Arecipe calls for 1 1/2 teaspoons of cinnamon to make 2 dozen oatmeal cookies. how many teaspoons of cinnamon are needed to make 60 oatmeal cookies?

teaspoons.

Step-by-step explanation:

We have been given that a recipe calls for teaspoons of cinnamon to make 2 dozen oatmeal cookies.

First of all, we will find number of teaspoons needed to make one oatmeal cookies.

1 dozen = 12

2 dozens = 24

Convert mixed fraction into improper fraction:

Convert to division problem by flipping the second fraction as:

Now, we will multiply amount needed for one cookie by 60 to find amount needed to make 60 cookies as:

Therefore, teaspoons are needed to make 60 oatmeal cookies.

From the question:

1 1/2 teaspoons of cinnamon =  2 dozen oatmeal cookies

1 dozen = 12

2 dozen oatmeal cookies = 2 x 12

= 24 oatmeal cookies

Hence:

1 1/2 teaspoons of cinnamon =  24 oatmeal cookies

The number of teaspoons of cinnamon needed to make 60 oatmeal cookies is calculated as:

24 oatmeal cookies = 1 1/2 teaspoons of cinnamon

60 oatmeal cookies =  c

Cross Multiply

24 oatmeal cookies x c = 60 oatmeal cookies x 1 1/2 teaspoons of cinnamon

c =  60 oatmeal cookies x 1 1/2 teaspoons of cinnamon/ 24 oatmeal cookies

x = 3 3/5 teaspoons of cinnamon

Therefore, the number of teaspoons of cinnamon  needed to make 60 oatmeal cookies is 3 3/5 teaspoons of cinnamon

To learn more, visit the link below:

link

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