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Illusion [34]
2 years ago
10

How many grams of salicylic acid should be added to 75 g of a polyethylene glycol ointment to prepare an ointment containing 6%

w/w of salicylic acid?
Mathematics
1 answer:
Alla [95]2 years ago
6 0

Answer:

4.79 g

Step-by-step explanation:

mass of salicylic acid = ??

Mass of polyethylene = 75 g

% w/w concentration = 6% w/w

Let the mass of  salicylic acid be x

Let the mass of solution = 75 + x

from

% w/w = mass of solute/ mass of solution * 100

Hence concentration of salicylic is;

6 = (x/75 + x) * 100

6/100 = x/75 + x

0.06 (75 + x) = x

4.5 + 0.06x =x

4.5 = x-0.06x

x = 4.5/0.94

x= 4.79 g

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Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches
sergeinik [125]

Answer:

\large \boxed{\text{5.00 lb}}

Step-by-step explanation:

\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}

Check:

\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}

OK.

5 0
2 years ago
An epidemiologic survey of roller-skating injuries in Metroville, a city with a population of 100,000 (during the midpoint of th
Ahat [919]

Answer: c. \dfrac{90}{1800}\times100\%

Step-by-step explanation:

As per given , we have

Total number of residents injured from roller-skating =1,800

Total number of deaths from roller-skating = 90

Formula for Mortality rate : Mortaility\ rate= \dfrac{Deaths\ due \ to\ injury}{Tota\ injuries}

Then, the proportional mortality ratio (%) due to roller-skating was

=\dfrac{90}{1800}\times100\%

= 5%

Hence, the correct answer is c.\dfrac{90}{1800}\times100\%

8 0
2 years ago
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number
Masja [62]

Answer:

<h2>√512 by √512 </h2>

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

5 0
2 years ago
A guy wire is used to support flagpoles in windy areas. These wires are anchored in the ground to provide constant stability. Yo
r-ruslan [8.4K]

Answer: a) Length of wire to replace old one=9ft

b) Length of wire=3.09ft

Leftover wire=0.91ft

Step-by-step explanation: from the right angle triangle, Tan&=20/15

&=53.13°

Length of wire,x=cos 31.13=x/15

15cos31.13

X=9

b) Tan&=10/6

Tan^-110/6

&=59.05

Length= 6cos59.04

X=3.09

4-3.09=.91= leftover wire

8 0
2 years ago
Two planes, which are 3400 miles apart, fly toward each other. Their speeds differ by 80mph. If they pass each other in 5 hours,
Andreas93 [3]

Answer : The speed of both planes is 61.25 mph and 18.75 mph  respectively.

Explanation:

Let the speed of first plane be x mph

Let the speed of second plane be y mph

Since we have given that difference of speeds is 80 mph

i.e.  x - y= 80   (Eq^n   1)

Distance between two planes = 3400 miles

As they are flying towards each other i.e. they are in the opposite direction.

So, Relative speed  will  be the sum of their speeds i.e.

Relative speed = x + y

And we know speed = \frac{Distance}{Time}

Speed= \frac{3400}{80}

⇒ Speed = 42.5 mph

Hence, Relative speed becomes 42.5 mph

⇒ x+y=42.5  (Eq^n   2)

Now, by using the elimination method of solving the system of equation, we  have ,

x= 61.25 mph

and y = 18.75 mph



4 0
2 years ago
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