Responda:
13 gramas
Explicação passo a passo:
65 + 20% = 13
what are the multiples of 5,6,8,9?
What is the value of this expression when n approaches infinity?
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
graph y=8 sec1/5 Ø the answers are graphs I am just unsure of how to answer
Answer:
Use a graphing calc.
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
Which equation represents the statement below?
Thirteen less than a number is forty-two.
Select one:
a. n – 13 = 42
b. 42 – 13 = n
c. 13 – n = 42
d. 13 – 42 = n
The answer is option A
Step-by-step explanation:
Thirteen less than a number is written as
n - 13
Equate it to 42
We have
n - 13 = 42
Hope this helps you
Help me please! I need an answer!
Answer: [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
Inversely proportional means a x b = k --> b = k/a
Given that a₁ = 2 --> b₁ = k/2
Given that a₂ = 3 --> b₂ = k/3
[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]
Pls help with this area question
Answer:
1
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = 2πrh
The total area is that added to the areas of the two circular bases:
A = 2πr² +2πrh
We want the ratio of these to be 1/2:
LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr
Multiplying by 2(r+h) gives ...
2h = r+h
h = r . . . . . subtract h
So, the desired ratio is ...
h/r = h/h = 1
The ratio between height and radius is 1.
A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or Fleury's Algorithm to find one such path starting at Upper A, with Upper D as the fourth and seventh vertex, and with Upper B as the fifth vertex. A C B D E A graph has 5 vertices labeled A through E and 7 edges. The edges are as follows: Upper A Upper C, Upper A Upper B, Upper A Upper D, Upper C Upper D, Upper C Upper E, Upper B Upper D, Upper D Upper E. a. Choose the correct explanation below. A. It has exactly two odd vertices. Your answer is correct.B. It has exactly two even vertices. C. It has more than two odd vertices. D. All graphs have at least one Euler path. b. Drag the letters representing the vertices given above to form the Euler path.
Answer:
a. It has exactly two odd vertices
b. A C E D B A D C
Step-by-step explanation:
(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.
__
(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.
Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.
The Euler path meeting the requirements is ...
A C E D B A D C
It is shown by the arrows on the edges in the graph of the attachment.
Is the area of this shape approximately 24 cm* ? If not give the correct area.
311
101
True
False
Answer:
19.2 feet square
Step-by-step explanation:
We khow that the area of an octagon is :
A= 1/2 * h * P where h is the apothem and p the perimeter
A= (1/2)*1.6*(3*8) = 19.2 feet squareHow do you write 0.00609 in scientific notation? ____× 10^_____
Answer:
6.09 * 10 ^-3
Step-by-step explanation:
We want one non zero digit to the left of the decimal
Move the decimal 3 places to the right
6.09
The exponent is 3 and it is negative since we move to the right
6.09 * 10 ^-3
Answer:
6.09(10⁻³)
Step-by-step explanation:
Step 1: Put number into proper scientific decimal form
6.09
Step 2: Figure out how many decimals places it moves
Since it moves to the left 3, our exponent would be -3
volume of a cube size 7cm
Answer:
343 cm3
Step-by-step explanation:
Answer:
side(s) =7cm
volume (v)=l^3
or, v = 7^3
therefore the volume is 343cm^3.
hope its what you are searching for..
It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store
Answer:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=15, p=0.23)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find the following probability:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
by which number -7 /25 should be divided to get -1/15?
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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For the triangle show, what are the values of x and y (urgent help needed)
we just have to use the Pythagoras theorem and then calculate the value of x and y.
co
Which graph represents the inequality?
-2
1-1
-12
1
1 2
NE
1
Y>-
2
2
А
++
1 -1
-12
ou
-2
od
1
NIE
1
B
1 2
2
2
---
Oto
-2
-1
1 2
-12
-
NIE
NI
12
D
-2
1 - 1
1
0
1
1 2
NIS
2
NI
Answer:
A
Step-by-step explanation:
Given the equality y > -½, it means the values of y is greater than -½.
The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .
Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.
Therefore, the graph that indicates the inequality y > ½ is A
Answer:
A
Step-by-step explanation:
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it.
The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pie.
A. 1,980
B. 1,788
C. 1,034
D. 1,884
Answer:
B. 1788
Step-by-step explanation:
The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by
length * height * width
The volume for current object is :
12 * 28 * 5
= 1788 cubic yards.
Answer: 1778
Step-by-step explanation:
because Ik I had the question
Please answer this correctly
Answer:
Option 2
Step-by-step explanation:
The average temperature in January is -1 degrees celsius. Last year, it was 1 degrees celsius higher than the average.
-1 + 1 = 0
Answer:
The second answer.
Step-by-step explanation:
The average temp. is -1C.
'was 1C warmer' = +1
-1+1=0
A model for consumers' response to advertising is given by the equation N(a)=2600 + 470ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
Required:
a. How many units were sold after spending $1,000 on advertising?
b. Find N′(a).
c. Find the maximum value, if it exists.
d. Find lim a→[infinity] N′(a).
Answer:
a. [tex]N(1)=2600[/tex]
b. [tex]N'(a) = 470/a[/tex]
c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)
d. lim a→[infinity] N′(a) = 0
Step-by-step explanation:
a.
the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:
[tex]N(1)=2600 + 470ln(1)[/tex]
[tex]N(1)=2600 + 470*0[/tex]
[tex]N(1)=2600[/tex]
b.
To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:
[tex]N'(a) = 2600' + (470ln(a))'[/tex]
[tex]N'(a) = 0 + 470*(1/a)[/tex]
[tex]N'(a) = 470/a[/tex]
c.
The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).
The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.
d.
When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.
Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
Write the fraction in simplest form. (3/6) x (7/10)
Estimate the area under the graph of f(x)=2x^2-12x+22 over the interval [0,2] using four approximating rectangles and right endpoints.
Answer:
The right Riemann sum is 21.5.
The left Riemann sum is 29.5.
Step-by-step explanation:
The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the right endpoints:
[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]
The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the left endpoints:
[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]
At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answer:
1.39 km/h
Step-by-step explanation:
Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...
A = -120 +20t . . . (east of the origin)
and the position of B is ...
B = 15t . . . (north of the origin)
Then the distance between them is ...
d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)
And the rate of change is ...
d' = (625t -2400)/√(625t² -4800t +14400)
At t = 4, the rate of change is ...
d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h
The distance between the ships is increasing at about 1.39 km/h.
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
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A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz