In the following passage we have proven the Pythagoras' theorem.
What is Pythagoras' theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given in the question that one side of the wall 5 feet
So as it is a rectangular bedroom it can be split into 2 right-angled triangles.
So the hypotenuse of the triangle is 13 feet
Now using the Pythagoras theorem we can find out the length of the other wall
b²=h²-p²
AB² + BC² = AD × AC + CD × AC
AB² + BC² = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC² = AB² + BC²
So we have p² + b² = h².
Hence, we prove the Pythagoras theorem using two triangle.
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PLEEEEEASE HELP ME ASAP
By evaluating the function we will see that the difference is:
f(1) - f(-7) = 3
How to evaluate the piecewise function?Here we have a piecewise function, this is a function that behaves differently on different intervals of its domain.
On the image you can see the different pieces of the function, and on the right the domain of each of the pieces.
The first part works for all the values smaller than -4 and x = -4.
So if we want to evaluate the function in x = -7, we need to use that piece:
f(-7) = |-7 + 5| - 9 = -7
And the second piece works on the interval (-4, 1], so to evaluate in x = 1 we need to use that piece.
f(1) = -1³ - 3*1 = -4
Then the difference is:
f(1) - f(-7) = -4 + 7 = 3
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use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 70 and 82 tails, inclusive? a) 0.2137 b) 0.1908 c) 0.2154 d) 0.1880 e) 0.2166 f) none of the above.
The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.
Here, we are given that a fair coin is tossed 130 times.
Thus,
number of trials ⇒ n = 130
p = P(getting tails in a single toss) = 0.5
mean of a binomial distribution = np
= 130*0.5
= 65
variance = np(1-p)
= 65*0.5
= 32.5
standard deviation = sqrt(variance)
= sqrt(32.5)
= 5.7
Now, x = number of tails
X follows a normal distribution with mean 65 and variance 5.7
P(70 < x < 82)
= P( 69.5 < X < 82.5) [applying continuity correction]
= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]
= P(0.79 < Z < 3.07)
= P(Z < 3.07) - P(Z < 0.79)
= 0.9989- 0.7852
= 0.2137
Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .
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please cluster the following points, (18, 10), (21, 11), (22, 22), (24, 15), (26, 12), (26, 13), (27, 14), (30, 33), (31, 39), (35, 37), (39, 44), (40, 27), (41, 29), (42, 20), (44, 28), (46, 21), (47, 30), (48, 31), (49, 23), (54, 24) use the numbers as pairs of x and y values which represent their locations. all distances are measured with euclidean distance. hint: you'll probably want to code for this question, although hand tracing is not impossible.
a. Use the k-means algorithm, with
(24,15),(30,33), and(54,24) as the initial cluster centers, process the dataset until convergence, choose a method of your choice to evaluate the cluster result quality. (10pts) b. Use the agglomerative hierarchical clustering to cluster the data, use single link, complete link, and average link, respectively. Discuss the similarities and/or the dissimilarities between the 3 different link methods. (10pts)
Using the numbers to indicate their locations as pairs of x and y values. Euclidean distance is used to measure all distances.
a. Using the k-means algorithm, we can group the points into three clusters based on their initial cluster centers. The first cluster consists of the points (18, 10), (21, 11), (22, 22), (24, 15), (26, 12), and (26, 13), the second cluster consists of the points (27, 14), (40, 27), (41, 29), (42, 20), and (44, 28), and the third cluster consists of the points (30, 33), (31, 39), (35, 37), (39, 44), (46, 21), (47, 30), (48, 31), and (49, 23).
The silhouette approach, which compares how similar each point is to the points in its own cluster to the points in other clusters, can be used to assess the quality of the clusters. A high silhouette value denotes a well-clustered point, while a low silhouette value denotes a possible incorrect cluster assignment.
b. In hierarchical agglomerative clustering, we first create individual clusters for each point, which are then combined to create a single cluster that contains all of the points. Depending on how they calculate the separation between clusters, the three distinct link approaches will result in a variety of clustering outcomes.
The minimal distance between any two points in each of the two clusters is used by single link to calculate the separation between the clusters. Because it only takes into account the closest pair of points, this can lead to long, thin clusters.
The distance between the clusters is calculated using the maximum distance between any two points in the two clusters. Due to the fact that it only takes into account the farthest pair of points, this can lead to compact, spherical clusters.
The average link calculates the separation between the two clusters by averaging out all of the distances between the points in the two clusters. This takes into account all possible pairs of points and may lead to clusters with more symmetrical shapes.
In general, a single link will create clusters that are the most compact, a complete link will create clusters that are the most spherical, and an average link will create clusters that are more evenly shaped.
