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3 years ago

Use substitution to solve the system. X= 2y-5 4x+3y=-9

Mathematics

1 answer:

sergey [27]3 years ago

6 0

Step-by-step explanation:

x=2y-5 - equation 1

4x+3y=-9 -equation 2

Replace equation 1 in equation 2

4(2y-5)+3y=-9

8y-20+3y=-9

11y=-9+20

11y=11

y=11/11

y=1

If y=1, therefore x=2(1)-5=-3

x=-3,y=1

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A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official d

son4ous [18]

Answer:

For this sample, the estimated standard error is of 0.0277

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism.

This means that $n = 250, p = \frac{65}{250} = 0.26$

For this sample, the estimated standard error is

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.26*0.74}{250}} = 0.0277$

For this sample, the estimated standard error is of 0.0277

4 0

3 years ago

Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea. His altitude relative to sea level (in meters) as a functi

Ierofanga [76]

The equation for the flowing rate of aamir is as follows y = -12x +360

<h3>What is an equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

First of all let's write the slope-intercept form of the equation of a line, which is:

y = mx + c

So we just need to find to solve this problem.

Moreover, this problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is:

Negative slope because Amir is descending. So:

y = - 12x + b

To find, we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point. Therefore, substituting this point into our equation:

y = -12x + b

0 = -12(30) + b

b = 360

Finally, the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is:

y = -12x +360

To know more about equations follow

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4 0

2 years ago

Convert 6.5 ft to m.

djverab [1.8K]

Answer: 1.9812 meters

3 0

3 years ago

Read 2 more answers

Whisper the numbers in standard form and unit form 42

prisoha [69]

Answer:

In standard form 42= $4.2\times 10^1$

In unit form, 42 as 4 tens 2 ones

Step-by-step explanation:

<u>Standard form</u>: It is the way of writing down the numbers easily in a very large or small numbers.

Rules for writing a number in standard form is that first you write down a number between 1 and 10, then multiply the number with 10(to the power of a number).

Now, to write

42 in standard form: $4.2\times 10^1$ .

Unit form: it is a form that express the number by giving the number of place value within the number.

Unit form of 42:

42 is written as 4 tens , 2 ones.

7 0

3 years ago

Given the function rule f(x) = x^2 - 5x + 1, what is the output of f(-3)?

mojhsa [17]

f(x) = x²<span> - 5x + 1

f(-3) = (-3)</span>² - 5(-3) + 1
<span>
f(-3) = 25

</span>--------------------------------------------------<span>
Answer: f(-3) = 25 (Answer C)
</span>--------------------------------------------------

4 0

4 years ago