Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4? f(n 1) = f(n) 99.4, n ≥ 1 f(n 1) = f(n) – 99.4, n ≥ 1 f(n 1) = 99.4f(n), n ≥ 1 f(n 1) = –99.4f(n), n ≥ 1
The recursive formula for the given sequence is [tex]f(n+1)=f(n)-99.4[/tex]
What is recursive formula?Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula [tex]a_n = a_{n-1} + d[/tex]. [tex]a_n = a_{n-1}r[/tex] is the recursive formula for a geometric sequence.
We are given a sequence as:
99.4,0,-99.4,-198.8, and so on
We can see that the sequence is constantly getting decreased by -99.4
i.e. f(1)=99.4
Then, f(2)=f(1)-99.4
=99.4-99.4
=0
f(3)=f(2)-99.4
=0-99.4
=-99.4
Therefore, the recursive formula of the given series is [tex]f(n+1)=f(n)-99.4[/tex]
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Someone help me please
30-60-90 triangles
Answer:
Short leg = 10
Longer leg = 10[tex]\sqrt{3}[/tex]
Hypotenuse = 20
Step-by-step explanation:
The given is a special right triangle, its angle measures are as follows:
30-60-90 and the side lengths will follow as:
x, x[tex]\sqrt{3}[/tex], 2x respectively.
The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20
We can conclude x = 10 from this
So the length of short leg is 10
Then the length of longer leg is 10[tex]\sqrt{3}[/tex]
The length of hypotenuse is already given as 20
PLEASE HELP ME !!!
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the
cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
base area for cone= B
base area for pyramid= B, 3r heigh
A. V = pi r³
B. V = 1/3 pi r²
C. V = 2 pi r²
D. V = 1/9 pi r³
E. V = 3 pi r³
Answer:
The answer is A. V=pi r³
Step-by-step explanation:
:)
The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.
The cone is a three-dimensional figure with a vertex and a flat base.
The volume of a pyramid is given by the formula:
[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]
Given that:
The base area of the pyramid = B
The height is 3r
The base area of the pyramid is the same as that of the cone.
The base of the cone = [tex]\pi r^2[/tex]
The volume of the pyramid is calculated as:
[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]
V =[tex]\pi r^3[/tex]
Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.
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Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2
Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22
Someone please explain.50 points available.Thankyou so much!
Answers:
a) 49 square tiles - did the work on paper.
b) 83 circular tiles - did the work on paper.
c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.
Step-by-step explanation:
I did all the work on paper it took a while to do it. pls mark brainliest
Pick the correct answer
Help me please thanks so much
Answer:
E
Step-by-step explanation:
line I slopes downwards from left to right and has a negative slope.
line K is a horizontal line and has a slope of zero
line J slopes upwards from left to right and has a positive slope
slopes from least to greatest are therefore I, K, J
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?
Answer:
100 miles
Cost = $63
Step-by-step explanation:
Let us assume that the distance driven for both plans when they both equal in cost is X miles
Plan 1
Cost = 48 + 0.15X
Plan2
Cost = 53 + 0.1X
If they are both equal then
48 + 0.15X = 53 + 0.10X
Collecting like terms
0.15X - 0.10X = 53 - 48
0.05X = 5
X 5/0.05 = 100 miles
Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63
Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63
A bag contains 4 blue marbles and 7 red marbles. Two marbles are randomly drawn without replacement. Find the probability of the event ""the first marble is red and the second marble is blue""?
Answer:
8/11
Step-by-step explanation:
In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:
P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.
Round 51.6172 to the
thousandths place.
Answer:
51.617
Step-by-step explanation:
tythe answer is 51.617 hope it helps
Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.
