20 points please help

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

kobusy [5.1K]

Answer: (x,y)=(-22/69 , 2/23)

Y=6x+2
3x+12y=6x+2
Simplify the expression

-6x+y=2
-3x+12y=2
Multiply both sides of the equation by

-6x+y=2
6x-24y=-4
eliminate at least one variable by adding the equation

-23y=-2
Divide both sides

y=2/23
Substitute the value of y

-6x +2/23 =2
Solve the equation

x=-22/69
The possible solution of the system is the ordered pair

(x,y)=(-22/69, 2/23)
Check the solution

2/23=3x(-22/69)+12x 2/23=6x(-22/69)+2
Simplify

2/23=2/23=2/23
The ordered pair is a solution

Solution
(x,y)=(-22/69 , 2/23)

4 0

3 years ago

Can someone please explain for question 4.a) only please

shusha [124]

Answer:

Sample 1: P(R)=6/800

Step-by-step explanation:

The formula of probability is = no of possible cases upon number of total cases

7 0

3 years ago

Which value of xx makes 7+5(x-3)=227+5(x−3)=22 a true statement

kari74 [83]

Answer:

x=6

Step-by-step explanation:

The given equation is

$7+5(x-3)=22$

We need to find the value of x for which the given statement is true.

Using distributive property we get

$7+5(x)+5(-3)=22$

$7+5x-15=22$

$5x-8=22$

Add 8 on both sides.

$5x=22+8$

$5x=30$

Divide both sides by 5.

$\dfrac{5x}{5}=\dfrac{30}{5}$

$x=6$

Therefore, the given statement is true form x=6.

8 0

3 years ago

Find the slope of the line that passes through the pair of points.<br><br> (–5.5, 6.1), (–2.5, 3.1)

hjlf

Slope of the line is -1.

Step-by-step explanation:

Given points are,

(-5.5,6.1),(-2.5,3.1)

Here,

$x_{1} = -5.5 ,\ \ \ x_{2}=-2.5\\y_{1} = 6.1,\ \ \ y_{2}=3.1$

Slope = m = $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$

Putting values;

$m=\frac{3.1-6.1}{-2.5-(-5.5)}\\m=\frac{-3}{-2.5+5.5}\\m=\frac{-3}{3}\\m=-1$

Slope of the line is -1.

Keywords: Slope, line

Learn more about slopes at:

#LearnwithBrainly

7 0

3 years ago

A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=17-1=16$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical values.