The summation is Σ(xᵢ-4)², i=1,2,3...
What is summation ?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.
Series are summations of infinite sequences. They are related to the idea of limit but are not covered in this article.
Let x serve as the definition of a score.
Each score will be xi, i.e. x1, x2, x3, x4... for the first four consecutive scores, and so on.
By deducting 4 from each score, you get xi-4.
Squaring the Resulting Value = (xi-4)²
The sum of the squared numbers is equal to (xi-4)²
where i=1, 2, 3.
Σ(xᵢ-4), The set of instructions written in summation notation is 2.
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Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
What is Summation Notation?
The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.
Let a score be defined by x,
Each score will be xᵢ i.e. x₁, x₂, x₃, x₄... for the first four consecutive scores and so on.
Subtracting 4 from each score = xᵢ-4
Squaring the Resulting Value = (xᵢ-4)²
The sum of the squared numbers = Σ(xᵢ-4)², i=1,2,3...
Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
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While exploring a volcano, Zane heard some rumbling, so he decided to climb up out of there as quickly as he could.
Zane's elevation relative to the edge of the inside of the volcano (in meters) as a function of time (in seconds) is graphed.
A fourth quadrant coordinate plane. The horizontal axis is from zero to thirty-seven point five with a scale of two point five and is titled Time in seconds. The vertical axis is from negative thirty to ten with a scale of two point five and is titled Elevation in meters. The graph of the line is y equals five-sevenths x minus twenty-five. The graph ends at each axis.
A fourth quadrant coordinate plane. The horizontal axis is from zero to thirty-seven point five with a scale of two point five and is titled Time in seconds. The vertical axis is from negative thirty to ten with a scale of two point five and is titled Elevation in meters. The graph of the line is y equals five-sevenths x minus twenty-five. The graph ends at each axis.
How fast did Zane climb?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
252525 meters per second
(Choice B)
B
5775start fraction, 5, divided by, 7, end fraction meters per second
(Choice C)
C
7557start fraction, 7, divided by, 5, end fraction meters per second
(Choice D)
D
353535 meters per second
Zane's velocity climbing the volcano is given as follows:
B. 5/7 meters per second.
What is the linear function?The linear function in the context of this problem is defined as follows:
y = 5/7x - 25.
Hence the coefficients of the linear function are given as follows:
The slope is of m = 5/7.The intercept is of b = -25.The meaning of each of these coefficients is given as follows:
The slope of m = 5/7 means that each second, his position increases by 5/7, which gives his velocity climbing the volcano.The intercept of b = -25 means that at a time of 0, he was at a height of -25 meters, which was his initial height.Thus the correct option of Zane's velocity climbing the volcano is of option B.
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Solve for the requested variable.
s varies directly as the square of t, and s = 80 when t = 4. Find s when t is 8.
Answer:
[tex]\huge\boxed{\sf s = 320}[/tex]
Step-by-step explanation:
Given that,
[tex]s \propto t^2[/tex]
Converting proportionality into equality and adding a constant.
s = kt² ----------------(1)
Given that, s = 80 when t = 4
Put in Eq. (1)
80 = k(4)²
80 = k(16)
Divide 16 to both sides
80/16 = k
5 = k
k = 5Now,
Put t = 8 in Eq. (1)
s = (5)(8)²
s = (5)(64)
s = 320[tex]\rule[225]{225}{2}[/tex]
quadrilateral abcd is a rhombus with perimeter 52 meter. the length of diagonal ac is 24. what is the are in square meters of rhombus abcd?
The area of the Rhombus ABCD is 1.2 square meter.
What is Rhombus?
A quadrilateral with four equal-length sides is known as a Rhombus in plane Euclidean geometry. Another name for this shape is an equilateral quadrilateral because all of its sides are equal in length.
Let ABCD be the given Rhombus of Perimeter = 52 cm.
Since all the sides are equal to each other.
Therefore, each side of Rhombus measures = 13 cm
So,
AD = CD = 13 cm and AC = 24 cm.
