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4 years ago

Which graph represents the system 3x + 5y ≤ 9 and 2x + y ≥ 5?

Mathematics

2 answers:

shusha [124]4 years ago

7 1

Answer with Step-by-step explanation:

we are given system of inequalities:

3x + 5y ≤ 9 and

2x + y ≥ 5

We have to determine the graph of the above system

In Second and third graph point (0,6) lies in shaded region

Putting (0,6) in 3x + 5y ≤ 9

3×0+5×6≤9

⇒ 30≤9 which is incorrect

Hence, second and third are not its graph

In fourth graph (0,3) lies in shaded region

Putting (0,3) in 3x + 5y ≤ 9

3×0+5×3≤9

⇒ 15≤9 which is incorrect

Hence, fourth is not its graph

Hence, the only option we are left is graph first

Hence, first graph is the correct representation of 3x + 5y ≤ 9 and

2x + y ≥ 5

Alexandra [31]4 years ago

4 1

Graph A is the correct answer

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Solution:

Total number of outcomes N(S) = 36

Let A be the sum that is a multiple of 6 and

B be the sum that is a multiple of 4.

Sum that is a multiple of 6 = (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)

N(A) = 6

Sum that is a multiple of 4 = (1, 3), (2, 2), (2, 6), (3, 1), (3, 5),

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N(B) = 9

$$P(A)=\frac{N(A)}{N(S)}$

$$P(A)=\frac{6}{36}=\frac{1}{6}$

$$P(B)=\frac{N(B)}{N(S)}$

$$P(B)=\frac{9}{36}=\frac{1}{4}$

Probability that the outcome is a sum that is a multiple of 6 or a sum that is a multiple of 4:

$P(A \cup B)=P(A)+P(B)$

$$P(A \cup B)=\frac{1}{6} +\frac{1}{4}$

$$=\frac{2+3}{12}$ (Make the denominator same)

$$=\frac{5}{12}$

Hence the probability that the outcome is a sum that is a multiple of 6 or a sum that is a multiple of 4 is $\frac{5}{12}$ .

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3 years ago

The mean of the numbers 5, 2x, 4 and 3 is 5 find the value of x

Fittoniya [83]

Answer:

Mean = sum of outcomes/no. of outcomes

5 = (5+2x+4+3)/4

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8 = 2x

8/2 = x

4 = x

 $\\$ 

Step-by-step explanation:

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