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podryga [215]
3 years ago
13

I have to redo this test and I'm stuck on this question. Please help and please show work.

Mathematics
1 answer:
nexus9112 [7]3 years ago
5 0
This is the answer hope this helped u

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Use​ Gauss's approach to find the following sums​ (do not use​ formulas). 1+3+5+7+...999
muminat
S=1+3+5+\cdots+995+997+999
S=999+997+995+\cdots+5+3+1
\implies 2S=(1+999)+(3+997)+(5+995)+\cdots+(995+5)+(997+3)+(999+1)

2S=\underbrace{1000+1000+\cdots+1000+1000}_{500\text{ times}}

(We are adding 500 instances of 1000 because that's how many odd numbers there are between 1 and 1000, inclusive.)

2S=500\times1000=500000
\implies S=250000
4 0
3 years ago
Fred and Frank play a game. Fred picks an even number X and asks Frank to add all even numbers between 0 and X (inclusive) as fa
TiliK225 [7]

Answer:

The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2

The rule of arithmetic sequence = a + d(n - 1)

Where a is the first term and n is the number of terms

So, for the even numbers between 0 and X

The first term = a = 0

d = 2

So, we need to find n at the last term which is X

∴ X = 0 + 2 ( n -1 )

∴ n - 1 = X/2

∴ n = X/2 + 1

The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)

Substitute with a and d and X

So, the sum = (n/2) * (2*0 + (n−1)*2)

                   = (n/2) * ((n−1)*2)

                   = n(n-1)

                   = (X/2 + 1) * (X/2)

                   = X/2 by (X/2 + 1)

So, The quick way to add all even numbers between 0 and X always works.

8 0
3 years ago
The formula gives the height of an object in free fall at time t and acceleration g.
ale4655 [162]

t must equal √2h/g but I don't see that in the choices above

3 0
3 years ago
Kevin randomly selects 1 card from a standard deck of 52 cards. What is the probability that the card Kevin selects is a king or
ki77a [65]
<span>A, 13/52 of the cards are hearts, + three more kings (king of hearts has already gone) = 16/52. divide 16 and 52 by 4 = 4/13.</span>
4 0
3 years ago
Read 2 more answers
What is the answer ​
dybincka [34]

Answer:

C

Step-by-step explanation:

Just re-draw the triangle reflecting the y-axis

3 0
3 years ago
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