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Free_Kalibri [48]

3 years ago

13

Choosing a 6 one though six then a prime number

1 answer:

oksano4ka [1.4K]3 years ago

7 0

First off, there are 6 choices: 1, 2, 3, 4, 5, and 6

The probability of getting a 6 is 1/6
The probability of getting a prime number is 1/2

Multiply them and you get 1/12

The probability is 1/12.

Hope this helped!

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a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |<em>subtract $y$ from both sides</em>

$\dfrac{2}{3}x-y+b=0$ |<em>multiply both sides by 3</em>

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |<em>multiply both sides by $\sqrt{13}$ </em>

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |<em>divide both sides by 3</em>

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

2 years ago

Write (-5+8i)+(-5-8i) as a complex number in standard form

gizmo_the_mogwai [7]

$(-5+8i)+(-5-8i) =
-5+8i-5-8i=-10$

5 0

3 years ago

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aksik [14]

Answer:

( 5x+3y=7. < 3x - 5y = -23 you can use many ..

Step-by-step explanation:

hopefully its right

5 0

2 years ago

A bottle and its cork cost $1.20 of the bottle costs $1.10 more than the cork. What is the cost of bottle and of the cost of cor

777dan777 [17]

The cost of the bottle alone costs $1.15, and the cork costs $0.05, you add them together and you get $1.20. That is how the bottle costs $1.20.

8 0

2 years ago

Light travels about 3 x 10^5 metres per second. Find the time it takes to travel 1 metre. Give your answer in standard form.

Anna71 [15]

Answer:

t=3.3* $10^{-6}$

Step-by-step explanation:

t= $\frac{S}{v}$

As

S=1m

v=3* $10^{5}$ ms^-1

t= $\frac{1}{3*10^{5} }$

t=3.3* $10^{-6}$

3 0

2 years ago

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