Answer: 51.617
:)
Express 324000000 in scientific natation
Answer:
[tex]3.24*10^8[/tex]
Step-by-step explanation:
First, it is even so you don't need a negative power. Secondly, you put the decimal point after the first number which is three, and the next numbers which are not zeros go after it. Then you count the two numbers behind the decimal and the rest of the zeros. Then the number you get is the power of 10. And then just multiply and check your answer. :)
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 595, α=0. 05, n=17
Answer: Yes, the correlation coefficient is statistically significant
The correlation coefficient describes how one variable actions when it comes to every other. A high-quality correlation shows that the 2 circulate within the identical path, with a +1.zero correlation once they move in tandem. A poor correlation coefficient tells you that they as a substitute flow in opposite directions. A correlation of 0 shows no correlation in any respect.
where ρ corresponds to the population correlation.
The sample size is n = 17,
so then the number of degrees of freedom is df = n-2 = 17-2 = 15
The corresponding critical correlation value re for a significance level of a 0.05, for a two-tailed test is た= 0.482
Observe that in this case,
the null hypothesis H0 : ρ-0 is rejected
if |r> re 0.482.
Based on the sample correlation provided, we have that lrl = 0.595 >=0.482,
which is concluded that the null hypothesis is rejected.
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Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
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Urve revolves around the x-axis. if you cannot evaluate the integral exactly, use your calculator to approximate it. (round your answer to four decimal places. ) y = 16 − x2 from x = −1 to x = 1
The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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What is the exponent of x in in the expression -4x^3y^2 + 6
Answer:
3
Step-by-step explanation:
- 4x³y² + 6
the x is raised to the power of 3 , that is exponent of x is 3
A 3D electron microscope magnifies objects 1 000 000 times. A water molecule has a diameter of
[tex]2 \times {10}^{ - 10} [/tex]
m.
How large will it appear in the microscope?
give your answer in milimetres.
The diameter of the water molecule is 2 * 10^-4 m or 0.2 mm.
What is a microscope?The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.
Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;
Electron microscopeCompound microscopeScanning electron microscope Light microscope etc.Each of these microscopes have a unique instance in which they could be utilized.
Given that the diameter of water is about 2 * 10^-10 m, a magnification by 1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.
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15 points please help me ASAP
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
What is a mean?A mean is also referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
Mathematically, the distance between the means of both players A and B is given by:
Distance = Mean of player B - Mean of player A
Distance = 10 - 6
Distance = 4.
The mean absolute deviation (MAD) for player A is given by:
MAD A = 1/11[2(3 - 6) + 2(4 - 6) + (5 - 6) + (6 - 6) + (7 - 6) + 2(8 - 6) + 2(9 - 6)]
MAD A = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]
MAD A = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]
MAD A = 1/11 × [22]
MAD A = 22/11
MAD A = 2.
Also, the mean absolute deviation (MAD) for player B is given by:
MAD B = 1/11[2(7 - 10) + 2(8 - 10) + (9 - 10) + (10 - 10) + (11 - 10) + 2(12 - 10) + 2(13 - 10)]
MAD B = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]
MAD B = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]
MAD B = 1/11 × [22]
MAD B = 22/11
MAD B = 2.
Therefore, distance between the means = two (2) times the MAD.
Distance = Means × MAD
4 = 2 × 2.
In conclusion, we can infer and logically deduce that there is some overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.
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In the figure below, what is the length of BC?
A) 12
B) 13
C) 17
D) 18
E) 22
B is the answer
i simplified the theorem, but i hope this makes sense!
Answer:
B
Step-by-step explanation:
Qusai made a scaled copy of the following trapezoid. he used a scale factor less than 111. what could be the length of the longer base of the scaled copy of the trapezoid?
The length of the longer base of the trapezoid could be 0.75 units, [tex]\frac{7}{3}[/tex] units, 4 units.
What is a trapezoid?A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
Given: The original length of trapezoid= 6 units
The scale factor of less than 1
So, compare the given lengths with the trapezoid longer base length,
0.75 units<6 units
[tex]\frac{7}{3}[/tex] units<6 units
8.75 units< 6 units
But, 12 units> 6 units
Therefore, the length of the longer base can be 0.75, [tex]\frac{7}{3}[/tex], 4 units.
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The complete question is:
“ Qusai made a scaled copy of the following trapezoid. He used a scale factor less than 1.What could be the length of the longer base of the scaled copy of the trapezoid?