Area of the triangle ACD = √[ s (s - a) (s - c) (s - d) ] ….. Heron’s Formula.
where s = semi-perimeter,
a, c, and d are side measures.
s = (1/2) [ 13 + 13 + 24 ] = 25
Area (A) = √[ 25 (25 – 13) (25 – 13) (25 - 24) ] = 60
Hence Area of the entire Rhombus = 2 * 60 = 120 cm²
Convert 120 cm^2 into meter square
⇒ 120 cm^2 = 1.2 m^2
Hence, the area of the Rhombus ABCD is 1.2 square meter.
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show that differentiation reverses parity: if f is even, then f' is odd, and if f is odd, then f' is even. hint: differentiate f (-x ).
Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .
First, let's we start with the definition of even and odd functions.
f is even if and only if f(x) = f(-x) --(1)
f is odd iff f(x) = -f(-x) ---(2)
If f is even and differentiating equation (1) we get,
f'(x) = f'(-x)× (-1) = -f'(-x).
f'(x) = - f'(-x).
Since, f'(x) is some function, then let
g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.
If f is odd then: f(x) = -f(-x)
differentiating above function with respect to x we get ,
f'(x) = -f'(-x)× (-1 ) = f'(-x).
Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.
Hence, Differentiation reverses the parity is hold.
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*100/50 points* It's a timed question! (in attachment)
Answer: last one should be it
Step-by-step explanation:
Answer:
3rd one is correct.
Step-by-step explanation:
Question
What is another way to write the expression t⋅(14−5)?
helpp meee
14t-5t is another way to write the expression t⋅(14−5)
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is t(14-5)
An expression is combination of variables, numbers and operators.
t times of fourteen minus five
Here t is the variable
We need to find other way to write this expression
t(14-5)
Apply distributive property
14t-5t
9t
Hence, 14t-5t is another way to write the expression t⋅(14−5)
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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.
DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(2x - 3y)(4x - y)
Answer:
8x^2-14xy+3y^2 (I think)
Step-by-step explanation:
You probably don't need it now but like here
what is the area of the largest rectangle with lower base on the x axis and upper vertices on the curve y
4 square units will be the area of the largest rectangle.
Given,
First, let's build a rectangle ABCD, where A is the point at the bottom right corner and B,C, and D are the points designated in accordance with A.
Now,
Let A = (p, 0)
B = (-p, 0)
C = (-p, 3 - p²)
D = (p, 3 - p²)
Then the area of rectangle is given as: BA×AD
= 2p × 3 - p²
A = 6p - 2p³
Taking the derivative with respect to p, we have
A' = 6 - 6p²
Now,
A' =0
⇒ 6 - 6p² = 0
⇒ 6p² = 6
⇒ p² = 1
Since, we have to find the greater area, therefore we will take p = 1.
Now, substituting the value of p in (A), we have
Greater area = A= 6 - 2 x 1 = 4 square units
Therefore,
The area of the largest rectangle should be 4 square units.
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Question is incomplete. Completed question is given below;
What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?
A bag contains 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability that the marble chosen is blue?.
Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
Total number of marbles in bag,
=3+6+5+2
=16 marbles
Number of blue marbles=6
Probability of selecting blue marbles,
=6/16
=3/8
The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.
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a pet store has 16 1/2 pounds of dry cat food. the manager divides the food into containers, putting 2 3/4 pounds in each container how many containers does the manager fill
what is $639 with a markup of 10%
Answer:
$63.90
Step-by-step explanation:
cost = $639
markup = 10%
cost * markup = $63.90
bailey has 5 skirts, 9 blouses, and 8 pairs of shoes. how many different skirt-blouse-shoe outfits can she wear? (assume that each item matches all the others, so she is willing to wear any combination.)
There are 360 different skirt-blouse-shoe outfits can she wear.
What is outfits?
A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."
A dress is different from a blouse and a skirt! So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.
You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;
= 5*9*8 = 360
Hence, there are 360 different skirt-blouse-shoe outfits can she wear.
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Mihir has 14,203 beads. He uses 36 beads to
make one necklace. How many necklaces can
he make?
And I also need the remainder
Answer:
394.527
Step-by-step explanation:
Divide the total number of beads by the number he needs to make each necklace and you will have your answer.
Luke climbed from an elevation of 23,201 ft up to the summit of k2 which is at 28,251 ft. How many ft did Luke climb?
