All categories

2 years ago

Solve the system of equations by using substitution. y = 2x +3 y = -x + 6

Mathematics

1 answer:

padilas [110]2 years ago

4 0

Answer:

x =3, y =3

Step-by-step explanation:

From the second equation( y= -x+6) we can get x alone.

Subtracting 6 from both sides we get, y-6 = -x

And then dividing both sides by -1, -y+6 = x

Then we can substitute this value of x into the first equation.

y = 2(-y+6) +3

Simplifying,

y = -2y + 12+ 3

3y = 15

y = 3

Substituting this back into second equation we get 3 = -x + 6

and -x = -3

Dividing both sides by -1,

we get x =3

You might be interested in

Which of the following is a correct solution to the inequality 3x - 12 > 15?

pishuonlain [190]

Solve the inequality just like you would solve an equation
<span>3x - 12 > 15
add 12 to both sides
3x > 27
divide both sides by 3
x > 9
Or read as "the solution to </span><span>3x - 12 > 15 is x is greater than 9"

Hope this helps :)</span>

4 0

2 years ago

Suppose a sociologist studying the sleep habits of teenagers in the U.S. randomly surveyed 1873 teenagers. Of those, 297 teenage

dem82 [27]

$\hat{p}=p\pm\frac{\sqrt{p(1-p)}}{\sqrt{n}}\\p=\frac{297}{1873}=0.1586\\ \hat{p}=0.1586\pm\frac{\sqrt{0.1586(1-0.1586)}}{\sqrt{1873}}\\=0.1586\pm\frac{\sqrt{0.1586(0.8414)}}{43.2782}}\\=0.1586\pm\frac{\sqrt{0.1334}}{43.2782}}\\=0.1586\pm\frac{0.3653}{43.2782}}\\=0.1586\pm0.0084$

5 0

3 years ago

Number of passengers who arrive at the platform in an Amtrack train station for the 2 pm train on a Saturday is a random variabl

Svetradugi [14.3K]

Answer:

$P(80$

And we can find this probability with this difference:

$P(-4$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-4$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the number of passengers who arrive at the platform of a population, and for this case we know the following info

Where $\mu=180$ and $\sigma=25$

We are interested on this probability

$P(80$

For this case we can assume that the random variable is normally distributed.

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(80$

And we can find this probability with this difference:

$P(-4$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-4$

5 0

3 years ago

Two numbers are in the ratio of 3 to 4. If the minor is 27, find the sum of both.

german

Answer:

Step-by-step explanation:

First we must find the missing number, for that we apply a simple rule of three:

3. 4

27 ------ x

x = 27 (4) / 3 = 36

Now we just do the sum:

27 + 36 = 63

4 0

3 years ago

Read 2 more answers

Please answer Ill give 5 stars to right answers: a neighbors dog barked at tana the last 4 out of 5 times she walked by their ho

oksian1 [2.3K]

Ratio of dog bark is 4:5

Multiply that by 20 each side

Ratio is now 80:100

So 80%

If they walk past 45 time you just have to multiply the ratio 4:5 by 9

36:45

So the dog would bark 36 times

6 0

1 year ago