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3 years ago

Solve the system x - 2y = -6 3x + y = -4

Mathematics

1 answer:

stepan [7]3 years ago

5 0

{x-2y=-6

{3x+y=-4 /*2

{x-2y=-6

<u>{6x+2y=-8 </u> (+)

7x=-14 /:7

x=-2

3x+y=-4

3*(-2)+y=-4

-6+y=-4

y=2

Solution: (-2; 2)

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If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago

Hellllp me with this plz thaks

Oksana_A [137]

The answer is 64 fluid ounces

6 0

3 years ago

Luis wants to buy a skateboard that usually sells for $79.74. All merchandise is discounted by 12%. What is the total cost of th

eduard

Answer:

75.26

Step-by-step explanation:

Most sales taxes work by not being calculated until cash in some form changes hands. So you take the discount first and then you add the sales tax on the new amount.

Take the discount first

Original cost = 79.74

Discount amount = 79.74 * 12% = 79.74 * 12/100 = 9.57

New price = 79.74 - 9.57 = 70.17

Now you are ready to add on the sales tax

70.17 * 7.25/100 = 5.09

The total is 70.17 + 5.09 = 75.26

7 0

2 years ago

Explain the difference between using area and volume with 2-D and 3-D figures.

Marianna [84]

The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.

<h3>What is the difference between Area and Volume?</h3>

The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.