I need to explain the variable
write an equation
and solve it
The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft
How to find the feet climbed?The number of feet that Luke climbed, can be found by the formula:
Number of feet climbed = Summit of K2 - Luke's starting elevation
Summit of K 2 = 28, 251 ft
Luke's starting elevations = 23, 201 ft
Elevation climbed by Luke was therefore:
= 28, 251 - 23, 201
= 5, 050 ft
In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.
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When rounded to the tens place, which of the numbers below round to 34,590? Select all that apply.
A) 34,587
B) 34,650
C) 34,594
D) 34,595
E) 35,005
Answer:
A), C)
Step-by-step explanation:
Let's round all numbers below to the nearest 10.
A) 34,590
B) 34,650
C) 34,590
D) 34,600
E) 35,010
Monica deposits $200 into a savings account that pays a simple interest rate of 3.7%. Paul deposits $300 into a savings account that pays a simple interest rate of 2.9%. Monica says that she will earn more interest in one year because her interest rate is higher, is she correct? justify your response.
Paul earns more interest than Monica does.
What is simple interest?Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.
Given that,
Money deposited by Monica is $200 at simple interest of 3.7%.
Money deposited by Paul is $300 at simple interest of 2.9%.
The expression to calculate simple interest is given as,
(P × r × t)/100
Substitute the corresponding values to obtain the simple interest for both cases as follows,
Interest gained by Monica is (200 × 3.7 × 1)/100 = $7.4.
Interest gained by Paul is (300 × 2.9 × 1)/100 = $8.7.
Hence, monica is not correct as the interest earned by Paul is greater than that of monica.
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Last year, Pinwheel Industries introduced a new toy. It cost $2500 to develop the toy and S25 to manufacture each toy. Fill in the blanks below as appropriate.
A.) Give a linear equation in the form Cmn + b that gives the total cost, C, to produce n of these toys Preview
B.) The total cost to produce n 3000 toys is S
C.) With $32500, a total of toys can be produced.
a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.
What is meant by the term linear equation?An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.
The three different types of linear equations are: 1) Standard Form
2) The slope intercept form
3)Point Slope Form
How to solve?
A) Linear equation y=mx+b,
C (total cost) = y and n (number of toys) =x.
C=25n + 2500
B) Put n=1750
C= 25(3000) + 2500
C= $77,500
C)
32500= 25n +2500
30000=25n
n = 1200
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trey walks 12 miles in 3 hours which graph has the slope that best represents this rate?
The graph of the proportional relationship d = 4t is given by:
Graph B.
What is the proportional relationship?The general model of a proportional relationship is given as follows:
y = kx.
Meaning that it's graph is that of a linear function, in which:
The slope is the constant of proportionality k.The intercept is of zero.The relation between velocity, distance and time is given as follows:
v = d/t.
Then the equation for the distance as a function of time is given as follows:
d = vt.
Meaning that the slope is the velocity.
Trey walks 12 miles in 3 hours, hence the slope of the graph is of:
v = 12/3 = 4 miles per hour.
Among the options given by the image shown at the end of the answer, the correct option is:
Graph B.
As it goes through point (4,16).
Missing InformationThe options are given by the image shown at the end of the answer.
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-2/3^8
two thirds to the power of eight
pls help me
Answer: i think either 256/6561 or -256/6561
Step-by-step explanation:
what is the difference between a convex set and a convex function with respect to linear programming?
A real-valued function defined on an interval with the property that its epigraph—the collection of points on or above the function's graph—is a convex set—is said to be convex. The challenge of minimizing convex functions over convex sets is the subject of the optimization discipline known as convex minimization.
What is linear programming?A mathematical model whose needs are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming. When a linear function is subjected to various constraints, it is maximized or minimized using the mathematical modeling technique known as linear programming. In business planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
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(I NEED HELP URGENTLY, THIS IS DUE TOMORROW!)
The table represents a proportional relationship.
A. Find the constant of proportionality:
B: Write a equation to represent the relationship. Equation: y=
The constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
What is the constant of proportionality?The value of the proportionality constant is determined by the type of proportion between the two specified values.
Proportional relationships are written in the form y = kx
where k is the constant of proportionality.
As per the given table, the constant of proportionality will be
k = (1 - 2/3)/(3-2)
k = (1/3)/1
k = 1/3
So, the equation is y = (1/3)x.
