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Circle : Stalls

    2   :    5

5/2  = S/C

(5/2)C  =  S

So  the  number that can possiblt occupy S  = (5/2)(528)  = 1320

But only 2/3 of these showed up  = 880

So  the %   of  occupancy  =    [ 528 + 880 ]  / [528 + 1320]   = 1408 / 1848  = .76  = 76%

First question:

a)  Plot the point (4, 2600) on the graph.

b)  The relationship is linear with the older the car, the lesser value it has (the line has a negative slope).

c)  To estimate the value, plot these points on a sheet of graph paper, draw what you feel is the line through these data points that best represents the data (a "best-fit" regression line), and find the y-value of the point that is (3.5, something).

Second question:

a)  All of the points, except for one, is on a line from the lower left to the upper right. There is one point that is plotted away from the others, above the others, it is point (140, something)  -- this point is the outlier.

b)  The other points form a linear, positive, relationship (positive because the slope of the regresstion line is positive).

c)  Plot these points on a sheet of graph paper, draw what you feel is the best-fit line for these points, and then find where the line  y = 45 kg intercepts this line  -- this will give you his predicted height.

Second one.....this one is a little  difficult  !!!

Note  that  the ratio of 2  to 7   is the same as   6 to 21

So the ratio of blue to green  =  6 : 21

And  red : green  =  1 : 3   =    7 : 21

So.....we have the following possibilities

B      R      G          Total

6      7       21          34

12   14      42          68

24   28      84        136

So....the greatest number of red sweets possible   =   24

diagram: 

First one

M    :     W     :    C

17          9         12

Let  the number of women  =  x

So.....the  number of men  = x + 3512

And we know that

W             9

___  =    ____

M             17

So this implies that

9             x

__  =  ________        cross-multiply

17      x + 3512

9 ( x + 3512) = 17x     simplify

9x + 31608  = 17 x        subtract  9x from both sides

31608  =  8x       divide both sides by 8

3951  = x  = the number of women

We also know  that

 C           12         4

___  =    ___  =  __

 W            9         3

So  multiplying both sides of this  by W  we have that

C  = (4/3)W

C = (4/3)3951   = 5268  =   number of children

If you want to know the best point estimate of estimates that range from 47% to 63%, find the mean (or middle value) of these two numbers.

Calculate this, for you will need this to answer the next two questions.

The poll's margin of error is the amount from the mean to either of its endpoints (subtract the mean from the larger given value).

The best point estimate of that town's adult population can be found by multiplying the mean times the population.

x / y  = 5/3

This mplies that

x = (5/3)y

And we know that  x + y  =  56

So

(5/3)y + y  = 56

(5/3)y  + (3/3) y  = 56

(8/3)y = 56         mutiply both sides by  3/8

y = 56 (3/8)  =  21

And x = (5/3)y  =  (5/3)(21)  =  35

So

x - y  =  35  - 21   =   14

Let P be the beginning poulation

At the  end of  2005  the  new poulation is   (1.20)P

At the end of  2010, the population was  (1.30) [ (1.20)P]  = 1.56P

So....the poulation increased by  (1.56 - 1)  = .56 =  56%  from 2000 to 2010

have mercy

_.

Not sure about this....but

A   gcm of 24, 8   = 24

     gcm of 24, 7   = 168        meets the criteria  

B  gcm of 24, 7  = 168

     gcm  of 24 , 8 = 24        does not  meet the criteria

D  gcm  of 24,7=  168

     gcm of 24.,6  = 24       does not meet the criteria

E  gcm of 24,6  = 24

    gcm of 24, 7  = 168    meets the criteria

C gcm 24, 3   = 24

    gcm 24, 2   = 24     gcm's  are the same.....but  gcm of 24,y  >  gcm of 24,x

So this is the one that cannot  be true

So   y/x  cannot equal 2/3

cubrt (1000 x 3 x 3 x 3 x 3 x 2 x 2 )

10 cubrt ( 3 x 3 x 3 x 3 x 2 x 2)

30 cubrt (3 x 2 x 2 )

