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3 years ago

What is the slope of all lines parallel to the line 4x-5y+-1?

Mathematics

1 answer:

Bond [772]3 years ago

5 0

Given equation of the line ,

$\implies 4x - 5y +(-1) = 0$

Simplify ,

$\implies 4x - 5y - 1 = 0$

Transpose terms to RHS ,

$\implies 5y = 4x - 1$

Divide both sides by 5 ,

$\implies \boxed{ y =\dfrac{4}{5}x -\dfrac{1}{5}}$

Now we know the slope intercept form of the line as $y = mx + c$ we have ,

$m =\dfrac{4}{5}$

As we know that the slope of all parallel lines are same . Henceforth ,

$m_{|| \ lines } =\dfrac{4}{5}$

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The sum of three times a number and ten is negative 5

ki77a [65]

Yes 3n+10=-5 so it’s 5

8 0

3 years ago

At a hockey game, a vender sold a combined total of 204 sodas and hot dogs. The number of sodas sold was three times the number

Zielflug [23.3K]

Answer:

Step-by-step explanation:

Given that at a hockey game, a vender sold a combined total of 204 sodas and hot dogs.

The number of sodas sold was three times the number of hot dogs sold.

Let no of hot dogs be sold be x then no of sodas sold will be 3x

Total number of sodas and hot dogs $= x+3x=204\\x=51\\3x=153$

the number of sodas =153

and the number of hot dogs sold=51

6 0

4 years ago

It is known that IQ scores form a normal distribution with a mean of 100 and a standard deviation of 15. If a researcher obtains

sdas [7]

Answer:

$X \sim N(100,15)$

Where $\mu=100$ and $\sigma=15$

We select a sample of n=16 and we are interested on the distribution of $\bar X$ , since the distribution for X is normal then we can conclude that the distribution for $\bar X$ is also normal and given by:

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

Because by definition:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$E(\bar X) = \mu$

$Var(\bar X) = \frac{\sigma^2}{n}$

And for this case we have this:

$\mu_{\bar X}= \mu = 100$

$\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75$

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 IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(100,15)$

Where $\mu=100$ and $\sigma=15$

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

Because by definition:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$E(\bar X) = \mu$

$Var(\bar X) = \frac{\sigma^2}{n}$

And for this case we have this:

$\mu_{\bar X}= \mu = 100$

$\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75$

6 0

3 years ago

Newa

Aliun [14]

Answer: They all look correct to me. The only on the might work is the House of Representatives and Senate pass the bill along with a majority vote.

Step-by-step explanation:

5 0

3 years ago

Which expression has the greater value justify your answer <br><br><br> A. -8+4 <br> B. -8×3

vlada-n [284]

Answer:
A has the greater value

Explanation:
-8 is a negative number, so if you multiply it by any positive number greater than 1 it will only go further left on the number line (become “more” negative). However, if you add a positive number to a negative number, it will go further right on the number line.

Proof:
B: -8*3=-24
A:-8+4=-4

-4>-24

I hope this helps!

8 0

3 years ago