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Which number is greatest? A. 3.4 × 10-2 B. 4.3 × 10-3 C. 5.2 × 10-4 D. 6.1 × 10-4
Mathwy is To solve this type of3.4 x 10-2 PEMDAS
The enrollment at Grove
Middle School is expected to increase
by 40 students each year for the next
5
years.
If their current enrollment is
600 students, find their enrollment
after each of the next 5 years.
Answer:
After one year, the enrollment will be 600 + 40 = 640. After two years, the enrollment will be 640 + 40 = 680. After three years, the enrollment will be 680 + 40 = 720. After four years, the enrollment will be 720 + 40 = 760. After five years, the enrollment will be 760 + 40 = 800.
Step-by-step explanation:
c8 q8 v1: a random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 62.25. suppose that the population standard deviation is known to be 4.5. which of the following is correct? (note that you can answer these questions from understanding gleaned in lecture and lab, but may find r helpful.)
99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
Given, the mean of the final grades of the sample be 62.25 and the standard deviation be 4.5
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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Factorise the following x^2+6x+8
Answer: (x+2) (x+4)
Hope this helps!
Select the reason why these triangles are similar. If they are not, select "Not similar."
Numbers selected in the triangle 2.5, 2.25,0.5,2,1, and 1
Answer choices: A. AA, B. Not similar, C. SAS, D. SSS
Answer: B
Step-by-step explanation: One is a triangle and one is not. The bigger one has four sides therefore it is not a triangle
Answer:
B. Not similar
Step-by-step explanation:
You want an appropriate choice of similarity reason for the triangles shown in the figure.
Side ratiosThe side ratios in the smaller triangle are ...
0.5 : 1 : 1 = 1 : 2 : 2
The side ratios in the larger triangle are ...
2.25 : 3 : 3.5 = 9 : 12 : 14
The side ratios are not the same, so the triangles are not similar.
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2. Stella's aunt donates 42 red roses, 70 pink carnations, and 56 yellow daisies for the party. The flowers will need to be arranged and placed on the tables. Stella wants each arrangement to have the same number of each color of flower. There are 12 tables at the party. Can she make an arrangement for each table and have no flowers left?
Answer:
no she will have 24 flowers left
Step-by-step explanation:
,Lm
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is a. much larger than one b. zero c. infinity d. None of these alternatives is correct.
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is much larger than one.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
Firstly, it is important to clarify that when people say ‘‘The Sun Will Rise Tomorrow’ they are implying only how It only appears to an observer on earth that the sun rises and sets. In reality the sun neither rises nor sets it only appears to do so because the earth takes one day (24 hours to rotate on its axis). It has appeared to do this for as long as the earth has existed (approx. 4.5 billion years). Although for the purpose of this short reflection, the idiom will signify part of the day-night process -being able to see the sun rise from the perspective of a human on earth.
Although the chances might be extremely high, they are not certain. Even thought it may be very improbably unless an infinite amount of days in which the sun has risen has occurred, the probability will not exactly be one. Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic and philosophy of mathematics, said, “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.” Although we may reasonably argue that the earth while rise tomorrow to a 99.99999999% chance, there still is that 0.000000001 which states that it would not in fact rise.
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Of the 52 plays attributed to a playwright, 19 are comedies, 10 are tragedies, and 14 are histories. If one play is selected at random, find the odds against selecting a tragedy
The answer is 3/5, or 60%
11 (comedies) + 19 (tragedies) = 30
30/50 = 3/5, or 60%
1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
C
2)
a
b
с
d = 104°
Answer: 24 26 37 60
Step-by-step explanation: im sure
There is a new ride share service that charges a rate of $5 for the
first 5 miles, then charges $0.50 per mile after that.
If you want to spend $12 or less, what is the maximum number of
miles you could go using the ride share service?
The maximum number of miles you could go using the ride share service for $12 or less is 14 miles
How to find the miles to go with $12The problem is solved by generating the equations
assuming x represents the number of extra miles
$5 is charged for the first 5 miles and $0.50 per mile after that
This can be represented using the equation
total cost, y = $5 + $0.5x
$0.50 for the extra miles
Having $12 the number of miles is calculated as below
$12 = $5 + $0.5x
0.5x = 12 - 5
0.5x = 7
x = 7 / 0.5
x = 14 miles
The number of miles that can be paid for using $12 is 14 miles and this is the maximum number since the amount will result to lesser miles
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the quotient of a number n and "-3" is no less than 6. What is the value of n?
