153 apples, 255 oranges, 357 pears are to be distributed to a group of children. Suppose each child in the group receives an equal number for each type of fruit.

a) Find the least possible number of children in the group

b) the maximum possible number of children in the group

c) the least possible number of apples, oranges and pears each child can receive

d) the maximum possible number of apples, oranges and pears each child can receive.​

Answers

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

a) we need the grestest common factor of  theses values

153 = 3 * 3 * 17

255 =  3 * 5*17

357 = 3 * 7 * 17

The GCF = 3 * 17 = 51.

a) the least possible number of children  is 3.

b) The maximum number is 51 ( as 51 is the GCF of the given values).

c) the least possible number of fruits is when  b)  occurs, that is:

153/51, 255/51 and 357/51

= 3 apples , 5 oranges and 7 pears.

d) the maximum number of fruits is :

153/3, 255/3 and 357/3

= 51 apples , 85 oranges and 119 pears.

Answer 2

Answer:

a) 3 children

b) 51 children

c) 3 apples, 5 oranges and 7 pears

d) 51 apples, 85 oranges and 119 pears

Step-by-step explanation:

lnc - Least possible number of children in group

mnc - maximum possible number of children in group

a - Apples

o - Oranges

p - Pears

a = 153

o = 255

p = 357

a)

To solve this, find the highest divisor for the apples, oranges and pears.

[tex]a = \frac{153}{51} [/tex]

[tex]a = 3[/tex]

[tex]o = \frac{255}{85} [/tex]

[tex]o = 3[/tex]

[tex]p = \frac{357}{119} [/tex]

[tex]p = 3[/tex]

In order for each child to get 51 apples, 85 oranges and 119 pears, there would need to be a minimum of 3 children in the group.

[tex]lnc \: = 3[/tex]

b)

To solve this, find the lowest divisor for the apples, oranges and pears.

[tex]a = \frac{153}{3} [/tex]

[tex]a = 51[/tex]

[tex]o = \frac{255}{5} [/tex]

[tex]o = 51[/tex]

[tex]p = \frac{357}{7} [/tex]

[tex]p = 51[/tex]

In order for each child to get 3 apples, 5 oranges and 7 pears, there would need to be a maximum of 51 children in the group.

[tex]mnc = 51[/tex]

c)

In a group of 51, each child will get:

- 3 apples

- 5 oranges

- 7 pears

d)

In a group of 3, each child will get

- 51 apples

- 85 oranges

- 119 pears


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Answers

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Answers

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A 2-column table with 6 rows. the first column is labeled week with entries 1, 2, 4, 6, 8, 10. the second column is labeled miles run with entries 5, 8, 13, 15, 19, 20. rita is starting a running program. the table shows the total number of miles she runs in different weeks. what is the equation of the line of best fit for the data? state each number to the thousandths place. y ≈ x

Answers

The line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x

How does linear regression works?

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.

The following data for the Week and miles run variables are provided to construct linear regression model:

Week miles run

      1    5

      2    8

      4    13

     6    15

     8    19

    10    20

The independent variable is Week(represented by x), and the dependent variable is miles run(represented by y). In order to compute the regression coefficients, the following table needs to be used:

Let week = x, and miles run = y, then we get this table:

              x      y      xy    [tex]x^2[/tex]     [tex]y^2[/tex]

----------------------------------------------------

             1       5       5      1      25

             2      8       16    4     64

             4      13      52   16   169

             6     15       90   36  225

            8      19      152   64  361

           10     20     200  100 400

-----------------------------------------------------

Sum =  31   80    515   221  1244

Based on the above table, the following is calculated:

[tex]\bar X = \frac{1}{n} \sum_{i=1}^{n} X_i = \frac{ 31}{ 6} \approx 5.167[/tex]

[tex]\bar Y = \frac{1}{n} \sum_{i=1}^{n} Y_i = \frac{ 80}{ 6} \approx 13.33[/tex]

[tex]\large SS_{XX} = \sum_{i=1}^{n} X_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right)^2 = 221 - 31^2/6 \approx 60.833[/tex]

[tex]\large SS_{YY} = \sum_{i=1}^{n} Y_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} Y_i\right)^2 = 1244 - 80^2/6 \approx 177.33[/tex]

[tex]\large SS_{XY} = \sum_{i=1}^{n} X_i Y_i - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right) \left(\sum_{i=1}^{n} Y_i\right) = 515 - 31 \times 80/6 \approx 101.67[/tex]

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

[tex]m = \frac{SS_{XY}}{SS_{XX}} \approx \frac{ 101.67}{ 60.833} \approx 1.6712[/tex]

[tex]n = \bar Y - \bar X \cdot m = 13.33- 5.167 \times 1.6712 = 4.6986[/tex]

Therefore, we find that the regression equation is:

miles run = 4.6986 + 1.6712 Week

y = 4.6986 + 1.6712x (approximately)

To the thousandths place, it becomes:

y = 4.699 + 1.671x

Therefore, based on the information provided above, the following scatter plot and regression plot are obtained as the image attached below.

Thus, the line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x

Learn more about linear regression here:

https://brainly.com/question/18854090

Answer:

y-1.671

4.699

Step-by-step explanation:

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