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3 years ago

−10x − 5y ≥ 15 x + y ≤ −1 what are the quadrants containing a solution to the above system of linear inequalities.

Mathematics

1 answer:

Paraphin [41]3 years ago

5 0

Let's convert these inequalities to Slope Intercept Form so that we can graph them easily.

−10x − 5y ≥ 15
Add 10x to both sides.
-5y ≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y ≤ -2x - 3

x + y ≤ − 1
Subtract x from both sides.
y ≤ -x − 1

When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.

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You are at a stall at a fair where you have to throw a ball at a target. There are two versions of the game. In the first

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Answer:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Alternative 1

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=3, p=0.1)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We can find the probability of loss like this P(X=0) and if we find this probability we got this:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

Alternative 2

Let Y the random variable of interest, on this case we now that:

$Y \sim Binom(n=5, p=0.05)$

The probability mass function for the Binomial distribution is given as:

$P(Y)=(nCy)(p)^y (1-p)^{n-y}$

Where (nCx) means combinatory and it's given by this formula:

$nCy=\frac{n!}{(n-y)! y!}$

We can find the probability of loss like this P(Y=0) and if we find this probability we got this:

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

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3 years ago

Shane worked 8 hours per day for 3 days. Andrew worked 6 hours per day for 4 days. If the normal working week is 36 hours, which

creativ13 [48]

Shane:
8 x 3 = 24 Because it is 8h per day for 3 days. Per is like times
24h out of 36 24/36 GCF is 12 divide to and bottom by 12
24 / 12 is 2 36 / 12 is 3 2/3 Shane worked for 2/3 of 36h
Percentage: 100% / 3 (because there is 3 parts)= 33.333333333333
33.33333333333 x 2 (because it is there is 2 parts needed) = 66.6666666666%
Shane has worked for 66.6666666666% of 36 hours

Andrew:
4 x 6 = 24
Hey did you realise, the 24 is exactly the same! So the fraction would still be 2/3 of 36, and so on, there percentage is still the same, it's still 66.6666666666%

Answer: Both of Andrew and Shane has worked for the exact same time, therefore they have the exact same percentage

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Answer:

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Step-by-step explanation:

1) the rules are:

$log_a(bc)=log_ab+log_ac;$