Thus, the constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
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Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply)
A. Correlation does not imply causation.
B. He made a prediction outside of the range of forces observed.
C. He made a prediction outside of the range of stretched distances measured.
D. He had outliers or influential points in his data.
E. None of the above
The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.
The relevant points from the regression model are
B. He predicted something that was outside the range of forces seen.
C. He predicted something that was outside the range of stretched distances that were observed.
D. His data contained outliers or significant points.
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Diego states that diagonal WY bisects angles ZWX
and ZYX. Is he correct? Explain your reasoning.
The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.
How to prove bisection of angles?Bisection of an angle is simply defined as dividing an angle into two equal parts.
We are given that Diagonal WY bisects angles ZWX and ZYX.
Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.
Similarly, XW is congruent to ZW and as such; XW ≅ ZW
Since XY is congruent to ZY and XW is congruent to ZW, then the statement that diagonal WY bisects angles ZWX and ZYX is true
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The density of some steel is 7.92/cm³
What is the mass of 60cm³ of this steel?
Give your answer to 1 d.p.
Answer:
below
Step-by-step explanation:
density * volume = mass
7.92 g / cm^3 * 60 cm^3 = 475.2 g
Value of x?
-3(4x + 3)-4(5x + 1) = 79
Answer:
-2.875
Step-by-step explanation:
-12x-9-20x-4=79
-32x-13=79
-32x=92
92/-32= -2.875
Answer:
-23/8 OR 2.875Step-by-step explanation:
Split 「-3(4x + 3)-4(5x + 1)」 out into -3(4x+3) and -4(5x+1):-3(4x+3)= (-3)(4x)+(-3)(3) = -12x-9-4(5x+1)= (-4)(5x)+(-4)(1) = -20x-4Substitute it back to the formula:-12x-9-20x-4= 79 -32x-13= 79 -32x= 79+13 -32x= 92 x= 92/-32 x= -23/8 OR 2.875The probability of getting a six, when you are tossing a coin is ?
Solution needed ~
Answer: The possible outcomes are — 1, 2, 3, 4, 5, and 6. The probability of getting any of the outcomes is 1/6
Step-by-step explanation:
Help please!
-8+2(3 + 8) = -4(g + 1)
Answer: -9/2
Let's solve this equation step-by-step.
−8+2(3+8)=−4(g+1)
Step 1: Simplify both sides of the equation.
−8+2(3+8)=−4(g+1)
−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)
−8+22=−4g+−4
(−8+22)=−4g−4 (Combine Like Terms)
14=−4g−4
Step 2: Flip the equation.
−4g−4=14
Step 3: Add 4 to both sides.
−4g−4+4=14+4
−4g=18
Step 4: Divide both sides by -4.
−4g/−4 = 18/−4
g = −9/2
- Clare removed marbles from a container of
water. When she removed 2 marbles, the
water level was 80 ml. When she removed
4 more marbles, the water level was 40 ml.
Write an equation for the water level y after
x marbles are removed.
Answer:
y = 100 - 10x
Step-by-step explanation:
Let y₀ be the original water level before any marbles were removed
Let y = water level after x marbles are removed.
Let d be the water level drop for every marble removed
Then we have the general equation:
y = y₀ - x.d
We have to find d and y₀
So we get one equation for the water level after removal of 2 marbles
80 = y₀ - 2d [1]
After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml
For each marble then, water level drop = 40/4 = 10ml. This is the value of d
Plug this value of d into [1] to get the original water level y₀
80 = y₀ - 2( 10)
80 = y₀ - 20
100 = y₀
or,
y₀ = 100
So original water level is 100ml and the equation for water level after x marbles are removed is
y = 100 - 10x
what are three equations that are equivalent to 60% of 25
The equation which is equivalent to 60% of 25 is x = 0.6 * 25
1. Equivalent equations: Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.
2. How to find equivalent equation : Steps to find weather the equations are equivalent are:
Distribute the coefficients Combine any like term on both side.Arrange the term in same order.If all the terms in two expressions are same then the equations are equivalent.An equation is used to show the relationship between variables, numbers.
Let x represent the value of 60% of 25. Hence:
x = 60% of 25
x = 0.6 * 25
Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25
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What is the value of x in this triangle?
Enter your answer in the box.
x =
Answer:
37+82+x=180
119+x=180
x=180-119
x=61