(a) 32 orange marbles
the ratio of red : blue = 18 : 48 = 3 : 8 ( in simplest form )
the ratio of green : orange = 3 : 8 ( equal ratio )
divide green by 3 to obtain 1 part of ratio then multiply this value by 8 to obtain the amount of orange marbles
3 parts → 12
8 parts → 12 × 
= 32 orange marbles
Answer:
x = 100
Step-by-step explanation:
Both angles are equivalent. 150-50=100. There's your answer! :)
Answer:
0.6 °C/min
Step-by-step explanation:
The relationship between rates and movement is ...
time = distance/speed
Here, the "distance" is measured in °C, and the "speed" is the rate of change of temperature.
For the first half of the heating, the time required is ...
(50°C -0°C)/(1.5 °C/min) = 50/(3/2) min = 100/3 min
For the second half of the heating, the time required is ...
(100°C -50°C)/(4/10 °C/min) = 50/(4/10) = 125 min
Then the total time is ...
((100/3) +125) min = (475/3) min
And the average rate of temperature increase is ...
total temperature change / total time
= (100°C -0°C)/(475/3 min) = 300/475 °C/min = 12/19 °C/min ≈ 0.6 °C/min
Answer: the cost of each bush is $15
the cost of each flower is $2
Step-by-step explanation:
Let x represent the cost of each bush.
Let y represent the cost of each flower.
Portia bought 12 bushes and 30 flowers for $240 to plant in her yard. This is expressed as
12x + 30y = 240- - - - - - - - - - -1
Later, she realized she did not have enough plants and bought 7 more bushes and 10 more flowers for $125. This is expressed as
7x + 10y = 125- - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 12, it becomes
84x + 210y = 1680
84x + 120y = 1500
Subtracting, it becomes
90y = 180
y = 180/90
y = 2
Substituting y = 2 into equation 1, it becomes
12x + 30 × 2 = 240
12x + 60 = 240
12x = 240 - 60 = 180
x = 180/12
x = 15
