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Sveta_85 [38]
3 years ago
6

An ounce of milk contains 20 milligrams of calcium and 60 micrograms of vitamin A.

Mathematics
1 answer:
vova2212 [387]3 years ago
6 0

Answer:

10 ounces of milk and 50 ounces of orange juice

Step-by-step explanation:

Let the amount of milk be x ounces and the amount of orange juice be y ounces.

1. An ounce of milk contains 20 milligrams of calcium and 60 micrograms of vitamin A. Then x ounces of milk contain 20x milligrams of calcium and 60x micrograms of vitamin A.

2. An ounce of orange juice contains 40 milligrams of calcium and 10 micrograms of vitamin A. Then y ounces of orange juice contain 40y milligrams of calcium and 10y micrograms of vitamin A.

<u>Calcium:</u>

20x milligrams in milk

40y milligrams in orange juice

2,200 milligrams in total

Hence,

20x+40y=2,200

<u>Vitamin A:</u>

60x micrograms in milk

10y micrograms in orange juice

1,100 micrograms in total

Hence,

60x+10y=1,100

Solve the system of two equations:

\left\{\begin{array}{l}20x+40y=2,200\\ \\60x+10y=1,100\end{array}\right.

Divide each equation by 10:

\left\{\begin{array}{l}2x+4y=220\\ \\6x+y=110\end{array}\right.

From the second equation:

y=110-6x

Substitute it into the first equation:

2x+4(110-6x)=220\\ \\2x+440-24x=220\\ \\2x-24x=220-440\\ \\-22x=-220\\ \\22x=220\\ \\x=10\\ \\y=110-6\cdot 10=110-60=50

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A chord subtends an angle 120° at the centre of the circle of radius 3.5cm. Find the perimeter of the minor sector.[r=22/7]​
Mamont248 [21]

Answer:

Step-by-step explanation:as we know that arc length is

s=r*∅

as given angle in degree so  convert it in radian we get

angle=2.09 rad

r=3.5 cm

hence we get

s=3.5*2.09 =7.315 cm

perimeter of sector = s +d  where d=2*r=2*3.5=7 cm

perimeter of sector=7.315+7=14.315 cm

if you like it then hit the stars and tag it a brain-list

4 0
3 years ago
A new car loses value at a constant rate. You purchase a new car for $21,500. After 3 years the value of the car was $14,120. Wh
Airida [17]

Answer:

Step-by-step explanation:

If the car is depreciating at a constant rate, this indicates that the function is linear.  We can find the equation for the linear function by first finding the slope of the line.  Let's do that using the slope formula.  The coordinates we will use to do this are found in (year, value).  Our coordinates are (0, 21500) and (3, 14120).  The first coordinate says that before any time goes by at all, meaning when the car was brand new, its value was 21500.  The second coordinate says that after 3 years, the value of the car was 14120.

m=\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

Filling in:

m=\frac{14120-21500}{3-0}=\frac{-7380}{3}=-2460

This is the slope.  In the context of our problem, it means that for each year that goes by, the car's value goes down $2460.  

Now we can use that slope and one of our coordinates to write the equation of the line.   We can choose either one of the coordinates to write our equation.  Let's use the first one, since it will be easier.  Rest assured that regardless of which one you choose, you will get the same equation. We fill in the slope-inteercept form of a line, y = mx + b, where y is the y value from the coordinate, m is the slope we solved for, x is the x value from the same coordinate, and b is the y-intercept.  We are solving for b.

21500 = -2460(0) + b and

21500 = 0 + b so

b = 21500.  Our equation, then, is

y = -2460x + 21500

If we want to find the value of the car, y, in 5 years, x, we plug in 5 for x and solve for y.

y = -2460(5) + 21500 and

y = -12300 + 21500 so

y = $9200

That means that in 5 year the car will be worth only $9200 when it is 5 years old.

5 0
3 years ago
The cheerleading squad at Belmont High School currently has 4 members. That is 20% fewer than were on it with the old coach. How
Sliva [168]

Answer:

20

Step-by-step explanation:

Divide 4 by 20%

20 cheerleaders.

5 0
2 years ago
Variables x and y are in direct proportion, and y = 48n when x = 16n. Which value of k correctly relates x and y in the equation
ella [17]
You want k.
k=y/x=48n/16n=3
3 0
3 years ago
A store had 235 MP3 players in the month of January. Every month, 30% of the MP3 players were sold and 50 new MP3 players were s
neonofarm [45]
The answer is A cause 30% is 0.7 and f(n-1) equals the amount being sold the +50 is for every 50 new one and the the 235 is for what they started with                                         
7 0
3 years ago
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