is when one of your limbs is amputated, you may feel like the limb is still there. That's called phantom sensation. You might feel pain in your "limb" even though it's not physically there.
PLEASE HELP ME THIS IS THE 5TH TIME I HAVE HAD TO POST THIS AND GIVING BRAINLIST TO FIRST ANSWER
B.
C.
D.
Answer:
C.
Step-by-step explanation:
The position of a 2 kg object is given as x(t) = Bt2 +5, where x is in meters and t is in seconds. (a) Determine the force F responsible for this motion. (3) (b) If the force only results in a change in the kinetic energy of the object of 200 J between tı = 0 s and t2 = 5 s, determine the value of B. (3) (C) Without using kinematics (equations of motion), determine the displacement of the object during these 5 seconds referred to in part (b). (2)
(a) Given the position function
x(t) = (B m/s²) t² + 5 m
it's clear that the object accelerates at B m/s² (differentiate x(t) twice with respect to t), so that the force exerted on the object is
F(t) = (2 kg) (B m/s²) = 2B N
(b) Recall the work-energy theorem: the total work performed on an object is equal to the change in the object's kinetic energy. The object is displaced by
∆x = x(5 s) - x(0 s)
∆x = ((B m/s²) (5 s)² + 5 m) - ((B m/s²) (0 s)² + 5 m)
∆x = 25B m
Then the work W performed by F (provided there are no other forces acting in the direction of the object's motion) is
W = (2B N) (25B m) = 50B² J = 200 J
Solve for B :
50B² = 200
B² = 4
B = ± √4 = ± 2
Since the change in kinetic energy and hence work performed by F is positive, the sign of B must also be positive, so B = 2 and the object accelerates at 2 m/s².
(c) We found in part (b) that the object is displaced 25B m, and with B = 2 that comes out to ∆x = 50 m.
The following system of equations will be used to answer all remaining questions.
(8 - 12)
x + 2y = 11
2x + 3y = 18
=
Write the system as a matrix equation then identify the coefficient matrix.
The given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
Given the system of equation;
x + 2y = 11 2x + 3y = 18This equation can be represented in matrix form as [tex]AX = b[/tex]
where:
A is the coefficient of the matrixX is the variablesb is a column matrixThe given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
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Fill in the missing numbers below.
5 feet + 12 inches =
yard(s)
inches = 1 foot + 1 yard
feet = 3 feet + 24 inches
Answer:
2
Step-by-step explanation:
5 feet + 12 inches = 2 yards
Therefore
5 feet + 12 inches = yard(2)
I solving for (s)
hope that helps
can someone please tell me these answers
Answer: For Y the rate of change is +4
For the rate of x its +5
Step-by-step explanation:
Melllissa owns 4 sets of jewelry. Each set contains 2 earrings, 1 neckles, 1 bracelet, 1 ring. How many pieces of jewelry does Melissa have all together?
Answer:
The answer is to the problem is 18.
What is the value of x?
O
O x = 32
O x = 36
x = 37
(x + 15)
xº
(4x - 20)
O x = 40
Answer:
x + (4x-20) = 180
by linear pair
therefore x= 70
Applying the definition of linear pair, the value of x is: D. 40.
What is a Linear PairA linear pair is a set of angles on a straight line.Straight line angle = 180 degrees.Linear pair of angles add up to 180 degrees.Therefore:
x + (4x - 20°) = 180°
Solve for x5x - 20 = 180
5x = 180 + 20
5x = 200
Divide both sides by 5x = 40
Therefore, applying the definition of linear pair, the value of x is: D. 40.
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Jeremiah buys 6 tacos and 8 enchiladas for 60 dollars. Kennedy buys 3 tacos and 2 enchiladas for 18 dollars.
Answer:
What's the question lol
Select all equations that have 5
as a solution by using substitution to determine if the eqution is true.
Simplify 4 to the seventh power over 5 squared all raised to the third power . (4 points)
a
4 to the tenth power over 5 to the fifth power
b
4 to the fourth power over 5
c
4 to the twenty-first power over 5 to the sixth power
d
12 to the seventh power over 15 squared
The answer is C, 4 to the 21st over 5 to the 6th power.
Figure B is a scale image of Figure A, as shown.