30 cubrt (12)

Let  the top  of the clock  = 0°

Every minute the minute hand  moves 6°  [in 60 min it moves 360°]

And every minute the hour hand moves   (1/2)°   [in 60 min it moves 30°...1/12 of a complete rotation ]

So in 48 minutes the minute hand has moved  48*6  = 288° from the top of the clock

And in the same time the  hour hand has moved 48 * (1/2)  = 24°  from the top of the clock

So.....the larger angle formed by the hands = 288 - 24  = 264°

So....the smaller angle  formed  = 360  - 264   = 96°

Ohh nooes! It's one of the questions the YouTube channel MindYourDecisions has covered! They are extremely hard (at least for middle schoolers)!

For teh second one:

Let's treat 20 as one data point. There are 10 data points less than 20, and 20 data points more than 20.

In case you didn't know, the median is the middlemost number in a data set, when it is arranged from greatest to least.

For example, in the array (1, 3, 5, 7, 9), 5 is the median as it is in the middle. There are 2 numbers to its left, and 2 numbers on its right.

When dealing with arrays that don't have a middlemost number (i.e. having an even number of data points) like (1, 2, 3, 4, 5, 6), we just find the two numbers closest to the middle. Here, the medians would be 3 and 4.

Using this information, could you estimate in which interval the median for the plant set will be? I trust you can! :D

This might be a good place to start - "https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.1069909.html"

AD = CF    (1)

BD = DF     

Using (1).....this must mean that

(AB + BD)  = (CD + DF)    (3)

Since BD = DF....then this implies that

(AB + BD)  =  (CD + BD)     subtract  BD  from both sides

AB   =   CD

Lmao its true AOPs has the best solutions!

Thanks CPhil !

For the first one:

The frequency is how many bags containing each number of apples there are.

The sum of the apple in the first 11 bags would be \((6 * 1)+(7*4)+(8*2)+(9*3)+(10*1)\)

which is \(6+28+16+27+10=87\) total apples in the first 11 bags :D

The formula for the average (mean) is the sum of all the data points divided by the number of data points.

The number of apples in the 12th bag is unknown, so let's call that x.

We know that the sum of all the data points is \(87+x\). That divided by 12 (the number of data points) equals the mean, which, as stated by the question, is \(8\).

So, our equation is that \(\dfrac{87 + x}{12} = 8\) :D

Multiplying the equation by 12 gets us \(87+x=96\).

Now, we can subtract 87 from the equation to get that \(x=96-87=9\).

So, the 12th bag contains \(9\) apples :D

I don't think we  need the Law of Sines or Cosines, here

Call home plate  point A

Call third base point B

Call the point  at the right field fence  C

We have a right triangle  ABC  with angle BAC  =  90°

The distance we are  looking for is the hypotenuse= BC

AC  is one leg  = 300

AB is the other leg  =  90 ft from home plate to third base

So

BC  = √ [ AC^2 + AB^2]  = √  [ 300^2 + 90^2]  = √ 98100  ≈  313.2 ft

Agreed. Very intriguing!

10x - 3y           3

_______  =   ___     cross-multiply

13x - 2y           5

5 [ 10x - 3y ]  =   3 [ 13x - 2y ]   simplify

50x - 15y =  39x  - 6y        add  15y to both sides.....subtract  39x  from both sides

11x  = 9y

x / y   =  9 / 11

x : y  = 9 /11

Thank you so much! I can try and understand some of what you wrote, but why did those numbers get there? Could you explain more? :D

So AE = AG + GE = 10.

This looks hard... if you found AE to be 10, how would you use that to find the length of other sides in the parallelogram? How could you use those to find the angle measurements? Using that information, how could you find EF? :D

The total number of  votes   must have been 60  / .24   =     250

To win....a candidate must get  more than  250/2 =  125  votes

Note that 126 votes would do the trick !!!!

The  hedgehog  originally got  .42 * 250   = 105 votes

So....out of the 60 voters.....he  (or she) needs to get at least    126 - 105  =    21 votes from them to win