Answer: n >= -18
Step-by-step explanation:
n/-3 >= 6
(-3) (-3)
n >= -18
Linear Equations w/ Distribution 2
(5y−1)=28
Answer:
29/5 or 5.8
Step-by-step explanation
First, we put the 1 on the other side which turns it positive 5y=29
Then, we divide 29 by 5 which gives us 29/5 which is equal to 5.8
A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
The shortest length of fence that the rancher can use is 6000 ft.
What is meant by length?
The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.
Main Body:
x = width of rectangle
y = length of rectangle
A = area of rectangle = xy = 1500000 ft^2
L = length of fencing needed = 2(x + y) + x = 3x + 2y
L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)
As x –> 0+, L –> +inf.
As x –> +inf, L –> (3x)+.
Sketch and see that there will be a minimum in Quadrant I.
dL/dx = 3 - 3(10^6)x^(-2)
Extrema occur when dL/dx = 0:
3 - 3(10^6)x^(-2) = 0
(10^6)x^(-2) = 1
x^2 = 10^6
x > 0, so x = 1000 feet for shortest length.
Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.
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Reid needs to purchase ties for a new job. Out of the choices below, which is the best one to buy?
(1): 6 ties for $25.50
(2): 4 ties for $18.00
(3): 5 ties for $21.00
Answer:1
Step-by-step explanation:
There is a lot more
a person stands on a scale in an elevator. as the elevator starts, the scale has a constant reading of 590 n. as the elevator later stops, the scale reading is 386 n. assume the magnitude of the acceleration is the same during starting and stopping.
Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
What is the magnitude?The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.
Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
So, the weight of the person will be:
The scale measures the passenger's normal upward force as it is applied by the floor.
When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).
When there is a downhill acceleration, the normal force is at its lowest.
For any such circumstance:
∑F y =ma y becomes for starting +591N−mg=+ma and for stopping +391N−mg=−ma.
Where a stands for the acceleration's magnitude.
To get rid of a and find mg, add these two simultaneous equations:
+591N−mg+391N−mg=0
OR
982N–2mg=0
Fg = mg = 982N/2 = 491N
Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.
each of two pesticide brands is applied to 100 containers of fire ants. brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours.
The pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
Let A represent the new pesticide and B be the Ant Killer. Then, you are given that
Brand1 kills ants in 65 of 100 containers:
Xa = 65/100 = 0.65
Brand2 kills ants in 58 of 100 containers:
Xb = 58/100 = 0.58
You know need to find sample variance for both,
s²A =∑(Xi - Xa)²
= 65(1-0.65)² + 35(0 - 0.65)²
= 22.75
s²B =∑(Xi - Xb)²
= 59(1-0.59)² + 41(0 - 0.59)²
= 24.19
You can know do a test for significance
t = (Xa - Xb) / √(sA /nA) +(sB/nB)
and derive the conclusion from there.
Here, Null and alternative hypothesis are generally,
Alternative hypothesis
Here, there are three samples are assumed. They are:
i) Samples are taken independently
ii) Samples must be selected randomly
iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5
i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁ = 100
q₁ = 0.35 ; q₂ = 0.42 , n₂=100
Corresponding p-value at Z = 1.01722
p-value = 0.15625 > 0.05
Hence, the pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
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MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write an
equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a
vertical line. Who is correct? Explain.
O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.
O Your cousin. You may need more than two points to write an equation in slope-intercept form.
O Your friend. If f is a function, then the line is not vertical.
O Your cousin. If the line is vertical, it will not have a slope.
The correct one is Your cousin. If the line is vertical, it will not have a slope.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
So, from the Discussion we came to know about Vertical Line.
But the slope of vertical line is undefined.
Then, the slope intercept form is not possible in vertical line.
Hence, the correct one is Your cousin. If the line is vertical, it will not have a slope.
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One day in February, the temperature at 9 A.M. is -6.8°F. At 3 P.M. on the same day, The temperature is 1.72°F.
a) Find the change in temperature.
b) Find the average hourly rate of change in temperature
Answer:
The change in temperature is -6.64
The average hourly rate of change is
6 hours or -3.32
Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week. How many weeks will it take leonardo to pay off the ring?.
It will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
Given, Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week.
So, he made a down payment of 10% of $600 i.e. $60
remaining amount to pay be,
600 - 60 = 540
Let he will take x weeks to pay the remaining amount.
Now, if he pay $65 per week
then, 65x = 540
x = 540/65
x = 8.31
So, it will take approx. 8 - 9 weeks to completely pay the remaining amount after the down payment.