Choose 3 answers:
WILL MARK U BRAINLIEST THANK U
Based on the radius of the being 4 units and the area of the equilateral triangle, the area of the shaded area is 32.85 units².
What is the area of the shaded area?First, find the area of the triangle.
The center of a triangle divides the median into a 2:1 ratio which means that the radius can be found as:
Radius = 1/3 x Area of Equilateral triangle
4 = 1/3 x (√3/ 2)a
a can be worked out to be:
= 8√3
The area of the triangle is:
= (√3 / 4) x a²
= (√3 / 4) x (8√3 )²
= 83.14 units ²
The area of the circle is:
= π x radius²
= 22/7 x 4 x 4
= 50.29 units²
The area of the shaded area is therefore:
= 83.14 - 50.29
= 32.85 units²
In conclusion, the area of the shaded area is 32.85 units².
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Solve the system of equations for x. The value of x is ____. 3x + 4y = −16 x = 4y
Taking into account the definition of a system of linear equations, the value of x is -4.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
This caseIn this case, the system of equations to be solved is
[tex]\left \{ {{3x+4y=-16} \atop {x=4y}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
3×4y +4y= -16
Solving:
12y +4y= -16
16y= -16
y= (-16)÷ 16
y= -1
Remembering that x=4y, then x= 4×(-1)= -4.
Finally, the value of x is -4.
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Identify ER rounded to the nearest tenth. The Figure shows right triangle M E R with right angle E. The length of hypotenuse M R is equal to 37 units. Angle R measures 61 degrees.
Answers;
a) ER ≈ 66.7
b) ER ≈ 32.4
c) ER ≈ 17.9
d) ER ≈ 22.3
Please give an explanation! :)
The value of length ER rounded to the nearest tenth is 17.9 units (Option C)
Trigonometric ratiosThe trigonometric ratios which has been proven as regarding right angle triangles are given below:
Sine θ = Opposite / Hypothenus
Cos θ = Adjacent / Hypothenus
Tan θ = Opposite / Adjacent
With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:
How to determine the length of ERFrom the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:
Hypothenus (MR) = 37 unitsAngle R = 61 °Adjacent (ER) = ?Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 61 = ER / 37
Cross multiply
ER = 37 × Cos 61
ER = 37 × 0.4848
ER = 17.9 units
Thus, the length of ER to the nearest tenth is 17.9 units
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In a certain company, there were five candidates running for President. After the vots were tallied, it turned out that Victor, like in the election, finished in thir place, and david beat him. Greg said that he didn't come in first, but he also didn't come in last. Mac in an interview, said that in this election he wasn't able to win, but at least he was one place hight than his old rival Bill. What place did each candidate come in?
Considering the situation described, the classification of the elections is given as follows:
David came in first place.Greg came in second place.Victor came in third place.Mac came in fourth place.Bill came in fifth place.How to find the classification of the elections?We take the situation that is described, and build the classification from it. The classification has the following format:
P1 - P2 - P3 - P4 - P5
With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.
From the text given in this problem, we have that:
Victor finished in third place, and David beat him, hence P3 = Victor, David = P1 or P2.Greg didn't come in first nor in last, hence, considering that Victor is P3, Greg = P2 or P4.Mac didn't win, but he finished higher than Bill, hence, considering that Mac didn't win and that Victor is P3, Mac = P4, Bill = P5.From the bullet points above, we can conclude that David = P1, Greg = P2.Hence the places of each candidate are given as follows:
David came in first place.Greg came in second place.Victor came in third place.Mac came in fourth place.Bill came in fifth place.A similar problem, in which a situation is interpreted, is given at https://brainly.com/question/5660603
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If you eat a diet with 2,000 kilocalories and 45 percent of those calories come from protein, about how many grams of protein did you eat?
The amount of Protein intake is 900 kilocalorie.
We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.
Wе have to find out the amount of protein intake.
If ' x ' students out of total ' n ' students in a class are infected by virus. Then, what percentage of students are infected.Percentage of students affected are - [tex]\frac{x}{n} \times 100[/tex]
In the question given -
Let the amount of Protein intake be y.
