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IrinaK [193]
3 years ago
12

Consider the system of equations

Mathematics
1 answer:
lyudmila [28]3 years ago
4 0
4)
I:3x+4y=67
II:5x-y=35

to eliminate y when they are added one of the equations must contain -ay and the other +ay (with a being some number)
in this case we have in I already a positive term and in II a negative, but they have different numbers
by using multiplication (property of equations) we can multiply II by 4 so the negative and positive parts match

II*4: 20x-4y=140

when I and 4*II get added this results in
3x+20x+4y-4y=67+140
23x=207

5)
in this case I and II were added which can be seen in the left side of the equation((3x+4y)+(5x-y)=8x+3y), so to get the right side we have to also add the right sides 67+35=102

so the full equation would be:
8x+3y=102
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Two bags with 3 oranges in each bag is the same amount as 3 bags with 2 oranges in each bag. Which property of multiplication do
kodGreya [7K]

Answer:

Commutative Property

Step-by-step explanation:

The property of multiplication that is being demonstrated is known as Commutative Property. This property basically shows that when multiplying two numbers the actual order in which they are multiplied does not matter and does not affect the result at all. For example, the in this scenario to get the total number of oranges we have to multiply the number of bags by the number of oranges in each bag, but whatever way we do this they equal the same

2 bags * 3 oranges per bag = 6 oranges

3 bags * 2 oranges per bag = 6 oranges

Therefore,

2 * 3 = 3 * 2

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2 years ago
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notsponge [240]
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3 years ago
An environmentalist wants to find out the fraction of oil tankers that have spills each month.Step 1 of 2:Suppose a sample of 47
torisob [31]

Answer: The proportion of oil tankers that had spills is \dfrac{156}{474} or 0.329.

Step-by-step explanation:

Since we have given that

Number of tankers is drawn = 474

Number of tankers did not have spills = 318

Number of tankers have spills = 474 - 318 = 156

Proportion of oil tankers that had spills is given by

\dfrac{Containing\ spill}{Total}=\dfrac{156}{474}=0.329

Hence, the proportion of oil tankers that had spills is \dfrac{156}{474} or 0.329.

3 0
3 years ago
A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more ar
frutty [35]

Answer:

There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.

Step-by-step explanation:

With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:

  • n=4 (the amount of batteries picked for the sample).
  • p=3/10=0.3 (the proportion of dead batteries).
  • k≥1 (the amount of dead batteries in the sample needed to not sell the package).

The probability of having k dead batteries in the sample is:

P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}

Then, the probability of having one or more dead batteries in the sample (k≥1) is:

P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76

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3 years ago
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Answer:

i think its 1000

Step-by-step explanation:

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