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]
Learn more here: https://brainly.com/question/24547297
What is the mode of this data set 17, 13, 18, 20, 17, 15, 12
Answer:
17
Step-by-step explanation:
The mode means the number that repeats the most
Help me with this question pls!
Answer:
1 is parallel to 3. 1 is perpendicular to 2. 2 is perpendicular to 3.
Step-by-step explanation:
The slope of line 1 is 5/3. This is because it is the m term from the equation y=mx+b.
The slope of line 2 is -3/5. You would have to solve the equation in the following format.
[tex]6x+10y-6x=-4-6x[/tex]
[tex]\frac{10y}{10}=\frac{-4-6x}{10}[/tex]
Which simplifies to y=-2/5 - 3/5x, making -3/5 the slope.
The slope of line 3 is 5/3, which can be found by dividing both sides of the equation by 3.
Parallel lines have exactly the same slope. So lines 1 and 3 are parallel.
Perpendicular lines have opposite reciprocal slopes. So lines 1 and 2, and 2 and 3 are both perpendicular.
find the equation of a line parallel to the given line in passing through the given point
y=3;(-2,7)
Answer:
Step-by-step explanation:
y = mx + b
The line y = 3 is a horizontal line with slope zero
y = 0x + 3
All parallel lines will also have a slope zero
a parallel line passing through (-2, 7) will have the equation
y = 0x + 7
y = 7
The sum of two numbers is 25 and their difference is 13. Find their product.
help pls! will do a 100 point giveaway someone pls help
Answer:
$7,865,000 + (Claire's cases)
Step-by-step explanation:
Euro 2,500,000 x 1.13 = $2825000
£4,000,000 x 1.26 = $5040000
$5040000 + $2825000 = $7865000
Answer:
Euros to USD = 2,889,000.00
Pounds to USD = 5,401,320.00
Step-by-step explanation:
2,889,000.00
+ 5,401,320.00
8,290,320.00
Dave wants to put a row of tiles in his kitchen. The row has to be 3m long.
Each tile is a square, with 25 cm sides. How many tiles does he need?
Answer:
12 tiles will be needed!
Step-by-step explanation:
Hope this helps x
whats 2+2x8-16x18+24 divided by 4+2 equals?
lets see if yall smart :))
Answer:
its 46
Step-by-step explanation:
what is |a| if a < 0
Answer:
a is an absolute number
Step-by-step explanation:
Answer:
TALKING ZONE
............
Plz, answer Math question gotta get a good grade :)
Answer:
-7/15 is the correct answer
Step-by-step explanation:
3. Solve x/5 = 15
о x = 20
O x = 75
O x = 10
O x = 3
Answer:
3
Step-by-step explanation:
cross multiple and divide the two variables
Please help
_________________
Answer:
Step-by-step explanation:
1 kg Carmel Corn = 0.54 dollars
3.5 kg Carmel Corn = 3.4 * 0.54 = 1.89
1 kg Cheddar = 1.32 dollars
4 kg Chedder = 4 * 1.32 5.28
Total 7.17
a) suppose {u,v,w} spans the vectore space V.
ptove that {u+v,u+w,v+w} also spans V.
b) suppose that the set of vectors {u,v,w} is linearly independent in a vector space v. prove that the set of vectors {u+v+w, u+v, u+w} must be linearly independentRocket,
Answer:
Victini V
Step-by-step explanation:
Best pokemon v is Victini V so yea ez dubs good luck on test.
Identify all of the expressions that result in a difference of 1\4 . A) 2\10 − 1\6 B) 3\4 − 1 4 C) 2\3 − 5\12 D) 7\8 − 3\12 E) 1]2 − 1\4
The expressions that result in a difference of 1/4 are; Choice C) 2\3 − 5\12 and Choice E) 1/2 − 1\4
For Choice A; 2\10 − 1\6
= 6/30 -5/30= 1/30For Choice B; 3\4 − 1 4
= 2/4= 1/2For Choice C; 2/3 - 5/12
= 8/12 - 5/12= 3/12= 1/4For Choice D;. 7\8 − 3\12
= 21/24 - 6/24= 15/24= 5/8For Choice D; 1/2 − 1\4
= 2/4 - 1/4= 1/4In essence, the expressions that result in a difference of 1/4 are; Choice C) 2\3 − 5\12 and Choice E) 1/2 − 1\4
Read more;
https://brainly.com/question/10532785
After six biology tests, Ruben has a mean score of 75. What score does Ruben need on the next test to raise his average (mean) to 77?
Ruben's score on the next test to raise his average (mean) to 77 is 89.
What is the average?The average is the quotient of the total divided by the number of items involved.
The average is also known as the mean.
The mean is one of the values of central tendency. Other values of central tendency include the mode and the median.
The number of biology tests taken by Ruben so far = 6
The mean score of the six tests = 75
The total score so far in the six tests = 450 (6 x 75)
The expected average for seven tests = 77
The total score for the seven tests = 539 (77 x 7)
The expected score for the seventh test = 89 (539 - 450)
Thus, Ruben is expected to score 89 for his average score to be 77.
Learn more about the average at https://brainly.com/question/20118982
#SPJ1
What are the solutions to the system of equations graphed below? Select all
that apply.