Then -
45 = y % of 2000
45 = [tex]\frac{y}{2000} \times100[/tex]
y = [tex]\frac{45\times2000}{100}[/tex]
y = 900 Kilocalorie
Hence, the amount of Protein intake is 900 kilocalorie.
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The area of a circle is 9pi cm². Find its radius.
Please do this question with full solution:)
Answer:
3 cm
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A = \pi r^2[/tex]
Where "r" represents the radius of the circle. We can substitute the given value for Area into the equation to solve for the radius.
Solve for Radius[tex]A=\pi r^2\\9\pi = \pi r^2[/tex]
Divide both sides by π
[tex]9=r^2[/tex]
Take the square root of both sides
[tex]\sqrt9=\sqrt {r^2}\\r=3[/tex]
The radius of the circle is 3 cm.
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what is a real world example of a rational function, and how could you graph it and put it in a table?
Is the given point interior, exterior, or on the circle (x 2)2 (y - 3)2 = 81? p(8, 4) click on the graphic to choose the correct answer.
From the equation we see that the center of the circle is at (-2,3) and the radius is 9.
So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...
d^2=(8--2)^2+(4-3)^2 and d^2=r^2=81 so
81=10^2+1^2
81=101 which is not true...
So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.
Thus the point lies outside or on the exterior of the circle...
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You deal 7 cards off of a 52-card deck and line them up in a row. how many possible lineups are there in which no card is a club?
Answer:
39C7 or 15380937
Step-by-step explanation:
There are 13 clubs in a 52 card deck. We can remove these from the possibilities. 52-13=39. The rest is simple, choose 7 from 39 using the choose function is 39!/(32!*7!)=15380937. Or just say 39C7 as your answer.
Which statements describe the function ? check all that apply. f(x) has one real zero because it crosses the x-axis once. f(x) has two real zeros because it crosses the x-axis twice. f(x) has real zeros at 1 and –1. f(x) has a real zero at 2.5. f(x) has x-intercepts at (1, 0) and (–1, 0). f(x) crosses the x-axis when x = 1 and x = –1. f(x) has an x-intercept at (2.5, 0).
Statements that describe the given function are:
(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.To find the statements that describe the given function:
The following function can be reorganized: [tex]f(x)=\frac{2*x-5}{2*(x-1)*(x+1)}[/tex]There is one real zero (numerator) in the function (x-intercept), which is x = 2.5. Besides, x = 1 and x = -1 are poles (denominator), that is, x-values so that function is undefined.Lastly, the correct answers are:
(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).Therefore, statements that describe the given function are:
(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).Know more about functions here:
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The complete question is given below:
Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.
(A) f(x) has one real zero because it crosses the x-axis once.
(B) f(x) has two real zeros because it crosses the x-axis twice.
(C) f(x) has real zeros at 1 and –1.
(D) f(x) has a real zero at 2.5.
(E) f(x) has x-intercepts at (1, 0) and (–1, 0).
(F) f(x) crosses the x-axis when x = 1 and x = –1.
(G) f(x) has an x-intercept at (2.5, 0).
The following lines are ______
4x + 2y = 10 y = -2x + 15
Answer:
Parallel
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 2y = 10 ( subtract 4x from both sides )
2y = - 4x + 10 ( divide through by 2 )
y = - 2x + 5 ← in slope- intercept form
with slope m = - 2
and
y = - 2x + 15 ← is in slope- intercept form
with slope m = - 2
• parallel lines have equal slopes
then the 2 lines are parallel
Answer:
Parallel
Step-by-step explanation:
They have the same slope, but different y intercepts.
4x + 2y = 10 Subtract 4x from both sides
2y = -4x +10 Now divide both sides by 2
y = -2x + 5 Compare to y = -2x + 15. Both equations have the same slope or steepness, but they do not cross the y axis at the same place. The first equation given crosses the y axis at 5 and the second equation crosses the y axis at 15
Which system of measurement uses the minim as the basic unit of liquid measure?
The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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