Prepare 350g of a 2% lidocaine cream using a 1% lidocaine cream a 5% lidocaine cream
Answers
5% lidocaine -y g, 0.05y pure lidocaine
(1)0.01x+0.05y=350*0.02
0.01x g we get from1% lidocoine and 0.05y g we get from 5% lidocoine
(2) x+y=350
x g is mass 1% lidocoine, we combine it with y g 5%,
so we get x+y, and we need 350g,
so x+y should be equal 350, x+y=350
we get system of 2 equations that we need to solve to find x and y
(1)0.01x+0.05y=350*0.02
(2) x+y=350
we can solve it by substitution, find x from (2) equation
x=350-y, substitute it into (1)
instead of x we put (350-y)
0.01(350-y)+0.05y=7
3.5-0.01y+0.05y=7
0.04y =3.5
y=87.5g 5% lidocaine
b)x=350-87.5=262.5 g 1% lidocaine
c) 350g =350000 mg
Define x and y:
------------------------------------------------------------------
Let x be the amount of 1% lidocaine needed.
Let y be the amount of 5% lidocaine needed.
------------------------------------------------------------------
Construct Equations:
------------------------------------------------------------------
x + y = 350
0.01x + 0.05y = 0.02 x 350
0.01x + 0.05y = 7
------------------------------------------------------------------
Solve x and y:
------------------------------------------------------------------
x + y = 350 ------------- (Equation 1)
0.01x + 0.05y = 7 ------------- (Equation 2)
------------------------------------------------------------------
From equation 1:
------------------------------------------------------------------
x + y = 350
x = 350 - y
------------------------------------------------------------------
Substitute x = 350 - y into equation 2:
------------------------------------------------------------------
0.01(350 - y) + 0.05y = 7
3.5 - 0.01y + 0.05y = 7
3.5 + 0.04y = 7
0.04y = 7 - 3.5
0.04y = 3.5
y = 87.5
------------------------------------------------------------------
Substitute y = 87.5 into equation 1:
------------------------------------------------------------------
x + y = 350
x + 87.5 = 350
x = 350 - 87.5
x = 262.5
------------------------------------------------------------------
Find x and y:
------------------------------------------------------------------
x = 262.6g (5% lidocaine cream)
y = 87.5g (1% lidocaine cream)
------------------------------------------------------------------
Convert 350g to milligram:
------------------------------------------------------------------
350g = 350 x 1000 mg
350g = 350 000mg
------------------------------------------------------------------
Answer:
(a) Amount of 5% lidocaine needed = 87.5g
(b) Amount of 1% lidocaine needed = 262.g
(c) 350g = 350 000mg
------------------------------------------------------------------
Related Questions
What are the zeros of the polynomial function?
f(x)=x^2+9x+20
Enter your answers in the boxes.
Answers
9^2-4*1*20=1.
Using the quadratic formula, we get the solutions:
[tex] \frac{-9-1}{2} =-5\\ \frac{-9+1}{2}=-4 [/tex]
the solutions are then -4 and -5.
Help please!!!! I dont know this.
Answers
The area of the semicircle is
.. (1/2)π(20 in)^2 = 200π in^2
The area of the triangle is
.. (1/2)*(24 in)*(32 in) = 384 in^2
The shaded area is the difference
.. (200π -384) in^2
2(Square root 80/5 -5) = ??
Please help and show work! =^-^=
Answers
Final answer:
To solve the expression 2(√(80/5) - 5), we simplify the square root first, then subtract 5, and finally multiply by 2, which results in the solution -2.
Explanation:
To solve the expression 2(√(80/5) - 5), let's first simplify the square root and the division inside it.
We have √(80/5) = √16 = 4, since 80 divided by 5 is 16, and the square root of 16 is 4.
Next, we subtract 5 from 4: 4 - 5 = -1.
Finally, we multiply the result by 2: 2 * (-1) = -2.
Therefore, the solution to the expression 2(√(80/5) - 5) is -2.
