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3 years ago

-8/-33 convert into a decimal

Mathematics

1 answer:

harina [27]3 years ago

6 0

Answer and Step-by-step explanation:

This fraction as a decimal is 0.24 repeating, which means the decimals keeps repeating the numbers 24 after the decimal place.

#teamtrees #PAW (Plant And Water)

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What Is an exponent?

just olya [345]

Answer:

a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g. 3 in 23 = 2 × 2 × 2).

Step-by-step explanation:

6 0

3 years ago

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

3 years ago

Help with this question ??

salantis [7]

Answer:

15 units per unit

Step-by-step explanation:

From the graph we can easily tell that y increases from 0 to 15 as x increases from 2 to 3.

Thus, the average rate of change of f(x) on the interval [2, 3] is:

1 15 - 0 15 units

--------- * ----------- = -------------- = 15 units (rise) per unit (run).

3 - 2 1 1

6 0

3 years ago

Jose wants to build a rectangular kennel for his dog. His dad will let him use a spot in the corner of the yard that is 12 feet

Butoxors [25]

Hello!

We don't need to find the exact perimeter of the fencing, just an estimate.

We will round 12 ft 3 in to 12 ft, because it is closer to 12 ft than 13 ft.

We will also round 8 ft 11 in to 9 ft because there are 12 inches in a foot, which makes 9 ft closer.

The formula for perimeter of a rectangle is:

P = 2l × 2w

The length is about 12 feet and the width is about 9 feet.

Substitute the length and width:

P = 2(12) + 2(9)

Solve:

P = 24 + 18

P = 42

Jose will need about 42 feet of fencing.

8 0

3 years ago

What is the LCM of 30 and 45? a0

Alik [6]

90 is the LCM of 30 and 45

8 0

3 years ago

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