On a certain hot summer's day, 225 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $435.25. How many children and how many adults swam at the public pool that day?

Step-by-step explanation:

Let us represent:

Number of children = x = 59

Number of Adults = y = 166

On a certain hot summer's day, 225 people used the public swimming pool.

x + y = 225

x = 225 - y

The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $435.25.

$1.75 × x + $2.00 × y = $435.25

1.75x + 2y = 435.25

We substitute 225 - y for x

Hence:

1.75(225 - y ) + 2y = 435.25

393.75 - 1.75y + 2y = 435.25

Collect like terms

-1.75y + 2y = 435.25 - 393.75

0.25y = 41.5

y = 41.5/0.25

y = 166 Adults

Note that:

x = 225 - y

x = 225 - 166

x = 59 children

Hence, the number of children is 59 and the number of Adults is 166

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.