Answers
The explicit formula for calculating the sum is
[tex]S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}[/tex]
The sum of the nth term of a sequence is expressed as;
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
a is the first term
d is the common difference
n is the number of terms
For the sequence 0 + 1 + 2 + 3 +...
[tex]S_n=\frac{n}{2}(2(0)+(n-1)1)\\S_n= \frac{n}{2}(n-1)\\S_n= \frac{n(n-1)}{2}[/tex]
Similarly for the sequence:
1 + 2+ 3 + 4+...
[tex]S_n=\frac{n}{2}(2(1)+(n-1)1)\\S_n= \frac{n}{2}(2+n-1)\\S_n= \frac{n(n+1)}{2}[/tex]
Taking the product of the sum to get the explicit formula for calculating the sum
[tex]S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}[/tex]
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Related Questions
A Ferris wheel can accommodate 70 people in 15 minutes how many people can ride in 3 hours
Answers
I did 12x70
Answer: 840 people?
Step-by-step explanation:
Who is the general information of acounting
Answers
Answer:
General accounting essentially refers to general ledger collection and accounting activities that include account charges in credits and debits and documenting financial statements for a quarter, calendar or fiscal year.
please help me calculation completing square?
x²+2x-24=0?
Answers
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
help me for Brainlyist !!
Answers
Answer:
3,4
Step-by-step explanation:
What is the value of the expression?
(323+1715)−(1135+213)
Enter your answer as a mixed number in simplest form by filling in the boxe
Answers
Answer:
690
Step-by-step explanation:
(323+1715)-(1135+213)
(2038)-(1348)
=690
The value of the expression is 690
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (323+1715)−(1135+213)
We have to find the value of expression
By using PEMDAS rule we solve the expression
Let us find the value in parenthesis
2038 -1348
We get 690
Hence, the value of the expression is 690
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ2
How do I find the percent of change
Answers
Answer:
200%
Step-by-step explanation:
It increases by 3 times. Because 100% increase is a 2x increase, 200% will be a 3x increase. Therefore, your answer is 200%.
b) Are there any overall patterns in the data set? Striking deviations? Use
mathematical reasoning to justify your answer. (2 points)
Answers
Answer:
There is an outlier at 0, and a gap at 1,2, and 3. The peak is at 5, and the plot is more or less skewed left.
Step-by-step explanation:
100 points. Math Question
Answers
Answer:
The answer is 2.
Step-by-step explanation:
Help my first time learning this it’s an easy problem
Answers
Answer:
I don't know but I I would just say C maybe?
Answer:
I say do B
Step-by-step explanation:
B and C look approximately the same but B look smaller
If I’m wrong I’m srry :<
In the final exams, 40% of the students failed chemistry, 25% failed physics, and 19% failed both chemistry and physics. What is the probability that a randomly selected student failed physics given that he passed chemistry?
I have answered the question in the image below, but I would like to know if it is correct. If it is not, please include an explanation of why, as well as the step by step to get the correct answer
Answers
Answer:
10%
Step-by-step explanation:
If 40% failed chemistry then 60% passed chemistry.
If 19% failed both chemistry and physics, and 25% failed physics, then 6% passed chemistry and failed physics.
If we let p' represent failing physics and c represent passing chemistry, then ...
P(p'|c) = P(p'c)/P(c)
P(p'|c) = 6%/60% = 0.10 = 10%
If the randomly chosen student passed chemistry, the probability is 10% that he failed physics.
__
Your answer is correct.
To solve this problem, we can use conditional probability.
Let's assume that there were 100 students in the final exam.
According to the problem, 40% of the students failed chemistry, which means that 60% of the students passed chemistry.
We can see that 25% of the students failed physics, and 19% of the students failed both chemistry and physics.To find the probability that a randomly selected student failed physics given that he passed chemistry, we need to use Bayes' theorem:
[tex]\sf P(Failed\: Physics | Passed\: Chemistry) = \dfrac{P(Failed\: Physics\: and\: Passed\: Chemistry)}{ P(Passed\: Chemistry)}[/tex]
We already know that P(Failed Physics and Passed Chemistry) = 6 students (from the Venn diagram), and P(Passed Chemistry) = 60 students (since 60% of the students passed chemistry).
Therefore,
[tex]\sf P(Failed\: Physics | Passed\: Chemistry) = \dfrac{6}{60} = 0.1\: or\: 10\%[/tex]
So the probability that a randomly selected student failed physics given that he passed chemistry is 10%.
