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4 years ago

11

How to round 983.625; to the nearest hundredths

2 answers:

MaRussiya [10]4 years ago

5 0

The answer would be 938.62.

igomit [66]4 years ago

5 0

The answer will be 983.63. Since .625, has a 5, and 5 rounds up while 4 and below rounds down

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Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

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

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

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

2 years ago

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x).

Svetradugi [14.3K]

Answer:

(f-g)(x)

= -x^2 - 2x + 2

Step-by-step explanation:

(f-g)(x) means

f(x) - g(x)

= x - 2 - (x^2+3x-4)

distribute the subtraction to all three of the last terms.

= x - 2 - x^2 - 3x + 4

combine like terms

= -x^2 - 2x + 2

8 0

2 years ago

The probabilities of the top-selling menu item in four towns' restaurants being different types of vegetarian and nonvegetarian

Masja [62]

So go with about B. 25.3%

7 0

3 years ago

Find the trigonometric ratio of tan 106

olga55 [171]

He said that it was the best

4 0

3 years ago

Adrian is a songwriter who collects royalties on his songs whenever they are played in a commercial or movie. Adrian will earn $

djverab [1.8K]

Answer:

commercial = 9

movie = 5

Step-by-step explanation:

Step one:

let the number of commercials be x and movies be y

so

40x+130y=1010-------------1

since there are a total of 14 commercials and movies combined

x+y=14--------------2

Hence the systems of equation is

40x+130y=1010------1

x+y=14-------------------2

Step two:

from equation 2

x=14-y

substui]te the value of x in equation 1

40(14-y)+130y=1010

560-40y+130y=1010

collect like terms

130y-40y=1010-560

90y=450

divide both sides by 90

y=450/90

y=5

movies is 90

put y=5 in equation 2

x+5=14

x=14-5

x= 9

commercial is 9 in numbers

and movie is 5

7 0

3 years ago