Hence, it will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
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Answer:
9 weeks
Step by step explanation:
It’s right.
oh no i have a F+in math please help me
Answer: 2 1/4
Step-by-step explanation: If you add all those numbers like : 1/3+3/4+4/6+1/2 = and you will get 2 1/4
Answer:
[tex]2\frac{1}{4}[/tex]
Step-by-step explanation:
add them all and you'll get that answer
14. Ronny is taking a jar with 50 dimes and
quarters to CoinMaster to redeem for dollar
bills. The total value of his jar is $8.
a. Write a system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar.
b. Solve the system to determine the number of
quarters and dimes in the jar.
The system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar is
d + q = 50
0.10d + 0.25q = 8
The number of quarters and dimes in the jar is 20 and 30 respectively.
How to determine the number of quarters and dimes?Let
number of quarters = qthe number of dimes = dd + q = 50
0.10d + 0.25q = 8
From (1)
d = 50 - q
Substitute into equation (2)
0.10d + 0.25q = 8
0.10(50 - q) + 0.25q = 8
5 - 0.10q + 0.25q = 8
- 0.10q + 0.25q = 8 - 5
0.15q = 3
divide both sides by 0.15
q = 3/0.15
q = 20
Substitute q = 20 into (1)
d + q = 50
d + 20 = 50
d = 50 - 20
d = 30
In conclusion, the given situation can be solved using simultaneous equation where number of dimes and quarters are 30 and 20 respectively.
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Find the nth term of this number sequence
15, 12, 9, 6, ...
Answer:
[tex]a_{n}[/tex] = 18 - 3n
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
12 - 15 = 9 - 12 = 6 - 9 = - 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 15 and d = - 3 , then
[tex]a_{n}[/tex] = 15 - 3(n - 1) = 15 - 3n + 3 = 18 - 3n
a jet flies 5985 miles in 4 3/4 hours. At the same rate, how long will it take the jet to fly 8505 miles?
[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 5985&4\frac{3}{4}\\[1em] 8505&h \end{array}\implies \cfrac{5985}{8505}~~ = ~~\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{h}[/tex]
[tex]\cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{\frac{h}{1}}\implies \cfrac{19}{27}=\cfrac{19}{4}\cdot \cfrac{1}{h}\implies \cfrac{19}{27}=\cfrac{19}{4h}\implies 76h=513 \\\\\\ h=\cfrac{513}{76}\implies h=\cfrac{27}{4}\implies {\Large \begin{array}{llll} h=6\frac{3}{4} \end{array}}[/tex]
A runner is 7/8 miles away from the finish line. If she can travel 3/8 miles per minute, how long will it take her to finish the race?
The time that runner takes to finish the race is 2.133 minutes.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The speed of the runner is given as 3/8 miles per minute.
The remaining distance to be travelled is 7/8 miles.
Then, the time taken by the runner is the ratio of distance to be travelled to the speed. It can be written as follows,
Time taken by runner = (7/8)/(3/8)
= 7/3
= 2.133
Hence,the time taken by the runner to finish the race is 2.133 minute.
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you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?
Maximum area to enclose a rectangular pasture with one side up against a river is equal to 500,000 square feet.
As given in the question,
Let 'l' be the length of the rectangular pasture
And 'w' be the width of the rectangular pasture
Condition:
One side of the pasture is up against a river
Perimeter of the rectangular pasture with one side up against river = l + 2w
⇒ 2000 = l + 2w
⇒ l = 2000 - 2w
Area of the rectangular pasture
=( 2000 - 2w )( w )
= - 2 ( w² - 1000w )
= -2( w² - 1000w + 250000 - 250000 )
= -2 ( w - 500 )² + 500, 000
Maximum area is at w = 500
Maximum area is 500,000
Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.
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you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. this is an example of the .
you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. This is an example of memory retrieval.
What do you mean by series?
The total of a particular sequence of terms is known as a series in mathematics. These phrases often refer to real or complex numbers, though considerably more generality is possible.
In calculus and its generalization, mathematical analysis, the study of series plays a significant role. Most mathematical disciplines employ series, including combinatorics, where generating functions are employed to explore finite structures.
Along with being widely utilized in mathematics, infinite series are also frequently employed in other quantitative fields like physics, computer science, statistics, and finance.
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Solve for bbb.
-11b+7 = 40−11b+7=40minus, 11, b, plus, 7, equals, 40
b =b=b, equals
The value of 'b' will be;
⇒ b = 7 / 11
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 40 - 11b + 7 = 40
Now,
Solve the expression for b as;
The expression is,
⇒ 40 - 11b + 7 = 40
⇒ - 11b + 7 = 0
⇒ 11b = 7
⇒ b = 7 / 11
Thus, The value of 'b' will be;
⇒ b = 7 / 11
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