What's the negative reciprocal of 5? Question 12 options: A) 1∕5 B) –5 C) –1∕5 D) 5
Answers
Answer:
[tex]\huge\boxed{C)\ -\dfrac{1}{5}}[/tex]
Step-by-step explanation:
The reciprocal of 5: [tex]\dfrac{1}{5}[/tex]
The negative reciprocal of 5: [tex]-\dfrac{1}{5}[/tex]
What is the perimeter of the shape to the right?
Answers
PLEASE NEED THIS ASAP
Answers
Answer:
The answer is in the above attachment.
A rectangular poster has a area of 504 centimeters. The width of the poster is 14 centimeters. How long is the poster?
Answers
Answer:
36 cm
Step-by-step explanation:
504/14=36
The school football team is hosting a fundraiser dinner. Tickets are $20 for adults, $15 for seniors, and $6 for children. The expression 20a + 15s + 6c represents the total sales for a adult, s senior tickets, and c child tickets. Mariel sold 6 adult, 4 senior, and 8 child tickets.
20a + 15s + 6c = 20 (6) + 15 (4) + 6 (8) = ? + ? + ?
Answers
120 + 60 + 48
228
Teresa measures five eighths foot of ribbon for a costume. She needs seven pieces of ribbon with that same length. What is the total length of ribbon Teresa needs to make all the costumes?
Answers
Help, with my homework. Please represent 2x^-5x-12 using algebra tiles
Answers
Answer:
2−4−12
Step-by-step explanation:
17 1/3 miles in 3 1/4 hours, how many miles per hour?
Answers
Step-by-step explanation:
24+3m>6
Plot this on a number line and show steps please
Answers
[tex]\\ \tt\rightarrowtail 24+3m>6[/tex]
[tex]\\ \tt\rightarrowtail 3m>6-24[/tex]
[tex]\\ \tt\rightarrowtail 3m>-18[/tex]
[tex]\\ \tt\rightarrowtail m>-6[/tex]
Refer to attachment
Please help. NEED THE ANSWER SOON AS POSSIBLE.
Answers
Answer:
y=4x-17
Step-by-step explanation: Distribute the 4(x-5)
4x-20
Then add three to both sides
y=4x-17
study the visual fraction below. Is it A,B,C, or D?
Answers
Answer: B
Step-by-step explanation: the pic shows this
you can see it on the pic btw
what is 3/4 divided by 11/20
Answers
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11
arrange the given the decimals in ascending order from least to greatest
Answers
To arrange in ascending order means to arrange numbers from the smallest value to the greatest value in the set of numbers provided.
9) 3.021 < 3.12 < 3.121 < 3.21
Look at the 1st decimal place after the point first. 0 is less than 2 & 1, so 3.021 is the least number. Now, for 3.12 & 3.121, look at the 3rd place. 3.12 = 3.120, so it’s smaller than 3.121. Then comes 3.21 which is the greatest number in this set.
10) 5.0090 < 5.05 < 5.059 < 5.5
Here, 5.0090 is the smallest number. Then comes 5.05 = 5.050 which is smaller than 5.059. 5.5 is the greatest number.
_________
RainbowSalt2222 ☔
please help.. no links
Answers
Use Pythagorean theorem,
[tex]29^2 = 21^2 + x^2 \\\\\implies x^2 = 29^2 -21^2 \\\\\implies x^2 = 400\\\\\implies x = \sqrt{400} = 20[/tex]
Albert is 5 years 6 months. How old is Albert in months
Answers
Answer:
5x12=60,+6=66
Step-by-step explanation:
Answer:
66 months
Step-by-step explanation:
12months x 5= 60
60 + 6= 66
124/72 simplified is?
Answers
Answer:
31/18
Step-by-step explanation:
On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 62 mph, hence [tex]\mu = 62[/tex].Standard deviation of 5 mph, hence [tex]\sigma = 5[/tex].Sample of 50 cards, hence [tex]n = 50, s = \frac{5}{\sqrt{50}} = 0.7071[/tex]The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 1 subtracted by the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66 - 62}{0.7071}[/tex]
[tex]Z = 5.66[/tex]
[tex]Z = 5.66[/tex] has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
A similar problem is given at https://brainly.com/question/24663213
Distributive property to simplify 6(8) + 6(-2)
Answers
Answer:
36
Step-by-step explanation:
You would multiply 6x8+6x(-2), and that would equal 48+(-12) which is basically 48-12 = 36.
ASAP
which of the following values of 'x' is the equation 4(x-2)-3x
= x +2 true?
A. -1
B. All Real Numbers
C. The equation has no solution
D. 3
E. 2
Answers
Answer: A
Step-by-step explanation:
PLS HELP ME PLS HELP ME PLS HELP ME
Answers
Answer:
Step-by-step explanation:
