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pogonyaev
4 years ago
6

Solve each system by graphing. If the solution is not unique, identify the system as “inconsistent” or “dependent”

Mathematics
1 answer:
lapo4ka [179]4 years ago
6 0

Answer:

therefore the solution of the system of equations is (x,y) = (4,2)

the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

Step-by-step explanation:

i) x + 2 = 6   \Rightarrow  x = 4

ii) x - y = 2 \Rightarrow  4 - y = 2 ,  therefore  y  = 4 - 2 ,   therefore y = 2

iii) therefore the solution of the system of equations is (x,y) = (4,2)

iv) the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

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If we inspect photocopy paper by randomly drawing 5 sheets without replacement from every pack of 500, what is the probability o
earnstyle [38]

Answer:

98.01% probability of getting 5 clean sheets

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, the order that the sheets are chosen is not important, so we use the combinations formula to solve this problem.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

0.4% of the sheets contain spots

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What is the probability of getting 5 clean sheets although 0.4% of the sheets contain spots?

Desired outcomes

2 are defective, so 5 sheets from a set of 500 - 2 = 498.

D = C_{498,5} = \frac{498!}{5!493!} = 250160254344

Total outcomes

5 sheets from a set of 500.

T = C_{500,5} = \frac{500!}{5!495!} = 255244687600

Probability:

P = \frac{D}{T} = \frac{250160254344}{255244687600} = 0.9801

98.01% probability of getting 5 clean sheets

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4 years ago
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Answer:

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Answer:

1st Option

Step-by-step explanation:

Step 1: Convert radicals to exponents

\frac{(x^2)^{\frac{1}{7}} }{(y^3)^{\frac{1}{5} }}

Step 2: Multiply exponents

\frac{x^{\frac{2}{7} } }{y^{\frac{3}{5} } }}

Step 3: Move the <em>y</em> term

(x^{\frac{2}{7} })(y^{\frac{-3}{5} })

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3 years ago
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