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2 years ago

What is 1 - 1/6 * 3/2 =

Mathematics

1 answer:

kolezko [41]2 years ago

4 0

1-1/6*3/2

multiply the two fractions

1/6*3/2

Cross out 3 and 6, divide by 3.

1/2 * 1/2

multiply the numerators together

1*1=1

multiply the denominators together

2*2=4

1-1/4

pretend that 1 has a denominator which is 1

1/1-1/4

find the common denominator for 1/1 which is 4

multiply by 4 for 1/1

1*4/1*4=4/4

4/4-1/4

Answer:

3/4

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What is the sum of the first 70 consecutive odd numbers? Explain.

expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1$

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

$\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)$

The second sum is simply the sum of N ones:

$\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N$

So, the final result is

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2$

which ends the proof.

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2 years ago

You survey your class and record each students first name, last name, and age. You then make ordered pairs of (first name, age).

ExtremeBDS [4]

Answer: Yes

Step-by-step explanation:

It is a relation because each person will most likely have a different name and you can have plenty of the same outputs just as long as the input doesn't repeat at all.

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2 years ago

J.K. Rowling and R.L. Stine are both reading the hunger games. J.K. reads 35 pages every 2 hours and R.L. reads 45 pages every 3

Lilit [14]

Attention:THIS IS PART B ONLY!

First,find the unit rate.

35/2 and x/1

35 divided by 2 = 17.5 so the unit rate for J.K. is 17.5 pages per hour.

now,R.L.

45/3 and x/1

45 divided by 3 = 15 so the unit rate for R.L. is 15 pages per hour

now we need to divide 355 by 17.5 and divide it by 15.Whichever quotient is smaller,finishes the book first

355 divided by 17.5 = about 20 hrs----J.K.

355 divided by 15 = about 24 hrs-----R.L.

So,who read faster?

5 0

2 years ago

Read 2 more answers

-104= 8x please help 4 people are stuck on this

skelet666 [1.2K]

Answer:

8x = -104

divide 8

x = 13

7 0

2 years ago

Help! What is 5(3^3*3^-3) (Use Laws of Exponents) Thanks:)

RideAnS [48]

(3^3)* (3^-3)= 3^0
Remember that if you have the same base, add the exponents.

3^0=1

5(1)=5

Final answer: 5

3 0

2 years ago