Answer:
(4, 6)
(-3, 13)
Step-by-step explanation:
Solutions are where the graphs intersect
(-3, 13)
(4, 6)
Simplify completely
x² + 4x - 45/x^2+10x+9
and find the restrictions on the variable.
Answer:
(x-5)/(x+1) and x cannot equal -1 because the denominator can't be zero.
Step-by-step explanation:
Factor the numerator:
(x+9)(x-5)
Factor the denominator:
(x+1)(x+9)
So you have
(x+9)(x-5)/(x+1)(x+9); see that you can cross out the (x+9) in both the numerator and denominator?
You're left with (x-5)/(x+1)
The only number that is restricted is -1, because that would make the denominator zero, which is a no no
Answer:
Step-by-step explanation:
To avoid ambiguity please write the given expression as
x² + 4x - 45
x² + 4x - 45/(x^2+10x+9) or (better) as ---------------------
x^2+10x+9
Notice that both numerator and denominator have the factor x + 9:
(x + 9)(x - 5)
---------------------
(x + 9)(x + 1)
This allows us to cancel out the (x + 9) factor, resulting in:
x - 5
------- ONLY for x ≠ -1 and x = -9
x + 1
We must exclude these two x-values because otherwise the denominator would be zero, which is not allowed.
how can a parabola be defined using its relation to a point and a line?
Answer:
Step-by-step explanation:
The set of all points in a plane where the distance to the point (focal point) is equal to the shortest distance to the line (directrix).
Pre college need help
Answer:
A is the correct answer.
Step-by-step explanation:
good luck with college.
What is the function?
Answer:
an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
in slope intercept form slope -5/2 passes through-8,-3
In a group of EXPLORE students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. Of these, 8 students like all three activities, while 30 like only one of them.
How many students like only two of the subjects
HELP ME PLEASE ITS PROBABILTY BRO JUST PLS HELP ME ON THE BLANK ONE
"Probability of Landing on Blue"
Answer:
1/4
Step-by-step explanation:
there are 2 blue sections out of a total of 8, so 2/8 or 1/4
who invented calculus?
Answer:
Isaac Newton and Gottfried Leibniz
Im pretty sure
what is 13= d divided by 6
Answer:
78
Step-by-step explanation:
You need to do inverse operations
13 x 6 = 78
D = 78
78 divided by 6 = 13
:)
Linnea’s company’s revenue in 2017 is 36/25 of its revenue in 2016
What is Linnea’s company’s revenue in 2017 as a percent of its revenue in 2016
Linnea’s company’s revenue in 2017 as a percent of its revenue in 2016 is; 1.44%.
Let Linnea’s company’s revenue in 2016 be x.Now, we are told that her revenue in 2017 is 36/25 of her revenue in 2016.
This means the revenue in 2017 = (36/25)xTo express this revenue as a percentage, we will multiply 36/25 by 100%.
⇒ 36/25 × 100%.
⇒ 1.44%
Thus, in conclusion Linnea’s company’s revenue in 2017 as a percent of its revenue in 2016 is 1.44%.
Read more at; https://brainly.com/question/21680230
Evaluate 4-7[(3-8)-(-5-8)]
Step-by-step explanation:
The Answer is 52
Hope it's Helpful
Nelson is 8 years old. His father is 36 years old. How old will Nelson and his father be when the sum of their ages is 62?
Answer:
Nelson will be 17, and his father will be 45.
Step-by-step explanation:
So let's say 9 years went by. N= Nelson, F= Father
N 8+9 = 17
F 36+9 = 45
45 + 17 = 62.
BOOOOOOM!!!!
Answer:
Nelson: 17, Father: 45
Step-by-step explanation:
8 + 36 = 44 13 + 41 = 54
9 + 37 = 46 14 + 42 = 56
10 + 38 = 48 15 + 43 = 58
11 + 39 = 50 16 + 44 = 60
12 + 40 = 52 17 + 45 = 62
Refer to check register to answer the questions
A) in the check register, what balance should have been entered on 7/31?
B) is the final balance on the register correct and if incorrect, what should the final balance be?
Yes/no (EXPLAIN SHOW YOUR WORK
Answer:
(a) In the check register, what balance should have been entered on 7/31?
Step-by-step explanation:
1056.37
(b) On the bank statement, what should have been entered for the total deposits?
1290.6
(c) On the bank statement, what should have been entered for the total withdrawals?
80
(d) On the bank statement, what should have been entered for the ending balance
976.37
(e) Which transaction caused an overdraft, and what was the overdraft amount?
Auto pay from the cable company and the overdraft was $85.77
(f) Is the final balance in the register correct? Show how you know.
No, its 976.37 because I did the math and it ended up at 967.37
(g) Why doesn’t the 8/6 ATM withdrawal appear on the bank statement?
Answer: (i dont know this one) it might be incorrect.
I need help asap please
Answer:
I think it is 35.
Step-by-step explanation:
Because I think what you do is subtract every number by each other for example 9 minus 10, 11 minus 15, 13 minus 20 so on and so on and then when you get all the answers add them all together and that's your answer. But I don't know so if it is wrong dont get mad at me because I'm only in 6th grade.
I need help and i have to show my work
Answer:
5.8x2.4=13.92
Step-by-step explanation:
if you put the two halves of a triangle like this together it makes a square then you times the length and width together and thats your triangle area
