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Nina [5.8K]
3 years ago
15

Solve:(1/7)x +(1/6)y =3 ; (1/2)x - (1/3)y =5​

Mathematics
1 answer:
Svetach [21]3 years ago
5 0

Answer:

(14, 6 )

Step-by-step explanation:

Given

\frac{1}{7} x + \frac{1}{6} y = 3 ( multiply through by 42 to clear the fractions )

6x + 7y = 126 → (1)

\frac{1}{2} x - \frac{1}{3} y = 5 ( multiply through by 6 to clear the fractions )

3x - 2y = 30 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 6x + 4y = - 60 → (3)

Add (1) and (3)term by term to eliminate x

11y = 66 ( divide both sides by 11 )

y = 6

Substitute y = 6 into either of the 2 equations and evaluate for x

Substituting into (1)

6x + 7(6) = 126

6x + 42 = 126 ( subtract 42 from both sides )

6x = 84 ( divide both sides by 6 )

x = 14

Solution is (14, 6 )

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David's chocolate bar is 37% cocoa. If the weight of the chocolate bar is 51 grams, how many grams of cocoa does it contain? Rou
OverLord2011 [107]

Answer:

18.9

Step-by-step explanation:

You need to find 37% of 51

In other words: 37% x 51

3 0
2 years ago
I also have three large chocolate candy bars that are perforated into eight sections each. If I divide the bars into these secti
solniwko [45]

3*8 = 24

You will have 24 sections.

Take a rectangle.  Divide it into 8 equal sections

Repeat two more times.  That will give you 24 equal peices.

4 0
3 years ago
What is 6.54 as a mixed number
Andrews [41]
The number given in the question is in decimal form. It has to be first changed to fraction and then only can it be changed to a mixed fraction. The calculations have to be done correctly and then the problem is very straight forward.Now let us concentrate on the problem in hand.
Then
6.54 = 654/100
       = 327/50
       = 6 27/50
From the above deduction we can definitely conclude that the mixed number for 6.54 is 5 27/50. I hope this simple procedure will help you to attempt such type of problems in future without requiring any additional help.
6 0
3 years ago
Read 2 more answers
−4(3m−3)+(−10+8m)=?
Valentin [98]
-4(3m-3)+(-10+8m)
12m+12-1+8m
12m+8m = 20m
+12 -1= +11
answer: 20m+11


*note negative times a negative equals positive and negative times positive is negative 
first: you multiply -4 by 3m which is -12m.
second: you multiply -4 by -3 which is +12
third: find the invisible which is 1. (located right here: +(1) (-10+8m)
fourth: multiply invisible 1 by -10 which is -10
fifth: multiply invisible one by +8m which is +8m 
sixth: combine like terms
seventh: answer
 
5 0
3 years ago
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in
nadezda [96]

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

4 0
3 years ago
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