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ziro4ka [17]
3 years ago
14

josiah has 147 toy cars. if he organizes them in groups of 9, how many cars will be in the final group?

Mathematics
2 answers:
Snowcat [4.5K]3 years ago
7 0
16 groups of 9. 17th group with 3 left.
meriva3 years ago
5 0

The answer is 17... You have to do 147 by 9


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Consider the following series. 1 9 1 18 1 27 1 36 1 45 Determine whether the series is convergent or divergent. Justify your ans
Vedmedyk [2.9K]

Answer:

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

Step-by-step explanation:

<u>Convergence of Infinite Series</u>

The series is given as the terms

1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...

For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.

Our series has two clearly different sequences, which define it as a piecewise general term:

If n is odd, then

a_n=1

Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is

a_n=9+9(n/2-1)=4.5n

if n is even.

If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.

The limit of the function

a_n=1

is 1 when n goes to infinity. Since it's not 0, this piece is not convergent and the entire series isn't either.

But it goes worse because of the limit of the second piece

a_n=4.5n

when n goes to infinity is infinite.

The answer is

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

8 0
3 years ago
83 Tee (CsT Sequences and Functions
NISA [10]

Answer:

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x                        y

1                         4

2                        -5

3                        -14

4                        -23

5                         -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.

3 0
2 years ago
Determine whether the improper integral converges or diverges, and find the value of each that converges.
Ksju [112]

Answer:converge at I=\frac{1}{3}

Step-by-step explanation:

Given

Improper Integral I is given as

I=\int^{\infty}_{3}\frac{1}{x^2}dx

integration of \frac{1}{x^2}  is  -\frac{1}{x}

I=\left [ -\frac{1}{x}\right ]^{\infty}_3

substituting value

I=-\left [ \frac{1}{\infty }-\frac{1}{3}\right ]

I=-\left [ 0-\frac{1}{3}\right ]

I=\frac{1}{3}

so the value of integral converges at \frac{1}{3}

8 0
3 years ago
Donna, Neil, and Frank are siblings. Donna is the oldest. Frank’s age is 1/4 of Donna’s age. Right in equation to represent Fran
shusha [124]
D of 1/4 = F
    OR
D x 1/4= F
8 0
3 years ago
A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?
OverLord2011 [107]
Let's call the 13¢ stamps a and the 18¢ stamps b: a+b = 42 and therefore a= 42-b (formula 1) 0.13a+0.18b= 6.66 In this formula, substitute the value of a according to formula 1: 0.13(42-b)+0.18b= 6.66 Multiply on the left to get rid of the parenthesis: 5.46-0.13b+0.18b= 6.66 Subtract 5.46 from both sides: -0.13b+0.18b= 1.20 Add on the left: 0.05b= 1.20 Divide both sides by 0.05 b= 24 You have 24 18¢ stamps and: 42-24= 18 13¢ stamps Check: (24 x 0.18) + (18 x 0.13)= 6.66 Correct.
5 0
3 years ago
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