The answer to the given question is: [tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) = \frac{2\sqrt{80}}{5} - 10 \][/tex]
To solve the expression step by step:
1. First, simplify the square root within the parentheses. The number 80 can be factored into [tex]\( 16 \times 5 \)[/tex], and since [tex]\( \sqrt{16} = 4 \),[/tex] we can rewrite[tex]\( \sqrt{80} \) as \( 4\sqrt{5} \).[/tex]
[tex]\[ 2\left(\frac{4\sqrt{5}}{5} - 5\right) \][/tex]
2. Next, distribute the 2 across the terms inside the parentheses:
[tex]\[ 2 \times \frac{4\sqrt{5}}{5} - 2 \times 5 \][/tex]
3. Simplify each term:
[tex]\[ \frac{8\sqrt{5}}{5} - 10 \][/tex]
4. At this point, we have the simplified form of the expression. However, if we want to combine the terms into a single fraction, we need a common denominator. The second term, -10, can be written as [tex]\( \frac{-10 \times 5}{5}[/tex]) to get the common denominator of 5:
[tex]\[ \frac{8\sqrt{5}}{5} - \frac{50}{5} \][/tex]
5. Now, subtract the two fractions:
[tex]\[ \frac{8\sqrt{5} - 50}{5} \][/tex]
6. This is the final simplified form of the expression. It cannot be simplified further algebraically because [tex]\( 8\sqrt{5} \)[/tex] and 50 do not have common factors other than 1.
Therefore, the final answer is: [tex]\[ \boxed{\frac{8\sqrt{5} - 50}{5}} \][/tex]
[tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) \][/tex]
And the final simplified answer is: [tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) = \frac{2\sqrt{80}}{5} - 10 \][/tex]
Find the probability of the independent event. 7) if p (e) = 0.9, p (f ∣
e.= 0.36, and e and f are independent, find p (f).
Answers
Four friends earned $5.20 for washing a car. They shared the money equally. How much did each friend get?
Answers
5.20 divided by 4 equals 1.3
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = − 8 x=-8 and x = − 4 x=-4 and passes through the point ( 0 , − 7 ) (0,-7) .
Answers
.. y = a(x +8)(x +4)
At x=0, this is
.. -7 = 32a
.. a = -7/32
The formula is
.. f(x) = (-7/32)(x +8)(x +4)
The formula for a parabola with roots at x=-8 and x=-4, and which passes through the point (0,-7), is y = -7/32(x + 4)(x + 8).
Explanation:The formula we're looking for is in the form of a quadratic function, generally expressed as
y = ax² + bx + c. Our roots are -8 and -4, which we represent in the factors of the equation as (x + 4) and (x + 8). As coefficients multiply to a, we seek a that makes our function pass through the specific point (0, -7). Thus, we substitute the point into the function giving -7 = a(0+4)(0+8) leading us to a = -7/32. So, the equation of the parabola asked is
y = -7/32(x + 4)(x + 8).
Learn more about Quadratic Function here:https://brainly.com/question/35505962
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What is the amplitude of the function below?
Answers
The amplitude is
[tex]2[/tex]
EXPLANATION
The amplitude is the height of the function from the centre line which is
[tex]y = 0[/tex]
to the peak or trough of the graph, which is
[tex]y = 2[/tex]
This means that,
[tex]amplitude = |2 - 0| = 2[/tex]
Or
The amplitude is distance between the lowest point on the graph and the highest point on the graph divided by 2.
[tex]amplitude = \frac{1}{2} |2 - - 2| = \frac{1}{2} \times 4 = 2[/tex]
Ben has 1/2 of a loaf of bread if he and his 3 friends share the 1/2 loaf equally how much of the whole loaf does each person get?
Answers
1/2 loaf of bread
3 friends
1/2 ÷ 3 ⇒ 1/2 * 1/3 = 1*1 / 2*3 = 1/6
In dividing fractions, get the reciprocal of the divisor and multiply it to the dividend
1/2 ÷ 3
or
1/2 ÷ 3/1
To divide fractions use Copy Dot Flip
Copy
1/2 ÷ 3/1
Dot
1/2 · 3/1
Flip
1/2 · 1/3
1/6 is your answer
Solve the division problem. Round answer to the nearest hundredth. 9.252.063
Answers
The square footage of a house is 1200 square feet. What type of data is this?
Answers
The explanation is shown above:
1- By definition, the area is the measure of a two-dimensional surface.Its units can be written in m^2, ft^2, in^2...However, in the International System of Units is m^2.
2. This is very useful when you want to know the surface of a house. If it is a rectangular house, you can calculate the area as below:
A=LxW
Where L is the length and W is the width
A person earns 26,800 one year and gets a 5% raise in salary. What is the new salary?
Answers
The new yearly salary is $28,140.
Explanation:Amount of raise.
5%=0.05
Multiply the original salary times the percentage of the raise.
$26,800×0.05=$1,340
New salary .
$26,800+1,340=$28,140
HOPE THIS HELPS! :)
This question is based on the concept of percentage. Therefore new salary when there is 5% raise in 26,800 is 28,140. There are many uses of calculating percent.
