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3 years ago

What is the gradient of the line 3y=2x-6

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

7 0

Answer:

2/3

Step-by-step explanation:

The gradient of any line in standard form, Ax + By = C is -A/B.

Divide each term by 3 and simplify.

3y = 2x - 6

3y / 3 = y

2x / 3 = 2/3x

6 / 3 = 2

So, y = 2 / 3 x - 2

slope or gradient = 2/3

Explanation:

The first step in finding the slope of a line that is written in standard form is to write the equation in slope-intercept form, y=mx+b. To do this, rearrange the variables. The standard form, Ax + By = C can be rewritten as By = -Ax + C.

Divide by B to simplify

In the equation By = -Ax + C, B needs to be distributed through the equation. To do this, divide both sides by B. The answer is y = (-A/B)x + C/B.

Find the slope

Once the equation of the line is in slope-intercept form and is simplified, then the slope equals the term in front of the x variable. In the standard form from step 2, the slope is -A/B.

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There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=

yulyashka [42]

Answer:

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

Mean = 0.879

Standard Deviation = 1.033

Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

P(X = 0) = $\frac{12P4}{12^{4} }$

P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) = $\frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }$

P(X=2) = 0.401

P(X=3) = $\frac{4C3 * 12P2}{12^{4} }$

P(x=3) = 0.025

P(X=4) = $\frac{12}{12^{4} }$

P(X=4) = 0.001

Mean, $\mu = \sum xP(x)$

$\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879$

Standard deviation, $SD = \sqrt{\sum x^{2} P(x) - \mu^{2}} \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2} * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}$

SD = 1.033

4 0

4 years ago

What are the values of x and y?

scZoUnD [109]

Answer:

x is equal to 24 and y is equal to 66.

Step-by-step explanation:

In order to find the value of y, we first have to note that the unlabeled angle in the larger triangle, y and the 78 degree angle create a straight line. The unlabeled angle is equal to 36 since it and the other two angles equal 180. So we take that 36, 78 and y and can set that equal to 180.

36 + 78 + y = 180

114 + y = 180

y = 66

Now that we have that value, we can use y and the 90 degree angle to find x.

x + y + 90 = 180

x + 66 + 90 = 180

x + 156 = 180

x = 24

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3 years ago

What is the average of the four smallest of integers ?

Elanso [62]

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