Question 3 1 pts
Tim has 74 socks, all in pairs. He has 1 more pair of white socks than black socks. How many individual socks of
each color does he have?

36 individual white socks

38 individual black socks

Step-by-step explanation:

Pairs of socks = 74

He has 1 more pair of white socks than black socks.

Take the colors of the socks to be white and black

Let

Black pairs of socks = x

White pairs of socks = x + 1

Individual socks of each color

A pair of white socks = 2 Individual white socks

= 2white

A pair of black socks = 2 individual black socks

= 2black

Total pairs of socks = black pairs of socks + white pairs of socks

74 = 2white + 2black

74 = 2(x) + 2(x +1)

74 = 2x + 2x + 2

74 = 4x + 2

Subtract 2 from both sides

74 - 2 = 4x

72 = 4x

Divide both sides by 4

x = 72/4

= 18

x = 18

Pairs of white socks = x = 18

A pair of white socks = 2whites

= 2(18)

= 36 individual white socks

Pairs of black socks = x + 1

= 18 + 1

= 19 pairs

A pair of black socks = 2black

= 2(19)

= 38 individual black socks

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.