What is percent ?Percent is a proportionate of a number. Percent is a dimensionless quantity that is it has no unit. Percent is always out of hundred whereas fraction is always from 1. It is represented with the sign %. There are many uses of calculating percent. It is used in calculating interest in bank. It used in calculating inflation rate.
Mathematically,
The new yearly salary of a person is 28,140.
percentage of raise in salary is
5%=0.05
Multiply the original salary and the percentage of the raise in salary
26,800×0.05=1,340
New salary =26,800+1,340=28,140
Therefore new salary when there is 5% raise in 26,800 is 28,140
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https://brainly.com/question/1987628
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Find the trace on the xy-plane of the sphere having center at (−1, 3, −1) and radius 2.
Answers
The sphere has for equation :(x+1)²+(y-3)²+(z+1)²=4
The xy plane has for equation z=0
The trace off the sphere in the xyplane is
(x+1)²+(y-3)²=4 (the circle of center (-1,3,0) &nd 2 as radius)
Final answer:
The trace on the xy-plane of a sphere with center (-1, 3, -1) and radius 2 is a circle with center (-1, 3) and radius 2, represented by the equation (x + 1)² + (y - 3)² = 4.
Explanation:
The question asks to find the trace on the xy-plane of the sphere having a center at (-1, 3, -1) and a radius 2.
The trace on the xy-plane of a sphere is essentially the circle that is formed when the sphere intersects the xy-plane.
Since the center of the sphere is (-1, 3, -1), and the sphere intersects the xy-plane (z=0), we keep the x and y coordinates of the center the same for the circle, meaning the center of the circle will be (-1, 3). The radius of the circle remains the same as the sphere, which is 2.
The equation for a circle in the xy-plane with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².
Therefore, plugging in the values for this specific circle gives us the equation (x + 1)² + (y - 3)² = 4.
This equation represents the trace of the sphere on the xy-plane.
A high school has 3636 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing greater than or equal to 194194 pounds?
Answers
To calculate the percentage of players weighing 194 pounds or more from a box plot, we need to know where 194 pounds falls in relation to the quartiles on the plot. Without the box plot details, we cannot perform the needed analysis.
The student's question appears to concern the analysis of a box plot depicted in their materials to find the percentage of players weighing 194 pounds or more on a football team. However, to accurately answer this question, we need the specific details from the box plot, including the median (Q2), first quartile (Q1), third quartile (Q3), and any outliers if provided. From the box plot, we would determine where the weight of 194 pounds falls in relation to the quartiles. If 194 pounds is at or above Q3, then you would expect a lower percentage of players above this weight; if it is below Q3, then the percentage could be higher.
The approach typically involves identifying the number of players within each quartile and calculating the corresponding percentages. Without the specific box plot data, we cannot perform these calculations. Should you provide the box plot details, we can review the quartiles and calculate the exact percentage of players weighing 194 pounds or more.
what is -6x = -24
13 points
Answers
.. (-6x)/-6 = (-24)/-6
.. x = 4
_____
You asked "what is ..."
Answer: it is a "one-step" linear equation in x.
If f(x) = −2 + 8, what is f(−1.8)?
Answers
.. f(-1.8) = -2 +8 = 6
We suspect x is missing. Perhaps you intend
.. f(x) = -2x +8
.. f(-1.8) = -2(-1.8) +8 = 11.6
on wednesday, 30 students went to after school tutoring. on thursday, 6 students went. what is the percent decrease in the numbers of students who went to toturing?
Answers
Answer:
the number decreased by 80%
Step-by-step explanation:
The percentage change can be computed using ...
percent change = ((new value)/(old value) -1) × 100%
Putting the given numbers into this equation gives ...
percent change = (6/30 -1) × 100% = -4/5 × 100%
percent change = -80%
A negative sign on the percent change means the change was a decrease. The number of students who went to tutoring decreased by 80%.
Answer:
thanks
Step-by-step explanation:
For a science experiment,Juanita records the height of a plant every day in centimeters.What is the attribute measured in her experiment.
Answers
In Juanita's science experiment, the attribute measured is the plant's height, a key phenotypic trait in studying plant growth, which she records in centimeters, using consistent and precise units for scientific reliability.
The attribute measured in Juanita's science experiment is the height of a plant, which is a phenotypic trait important in plant biology. Juanita is collecting data related to plant growth by observing and recording the plant's height in centimeters daily. This meticulous tracking allows for analysis of plant growth patterns over time and the effect of various treatments, such as different fertilizers or amounts of water. The typical unit of measurement for the height of a plant is in centimeters or meters, which are part of the metric system used in scientific research.
