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GalinKa [24]
2 years ago
8

Find the values of x1 and x2 where the following two constraints intersect.

Mathematics
1 answer:
Arte-miy333 [17]2 years ago
4 0

Answer: x1 = 251/26, x2 = -111/26

Step-by-step explanation:

Hi!

As you can see in the figure, the point you are looking for is the intersection of two lines.

The intersection point is found solving this system of linear equations (the point must satisfy both equations):

9x_1 +7x_2=57\\4x_1 + 6x_2 = 13

You can solve it, for example, by the method of substitution:

\text{solve for x1 in the first equation:}\\x_1 = \frac{1}{9}(57 - 7x_2)

Then plug x1 into equation 2, and solve for x2:

\frac{4}{9}(57-7x_2) + 6x_2 = 13\\\text{doing the algebra you get:}\\x_2 = \frac{-111}{26}

Then you use the value of x2 to get x1:

x_1 = \frac{1}{9}(57 - 7x_2)= \frac{1}{9}(57 + 7*\frac{111}{26}) = 251/26\\

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Suri's age is 4 less than 3 times her cousin's age. Suri is 17 years old. Which method can be used to find c, her cousin's age?
Mila [183]

Answer:

7 years

Step-by-step explanation:

Suri's age=17 years

Her cousin's age =c

Suri's age is 4 less than 3 times her cousin's age

4 less than 3 times her cousin's age means subtract 4 from 3 times her cousin's age

17=3c - 4

Find c which is her cousin's age

Add 4 to both sides

17+4=3c - 4 + 4

17+4=3c

21=3c

Divide both sides by 3

21/3=3c/3

7=c

Therefore,

C= 7

Her cousin's age = 7 years

4 0
2 years ago
A random sample of 50 units is drawn from a production process every half hour. the true fraction of nonconforming products manu
Naya [18.7K]

solution:

The probability mass function for binomial distribution is,

 

Where,

X=0,1,2,3,…..; q=1-p

find the probability that (p∧ ≤ 0.06) , substitute the values of sample units (n) , and the probability of nonconformities (p) in the probability mass function of binomial distribution.

Consider x   to be the number of non-conformities. It follows a binomial distribution with n   being 50 and p  being 0.03. That is,

binomial (50,0.02)

Also, the estimate of the true probability is,

p∧  = x/50

The probability mass function for binomial distribution is,

 

Where,

X=0,1,2,3,…..; q=1-p

The calculation is obtained as

P(p^ ≤ 0.06) = p(x/20 ≤ 0.06)

         = 50cx ₓ (0.03)x ₓ (1-0.03)50-x  

=    (50c0 ₓ (0.03)0 ₓ (1-0.03)50-0 + 50c1(0.03)1 ₓ (1-0.03)50-1 + 50c2 ₓ (0.03)2 ₓ (1-0.03)50-2 +50c3 ₓ      (0.03)3 ₓ (1- 0.03)50-3 )

=(   ₓ (0.03)0 ₓ (1-0.03)50-0 +  ₓ (0.03)1 ₓ (1-0.03)50-1 +   ₓ (0.03)2 ₓ (1-0.03)50-2   ₓ (0.03)3 ₓ (1-0.03)50-3 )



5 0
2 years ago
John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the tab
matrenka [14]

Answer:

The table should measure diagonally about 41.23 inches.

Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

a^{2} + b^{2} = c^{2}

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

32^{2} + 26^{2} = c^{2}

1024 + 676 = c^{2}

1700 = c^{2}

The square root of 1700 is (rounded to the hundreth's place) = 41.23

6 0
1 year ago
Marie bought 1/2 gallon of milk, which she finished after 6 days. If she drank the same amount of milk each day, how many gallon
Rama09 [41]
Gallons per day.......gallons / day.....so u put the gallons over the number of days, then divide

(1/2) / 6 = 1/2 * 1/6 = 1/12 of a gallon per day <==
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2 years ago
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jarptica [38.1K]
Number Line A, well the first number line.

The open circle shows us that -5 is NOT in the solution. All the numbers greater than -5 ( x > -5) are in the solution.

Faith xoxo
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1 year ago
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