Answer: She would need 206 paper cups.
Step-by-step explanation: First of all, Monica has a 10-gallon container full of lemonade and this translates into 37850 cubic centimetres volume of lemonade. The conversion rate has been provided as one gallon equals 3785 cubic centimetres, therefore ten gallons would be 3785 times ten which gives you 37,850 cubic centimetres of lemonade.
Each cone shaped paper cup has a diameter measuring 8 centimetres and 11 centimetres in height. The radius of the cone shaped cup therefore is 4 centimetres (radius equals diameter divided by two). The volume of each cup therefore is given as;
Volume of a cone = (πr²h)/3
Volume of a cone = (3.14 * 4² * 11)/3
Volume of a cone = 552.64/3
Volume of a cone = 184.2
If each cone could hold 184 cubic centimetres of lemonade, then the entire ten gallons would require the following number of cone shaped cups;
Number of cups = Total volume/Volume of a cup
Number of cups = 37850/184.2
Number of cups = 205.48
Rounded to the nearest whole number, this becomes
Number of cups ≈ 206
Therefore Monica would need 206 cone shaped paper cups to empty the entire 10 gallons of lemonade.
Answer:
Tamara incorrectly factored the whole expression.
Step-by-step explanation:
Note that
•21x=3·7·x;
•56xy=2·2·2·7·x·y.
Mark in bold all common factors, then GCF(21x,56xy)=7·x=7x.
Thus,
21x+56xy=7x(3+8y).
Hence, Tamara correctly found the GCF of numbers 21 and 56, but incorrectly factored the whole expression.
A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer.
Let x be the speed of the car
Car trip from New York to Cincinnati
We know Distance D = speed * time
time = 12.5 hours and speed =x
D = 12.5x
Return trip
The return trip by the same route took 1 hour longer. So 12.5+1 = 13.5 hours
he average rate of speed was 4 mph less. So speed is x-4
Distance D = speed * time
time = 13.5 hours and speed =x-4
D = (x-4)*13.5
D= 13.5x-54
The distance of ongoing trip and return trip are same
So we equate both the distance equations D= 13.5x-54 and D= 12.5x
12.5x = 13.5x-54
Subtract 13.5 on both sides
-1x = -54
x=54
speed of ongoing trip = 54 miles per hour
Distance D = 12.5x = 12.5 * 54=675 miles
The length of the route = 675 miles
Standard deviation (s): 2.7386127875258
*see attachment for the figure referred to
Answer/Step-by-step explanation:
1. PN = 29
MN = 13
PM = ?
(Segment addition postulate)
(subtract MN from each side)
(substitute)
2. PN = 34, MN = 19, PM = ?
(sediment addition postulate)
(subtract MN from each side)
(substitute)
3. PM = 19, MN = 23, PN = ?
(Segment addition postulate)
(substitute)
4. MN = 82, PN = 105, PM = ?
(segment addition postulate)
(subtract MN from each side)
(substitute)
5. PM = 100, MN = 100, PN = ?
(Segment addition postulate)
(substitute)