During a laboratory experiment like the one Juanita is conducting, it is essential to measure such variables with precision and consistency. Measurements should be recorded using uniform units and methods to ensure reliability in the results, which may include the plant height, recorded in centimeters, at regular intervals. A graph representing this data might portray the number of days since the start of the experiment along the X-axis and the plant's height along the Y-axis, thereby allowing a visual assessment of the plant's growth over time.
What is the center of the circle represented by this equation? x^2 + (y + 9)^2 = 25 A) (3, 5) B) (0, 25) C) (9, 25) D) (0, -9)
Answers
(x-h)² + (y-k)² = r²
(h,k) are the center and r is the radius.
So from the given equation we can see that the center is at (0,-9).
Hope this helps :)
Prime numbers have less 1.than two factors.
2.more than two factors. 3.exactly two factors. 4.less than or equal to two factors.
Answers
exactly 2 factors
Answer:
They just have 2 factors :/
Step-by-step explanation:
Bc yes
A bag contains 2 red balls and 18 green balls. A ball is chosen at random from the bag. What is the BEST answer for the probability of drawing a green ball?
Answers
18 green
18/20 = 9/10 probability
A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
6 in3
24 in3
36 in3
48 in3
Answers
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C
what is the distance between the two points located at 9,12 and 9,-11
Answers
[tex]\sf 12-(-11)[/tex]
The negatives cancel out:
[tex]\sf 12+11[/tex]
[tex]\boxed{\sf 23}[/tex]
So the two points are 23 units apart from each other.
1.3 to the second power
Answers
1.3^2 = 1.3 x 1.3 = 1.69
how to solve this word problem
Answers
.. (number in school)/(560 lunches sold) = (60 students sampled)/(40 eat lunch)
Then
.. (number in school) = 560*60/40 = 840
The access code for a car's security system consists of sixsix digits. the first digit cannot be zerozero and the last digit must be oddodd. how many different codes are available?
Answers
Are repetitions allowed? Is 999999 permitted.
Repetitions allowed.
9 * 10 * 10 * 10 * 10 * 5 The last digit must be odd.
450,000 <<<< answer.
No repetitions
Sorry this requires more thought.
Judy can decorate 6 cakes in 3 hours. Exactly how many cakes can Judy decorate in 3/4 of an hour?
Answers
The polynomial 8x2 – 8x + 2 – 5 + x is simplified to 8x2 – gx – h. What are the value of g and h?
g = –9 and h = 7
g = 9 and h = –3
g = –7 and h = 7
g = 7 and h = 3
Answers
Answer:
Its D i just took the test
Step-by-step explanation:
Answer:
D. g=7 and h=3
Step-by-step explanation:
You are deciding on two different designs for envelopes.
a. Which design has the greater area?
The area of the first design is
52 square inches and the area of the second design is
61.375 square inches.
b. You make 500 envelopes using the design with the greater area. Using the same amount of paper, how many more envelopes can you make with the other design?
Please answer part b with the information given.
-A student in need
Answers
The area of the two designs are given as 52 square inches and 61.375 square inches.
In these the second design 61.375 square inches is having the greater area.
If 500 envelops are made then area of paper = 61.375x500 =30687.5 square inches.
If envelops having 52 square inches are made out of 30687.5 square inches of paper ,number of envelops made =30687.5 ÷ 52=590.144
590 small envelops can be made having area as 52 square inches.
It is 590-500=90 more than the larger envelops made.
HELP PLEASE , THANK YOU IF YOU DO!!!!
Answers
5 goes right 5 units and that's where you begin.
-6 goes left and that's where you end up.
The answer is minus 1.
A number line works best when you are dealing with 1 sign between numbers. Two signs will only confuse you.
Please help me with this question:
Riley made a scale drawing of a triangular clock face. Riley used a scale factor of 3 when making her drawing. If the base and the height of Riley's drawing are 10 centimeters and 15 centimeters respectively, what is the area of the triangular clock face?
A. 75 square centimeters
B. 225 square centimeters
C. 675 square centimeters
D. 2,700 square centimeters
Answers
[scale factor ]=[real]/[drawing]
[real]=[drawing]*[scale factor ]
step 1
find the real values
if the base of Riley's drawing is 10 centimeters
[real]=[drawing]*[scale factor ]--------> 10*3-------> 30 cm
the base of the triangular clock face is 30 cm
the height of Riley's drawing is 15 centimeters
[real]=[drawing]*[scale factor ]--------> 15*3-------> 45 cm
the height of the triangular clock face is 30 cm
the area of the triangular clock face is-----> 45*30/2-------> 675 cm²
the answer is the option C. 675 square centimeters