7
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this: 42/53
Explanation:
Divide the side length for B over the corresponding side length for A.
scale factor = B/A = 7/(2.5) = 2.8
Let's now convert this to a fraction
2.8 = 2 + 0.8 = 2 + 8/10 = 20/10 + 8/10 = (20+8)/10 = 28/10
Then reduce that fraction
28/10 = (14*2)/(5*2) = 14/5
Note that 14/5 = 2.8
At the candy store, one pound of candy Cost $6.49. How much would it cost if Joey bought .79 pounds of candy ?
Answer:
5.12
Step-by-step explanation:
1 lb .79 lbs
------------ = -----------
6.49 x dollars
Using cross products
1x = 6.49 * .79
x =5.12 dollars
PLEASE HELP WILL MARK BRAINLIEST!
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve ~
[tex] \sf \sqrt{ {x}^{3} } [/tex][tex] \sf { ({x}^{3} ) }^{ \frac{1}{2} } [/tex][tex] \sf (x ){}^{3 \times \frac{1}{2 }} [/tex][tex] \sf{x {}^{ \frac{3}{2} } }[/tex]Hence, the required power in fractional form is ~
[tex] \sf \frac{3}{2} [/tex]The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)? Number of Hours Distance from Lighthouse (in oceanic miles) 2 53 4 95.5 6 138 8 180.5 10 223 12 265.5 14 308 16 350.5 A. y = 42.5x + 10.5 B. y = 10.5x + 32 C. y = 21.25x + 10.5 D. y = 12.25x + 28.5 E. y = 12.5x + 10.5
Answer:
ddd
Step-by-step explanation:
Avery had 25.92 in her wallet. If she bought lunch with 7 1/2 dollars from her wallet, how much did she have in her wallet after lunch?
Graph the equation. y= - 2x
Answer: The picture
Step-by-step explanation: if you mean graph that means graph the coordantes.
If f (x) = 3x + 2 and g(x) = x2 – x, find the value.
-
f (2)+1
Answer:
......
Step-by-step explanation:
What are the domain and range of the function below? (In picture)
Answer:
Domain: [0 , ∞)
Range: (-∞ , 4]
Step-by-step explanation:
I) DOMAIN:For domain, look along the x axis.
The graph starts from x = 0 and it's ending point isn't given in the graph as it continues moving along the positive x axis.
Hence, it's ending point must be ∞
Domain of a function is:
[minimum point in x, maximum point in x]
=> [0, ∞)
"),(" is used for infinity.
"],[" for points that lie within the domain of the function.
II) RANGEFor range, look along the y axis.
The graph starts at y = 4, and continues moving downwards till infinity.
Range:
[minimum in y, maximum in y]
=> (-∞, 4]
For parenthesis, same rule as domain will be applied. 4 is naturally greater than all values in negative. Hence, maximum point will be 4 and minimum will be -∞.What is the answer to the equation?
25. Which is a solution of the inequality y
(3,-5)
(2,-1)
(4,1)
(6,-4)
Step-by-step explanation:
B
D
A
с
2
2-1
1
2
3 4 5
2 1
2
2 4 5
A
B
2-1
1
2
B
5 4 3 2 1
1
2 3 4 5
The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm
The Formula of the relation is M = 8AT.
The mass of the metal sheet is 960 g.
The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).
Proportionality:
M ∝ ATRemoving the proportionality sign,
M = KATWhere:
K = constant of proportionality.make K the subject of the equation:
K = M/KT.................... Equation 1From the question,
Given:
M = 200 gA = 250 cm²T = 1 mm = 0.1 cmSusbtitute into equation 1
K = 200/(250×0.1)K = 8 g/cm³Formula:
M = 8AT................. equation 2Hence the formula of the relation is M = 8AT
If,
A = 400 cm²T = 3 mm = 0.3Substitute these values into equation 2
M = 8(400)(0.3)M = 960 gHence, the mass of the metal sheet is 960 g
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Mr. Jefferson's and Mr. Hamilton's fifth grade classes sold brownies every day at school for 6 months. If
the pattern continues, which class will earn more at the end of week 8? Use the table to help solve the
problem.
Answer:
It is B
Step-by-step explanation:
Find the equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5.
Answer:
The equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5 is
y = 3x - 1
A line is parallel to another when they both have the same slope.
The two equations above have a common slope of 3.
I hope this helped. Have a good new year!
What’s the difference for this equation!!!
Answer:
2x^2 + 11x – 1
Step-by-step explanation: