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
please help with this math
Answers
120 m
1:1000
Try this
A teacher selects 4 students from her class of 37 to work together on a project. How many ways are there for her to select the students
Answers
Answer:
The correct answer is 66,045
The initial population of a town is 3800, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Please show step by step!
Answers
Answer:
The population was 3040 people in 8 years.
Step-by-step explanation:
find unit rate;
3800/10 = 380
380 x 8 = 3040
At football practice on Monday, Brandon threw a football into the target 5 times. The next Monday, he tripled the number of targets he hit. On the following Monday, his hits double that of the week before. Write and evaluate a numerical expression to find how many times he hit the target during those three weeks.
Enter the correct answers in the boxes.
Expression:
Answers
Answer:
try using a different app, it helps with all types of mathematical equations
HELPPP LAST ATTEMPT!!
Answers
Find the area of the shaded shape
Answers
Answer:
105
Step-by-step explanation:
yeah-ya............. right?
There are 6 equally sized slices in a pizza. If Ken eats 5 of the slices,
what percent of the pizza has he eaten? Show your work.
Answers
Answer:
Step-by-step explanation:
5 / 6 = 0.83333333...
0.833333...•100 = 83.333333...
83.3%
Answer:
You can do this type of questions with inverse proportion.
_
%83,3
If you own a car with an assessed value of 23,300 in the state of West Virginia, which has a 1.66% tax rate, what would your property taxes be for your vehicle
Answers
Answer:
Average County Tax Rate
0.520%
(Mercer County)
Property Taxes
$121
(Annual)
Step-by-step explanation: I'm assuming this is the answer, if you can please can you mark me Brainliest.
Veronica has two offers for a $65,000 student loan. The first loan has a 6.3% interest rate for 15 years, and the second loan has a 4.8% interest rate for 20 years. Both loans have interest compounded every month. Veronica is interested in finding the loan that minimizes the amount of interest that she will pay over the life of the loan. Which loan has a lower amount of interest paid?
Answers
The second option has a lower amount of interest paid.
In order to determine the loan option that minimizes loan payment, the future value of both loan options has to be determined.
FV = P (1 + r)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
First loan option
65000( 1 + 0.063/12)^300 = 312,707.21
Second loan option
65000( 1 + 0.048/12)^240 = 169,435.51
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Help help help help help help help help help help help
Answers
Answer:
Step-by-step explanation:
A' = (2 + 3, 1 + 2) = (5, 3)
B' = (-1 + 3, -3 + 2) = (2, -1)
C' = (3 + 3, -3 + 2) = (6, -1)
Selina has a balance of $1,200 in his First State Bank checking account. He deposits a $387.89 paycheck, a $437.12 dividend check, and a personal check for $250 into his account. He wants to receive $400 in cash. How much will he have in his account after the transaction?
Answers
Answer:
$1,875.01
Step-by-step explanation:
Cash in Bank :
DEBIT(+) :
+ $1,200.00
+ $387.89
+ $250.00
+ $437.12
CREDIT (-) :
- $400.00
Capital:
DEBIT (-) :
- $400.00
CREDIT (+) :
+ $1,200.00
+ $387.89
+ $250
Accounts Payable :
DEBIT (-):
0
CREDIT (+):
+ $437.12
mega movies hotel a fil premiere on Friday night. they charged $7 for adults and $5 for children. One hundred twenty-three adults and children attended, and $829 was made in ticket sales. How many children and how many adults went to the film premiere?
Answers
Answer:
107 adults 16 children
Step-by-step explanation:
can i get brainlest
Ned fills 2/3 of a bucket in 15 of a minute. How much time will it take him to fill the bucket?
Answers
we know he filled 2/3 of the bucket in 15mins, how long for the "whole", namely 3/3 = whole, bearing in mind that 3/3 = 1, just the same as 7/7 = 1 or 1,000/1,000 = 1, so one whole is always 1 fraction wise.
[tex]\begin{array}{ccll} fraction&mins\\ \cline{1-2} \frac{2}{3}&15\\[1em] \underset{whole}{1}&x \end{array}\implies \cfrac{~~ \frac{2}{3}~~}{1}=\cfrac{15}{x}\implies \cfrac{2}{3}x=15\implies \cfrac{2x}{3}=15 \\\\\\ 2x=45\implies x=\cfrac{45}{2}\implies x=22\frac{1}{2}\qquad \textit{22 minutes and 30 seconds}[/tex]
Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 2 and 82 that are multiples of 9
Answers
Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,
[tex]D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}[/tex]
The odd multiples of 9, [tex]m[/tex], in the range [tex]2\le m \le 82[/tex] form the set
[tex]\{9,27,45,63,81\}[/tex]
Each member of the set is a term of the arithmetic progression
[tex]U_n=18n+9[/tex]
where the values of [tex]n[/tex] range from 0 to 4, or [tex]0\le n\le 4[/tex]
Putting these facts together, we get the result
[tex]D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}[/tex]
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what 5 + 5- just asnwer pls
Answers
Answer:
5+5=10
but if you mean
5+-5 then that = 0
Step-by-step explanation:
Use the GCF and the distributive property to find each sum 15 + 57
Answers
Answer:
(3*5)+(19*3)
Step-by-step explanation:
both numbers GCF is 3.
(3*5)=15
(19*3)=57
15+57=72
Hope that helps
An employer pays 75% of an employee's health insurance premium.
If the premium is $4855 annually, how much is the employee's share of the premium?
O S3884.00
O S3641.25
O S1213.75
O $971.00
Answers
Answer:
1213.75
Step-by-step explanation:
you turn the percent int a decimal, and then multiply it by 4855. then the answer you get (3641.25) you subract 4855 by it to get the answer
According to the central limit theorem, if a sample of size 100 is drawn from a population with a mean of 80, the mean of all sample means would equal _______. SHOW THE STEPS TO ARRIVE A T THE ANSWER (4 points)
Answers
Answer:
μX = the mean of X
σX = the standard deviation of X
If you draw random samples of size n, then as n increases, the random samples
¯¯¯¯¯
X
which consists of sample means, tend to be normally distributed.
¯¯¯¯¯
X
~ N (
μ
x
,
σ
x
√
n
)
The central limit theorem for sample means says that if you keep drawing larger and larger samples (such as rolling one, two, five, and finally, ten dice) and calculating their means, the sample means form their own normal distribution (the sampling distribution). The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by, the sample size. The variable n is the number of values that are averaged together, not the number of times the experiment is done.
To put it more formally, if you draw random samples of size n, the distribution of the random variable
¯¯¯¯¯
X
, which consists of sample means, is called the sampling distribution of the mean. The sampling distribution of the mean approaches a normal distribution as the sample size n increases.
The random variable
¯¯¯¯¯
X
has a different z-score associated with it from that of the random variable X. The mean
¯¯¯
x
is the value of
¯¯¯¯¯
X
in one sample.
z =
¯¯¯
x
−
μ
x
σ
x
√
n
μ
x
=
μ
¯¯¯
x
(mean of X = mean of
¯¯¯¯¯
X
. )
σ
¯¯¯
x
=
σ
x
√
n
= standard deviation of
¯¯¯¯¯
X
and is called the standard error of the mean.
Step-by-step explanation:
sorry if its hard/ confusing
Find the inequality represented by the graph in the picture
(Khan academy)
Answers
Answer:
[tex]y < 3x - 4[/tex]
Step-by-step explanation:
We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.
So we can tell that the slope is 3/1 or just 3.
Also, since the line crosses the y-axis at -4, this will be the y-intercept.
Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.
So all together, we have y < 3x - 4.
Hope this helps you :)
when 8 is subtracted from a certain number and the result is multiplied by 3 and the answer is 21 what is the original number
Answers
Step-by-step explanation:
The Real Answer Is 63
Maybe Positive Or Negative
A class of 22 students has taken an exam, and the mean of their scores is 76.5. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 23 exams? Round
to the nearest hundredth.
Answers
The mean score for all 23 students is 77.17.
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.
The first step is to determine the total scores of the 22 students.
Total scores = mean score x number of students
22 x 76.5 = 1683
The second step is to add the score of the student that took the exam late tot he total scores.
New total score = 1683 + 92 = 1775
The third step is to determine the new mean score.
new mean score = new total score / total number of students
1775 / 23 = 77.17
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if 5c-2=3c, then 24c=
Answers
Answer:
24
Step-by-step explanation:
Step-by-step explanation:
24 is 3×8
so, when
3c = 5c-2
then
8×3c = 24c = 8×(5c-2) = 40c - 16
A colony of bees doubles in size every month. If there are initially 5000 bee, create a model for the bee population
Answers
we know that the colony is doubling, namely the rate of growth is 100% of whatever is existent, thus
[tex]\textit{Amount of Population Growth} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A = 5000e^{1\cdot t}\implies \boxed{A = 5000e^t}[/tex]
Select all the statements that are true for △ABC.A. AH is an altitude.
