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erastova [34]
2 years ago
7

Indicate the relationship between the line: 2x - 5y = 10 , and the line: 10x + 4y = 20

Mathematics
1 answer:
Alex73 [517]2 years ago
5 0

Answer:

Perpendicular

Step-by-step explanation:

Here, we want to know the relationship between the two lines .

The easiest way to go about this is to get their slopes;

Mathematically, the equation of a straight line can be expressed in the form;

y = mx + c

where m is the slope;

Hence;

2x -5y = 10

Isolating the y part

5y = 2x -10

divide through by 5

y = 2/5x - 2

So the slope here is 2/5

for the second line

10x + 4y = 20

Divide by 2 all through

5x + 2y = 10

Isolate y

2y = 10-5x

Divide by 2 again

y = 5 -5/2x

The slope here is -5/2

What do we notice? we can see that if we multiply the two slopes by each other, we get -1

That is;

2/5 * -5/2 = -1

What this means is that both lines are perpendicular.

This is because the slopes of perpendicular lines, when multiplied by each other = -1

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3 years ago
For a normal distribution with μ=500 and σ=100, what is the minimum score necessary to be in the top 60% of the distribution?
STatiana [176]

Answer:

475.

Step-by-step explanation:

We have been given that for a normal distribution with μ=500 and σ=100. We are asked to find the minimum score that is necessary to be in the top 60% of the distribution.

We will use z-score formula and normal distribution table to solve our given problem.

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

Top 60% means greater than 40%.

Let us find z-score corresponding to normal score to 40% or 0.40.

Using normal distribution table, we got a z-score of -0.25.

Upon substituting our given values in z-score formula, we will get:

-0.25=\frac{x-500}{100}

-0.25*100=\frac{x-500}{100}*100

-25=x-500

-25+500=x-500+500

x=475

Therefore, the minimum score necessary to be in the top 60% of the distribution is 475.

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2 years ago
Write the product in its simplest form<br>-3y.3y4<br>Enter the correct answer.​
Sauron [17]

Answer:

\large\boxed{-9y^5}

Step-by-step explanation:

-3y\cdot3y^4=(-3\cdot3)(y\cdot y^4)\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=-9y^{1+4}=-9y^5

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Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a
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Based on the information given, it should be noted that the mean and standard deviation of Y will be 0.4899 and 0.699 respectively.

<h3>Calculating the mean.</h3>

Based on the information given, it should be noted that the probability distribution for y will be:

Y                   0        1.         2

Probability 0.63.   0.25.   0.12

The mean of Y will be:

= (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

= 0 + 0.25 + 0.25

= 0.49

The variance will be 0.4899. Therefore, the standard deviation will be:

= ✓0.4899

= 0.699

Learn more about mean on:

brainly.com/question/19243813

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2 years ago
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