Positive 11 minus negative 9

Write the equation of the line given points (-4,6) and (-8,10)

Advocard [28]

Answer:

the equation of the line in slope-intercept form is: $y=-x+2$

Step-by-step explanation:

First start by finding the slope of the segment that joins those two points using the general formula for the slope of the segments between two points $(x_1,y_1)$ and $(x_2,y_2)$ on the plane:

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Then for our case, calling (-4, 6) = $(x_1,y_1)$ and (-8, 10) = $(x_2,y_2)$ , we have:

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{10-6}{-8-(-4)}\\Slope=\frac{4}{-8+4}\\Slope=\frac{4}{-4}\\Slope= -1$

Now, knowing this, we can find the equation of the line by using the "point-slope" form of a line [of slope "m" and going through the point $(x_0,y_0)$ that tells us:

$y-y_0=m(x-x_0)$

We will be then using the found slope (-1) and for example one of the given points: (-4 , 6), thus:

$y-y_0=m(x-x_0)\\y-6=-1(x-(-4))\\y-6=-1(x+4)\\y-6=-x-4\\y=-x-4+6\\y=-x+2$

6 0

3 years ago

(Problem on image.)...

ANEK [815]

Hey there! :)

In order to the find the missing side length of this triangle, we'll need to use the Pythagorean Theorem!

That equation is : a² + b² = c²

a = adjacent side

b = long side of rectangle

c = hypotenuse

We're already given the values of both a & c, so let's plug everything in!

a² + b² = c² → a = 10 , b = ? , c = 20

(10²) + b² = (20²)

Simplify.

100 + b² = 400

Subtract 100 from both sides.

b² = 400 - 100

Simplify.

b² = 300

Get the square root of b² & 300.

$\sqrt{b^2} = \sqrt{300}$

Simplify!

b = 17.3

So, the missing side length is the first answer choice : 17.3

~Hope I helped!~

7 0

3 years ago

Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

Aleks04 [339]

Answer:

a) $\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) $P(\bar X \leq 77)=P(Z$

d) See figure attached

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

$E(X) = 75$

$sd(X) = 7$

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$