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3 years ago

Solve the system by substitution. y = 8x – 6 y = 2x

2 answers:

6 0

Since both equations equal to y, that would mean that both equations would equal each other. This means that the equation would turn into 2x = 8x - 6. Once you have this equation, you have to move all the terms that have the pronumeral x to the left. So, you would move 8x to the left. In order to do this, you have to minus 8x on both sides, 2x-8x=8x-8x-6. This is equation will simplify to -6x=-6. To find out what x is equal to, you then need to get rid of the -6 by dividing -6 by both sides. In the end, x should equal to 1. Then you need to find out what y is equal to. Since x=1, you can substitute it into one of the equations. Let’s use the equation y=2x. If you substitute x with 1, y should equal to 2. Now you know what y and x equals to.

motikmotik3 years ago

3 0

Answer:

x = 1

y = 2

Step-by-step explanation:

y =8x - 6 ---------------------------------(I)

y = 2x -------------------------------------(II)

substitute y = 2x in equation (I)

2x = 8x - 6

Add 6 to both sides

2x + 6 = 8x

Subtract 2x from both sides

6 = 8x - 2x

6 = 6x

Divide both sides by 6

6/6 = x

x = 1

Substitute x = 1 in equation (II)

y = 2*1

y = 2

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Step-by-step explanation:

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3 years ago

Estimate product using compatible numbers 0.67 x 623

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It could possible be 417.

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3 years ago

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

Sophia is at home, and has to

slamgirl [31]

Answer:

Sophia should start her homework at 5:55

Step-by-step explanation:

If it takes her 10 minutes to go to school, 30 minutes to do her homework, and 25 minutes to eat dinner, you should add those numbers together to get 65 because then you can subtract 65 minutes from 7:00 so you get the time she needs to start her homework in order to get to school at 7:00. So basically 10+30+25=65 and then 65 minutes subtracted from 7:00 is 5:55.

I hope this helps you :D

7 0

3 years ago

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