B. IH is a median.
C. JC is a median.
D. The medians and altitudes intersect at the same point.
E. The altitudes intersect outside of the triangle.
Answers
The relationships between the two medians and an altitude marked on
ΔABC can be used to determine the true statements.
The true statements are;
A. AH is an altitudeC. JC is a medianReasons:
A median line is a line that extends from the vertex to the midpoint of the
opposite side, bisecting the opposite side.
In the figure, we have;
The median of ΔABC are; JC, and BI
The point of intersection is the point K
The altitude is a perpendicular line from a vertex to the opposite side
known as the base of the triangle.
The given altitude of ΔABC is; AH
Therefore, the statements that are true are;
A. AH is an altitude
C. JC is a median
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Jen has 93 beads ana has 46 red beads and 29 blue beads.How many more beads does Ana need to have 93 beads Also?
Answers
Answer: 18
Step-by-step explanation: 93 - (46 + 29) = 18
Ninety (90) milliliters is equal to how many tablespoons?
Answers
Answer: 6.087 tablespoons. or rounded to nearest whole, 6
Step-by-step explanation:
I just know
A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below.
Completed Homework Did not Complete Homework Total
Passed the Course 25 7 32
Did not Pass the Course 5 18 23
Total 30 25 55
A student from the class is randomly selected. Determine the following probabilites. Enter your results as percents rounded to two decimal places.
What is the probability a student passed the course given that they completed their homework?
%
What is the probability a student passed the course given that they didn't complete their homework?
28
Correct%
What is the probability a student completed their homework given that they passed the course?
%
What is the probability a student didn't complete their homework given that they didn't pass the course?
%
Answers
Probabilities are used to determine the chances of an event.
Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment
(a) The probability a student passed the course given that they completed their homework?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(C) = 30}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{30}}[/tex]
[tex]\mathbf{Pr = 0.8333}[/tex]
Express as percentage
[tex]\mathbf{Pr = 83.33\%}[/tex]
Hence, the probability a student passed the course given that they completed their homework is 83.33%
(b) The probability a student passed the course given that they didn't complete their homework
From the table, we have:
[tex]\mathbf{n(P\ n\ C'= 7}[/tex]
[tex]\mathbf{n(C') = 25}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7}{25}}[/tex]
[tex]\mathbf{Pr = 0.28}[/tex]
Express as percentage
[tex]\mathbf{Pr = 28\%}[/tex]
Hence, the probability a student passed the course given that they didn't complete their homework is 28%
(c) The probability a student completed their homework given that passed the course?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(P) = 32}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{32}}[/tex]
[tex]\mathbf{Pr = 0.78125}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.125\%}[/tex]
Approximate
[tex]\mathbf{Pr = 78.13\%}[/tex]
Hence, the probability a student completed their homework given that they passed the course is 78.13%
(d) The probability a student didn't complete their homework given that they didn't pass the course
From the table, we have:
[tex]\mathbf{n(P'\ n\ C'= 18}[/tex]
[tex]\mathbf{n(P) = 23}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{18}{23}}[/tex]
[tex]\mathbf{Pr = 0.7826}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.26\%}[/tex]
Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%
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Solve for
x
6
(
x
−
6
)
=
5
(
x
+
1
)
Answers
Answer:
x = 41
Step-by-step explanation:
6(x−6)=5(x+1)
Step 1 - Expand the brackets:
6(x - 6) = 5(x + 1)
6x - 36 = 5x + 5
Step 2 - Add 36 to both sides of the equation:
6x - 36 + 36 = 5x + 5 + 36
6x = 5x + 41
Step 3 - Subtract 5x from both sides of the equation:
6x - 5x = 5x + 41 - 5x
x = 41
Hope this helps!
[tex]\large\underline{\sf{Solution-}}[/tex]
Given expression:
6(X - 6) = 5(X + 1)
⇛6X - 36 = 5X + 5
⇛6X - 5X = 5 + 36
⇛X = 41 Ans.
Read more:
Similar question
simplify 6/x-6+3x/x+5-1/(x-6)(x+5)....
https://brainly.com/question/9027174?referrer
(PHOTO) please help need this done by tomorrow thank you.
Answers
Answer: 125
Step-by-step explanation: ∠4 and 55 are supplementary angles. This means that ∠4 and 55 add up to 180. We can use this to solve for ∠4.
180 - 55 = ∠4
125 = ∠4
So, ∠4 is equal to 125 degrees.
Would appreciate brainly <3
y=7x+7 standard form
Answers
Answer:
7x - y = -7
Step-by-step explanation:
Hope this helps!