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Roman55 [17]
3 years ago
11

Find the sum of 23+24+25+...+103

Mathematics
1 answer:
tatyana61 [14]3 years ago
3 0

Let

S=23+24+25+\cdots+101+102+103

This sum has ___ terms. Its terms form an arithmetic progression starting at 23 with common difference between terms of 1, so that the n-th term is given by the sequence 23+(n-1)\cdot1=22+n. The last term is 103, so there are

103=22+n\implies n=81

terms in the sequence.

Now, we also have

S=103+102+101+\cdots+25+24+23

so that adding these two ordered sums together gives

2S=(23+103)+(24+102)+\cdots+(102+24)+(103+23)

\implies2S=\underbrace{126+126+\cdots+126+126}_{81\text{ times}}=81\cdot126

\implies S=\dfrac{81\cdot126}2\implies\boxed{S=5103}

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katen-ka-za [31]
Hello,

We must calculate the volume of water in one hour.

V=15000*PI*0.07²=230,9070600... m^3/h.

Volume of the pond=50*44*.21=462 m^3

Time=462 m^3/ 230.907... m^3/h=2,0008... h≈2 h


5 0
4 years ago
1. You purchase a car using a $20,000 loan with a 5% simple interest rate.
Vesna [10]

Answer:

A:4000

B:2000

C: More interest on the 4 year loan

Step-by-step explanation:

5% of 20000 is 1000 so the amount of years times the amount of interest per year. 4 years is (4x1000=4000) and 2 years is (2x1000) 4000 is greater than 2000.

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5 0
3 years ago
Read 2 more answers
H and J are both between G and K such that GH = JK and H is between G and J.
DIA [1.3K]

Answer:

32

Step-by-step explanation:

So the order of the points is: GHJK

GH = x+10 =JK

HJ=8

JK=2x-4

JK = x+10=2x-4

x+10=2x-4

10+4=2x-x

x=14

GH= 14+10 =24

GJ = GH +HJ = 24+ 8=32

6 0
3 years ago
"If two lines intersect, then the intersection is a point." What is the hypothesis? Two lines intersect
larisa86 [58]

Answer:

Hypothesis is: Intersection happens at a point

Step-by-step explanation:

A hypothesis in science is a suggested explanation of something that has a consequence or leads to an occurrence.  Usually it will be written in the form of an "if and then" statement.

Such statement explains what would occur, or follow if the possibility enunciated in the "if" part of the statement happens.

In this case the hypothesis is that if there is intersection of lines, it has to occur at a point. Therefore the closest to that statement among the options given in the problem is the last one: "Intersection happens at a point"

5 0
3 years ago
At a high school soccer league, each team has m players. There are 20 teams in
max2010maxim [7]

Answer:

20m

Step-by-step explanation:

Given:

Number of players per team = m

Number of teams in the league = 20

The number of players in the league is the product of the number of payers in each team and the number of teams in the league.

This the expression to obtain the total number of players goes thus :

Total number of players in the league = 20 * m

Total Numbr of players in the league = 20m

6 0
3 years ago
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