A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is

Let p(z)=0.54, p(y)=0.22, and p(z u y)= 0.62. Find each probability.

Marysya12 [62]

Answer : p(only z)=0.40 and p(only u)=0.08

Explanation :

We have given that ,

p(u)=0.22,

p(z∪u)=0.62,

p(z)=0.54

By using probability rule of union of 2 events, we have,

p(z)+p(u)-p(z∩u)=p(z∪u)

⇒0.54+0.22-p(z∩u)=0.62

⇒0.76-p(z∩u)=0.62

⇒(-)p(z∩u)=0.62-0.76

⇒(-)p(z∩u)= (-)0.14

⇒p(z∩u)=0.14

Now,

p(only z)=p(z)-p(z∩u)

=0.54-0.14

=0.40

and,

p(only u)=p(u)-p(z∩u)

=0.22-0.14

=0.08

∴ Each probability will be

p(only z)=0.40

p(only u)=0.08

3 0

2 years ago

How does poetry play an important role in mathematics?

ANEK [815]

Poetry has always been used as a vehicle of enlightenment, By expressing mathematics formula poetically, you can impact knowledge across the board.<span />

8 0

3 years ago

So I kinda forgot how to do this *nervous laughter* um help

natali 33 [55]

1) value of x =60

2) value of x = 3

Step-by-step explanation:

We need to use cross products to solve the proportions of x.

$1.\,\, \frac{3}{5}= \frac{x}{100}$

Solving:

$\frac{3}{5}= \frac{x}{100}\\Cross\,\,multiply\,\,:\\5x=3*100\\5x=300\\x=\frac{300}{5}\\x=60$

So, value of x =60

$2.\,\,\frac{x}{8}=\frac{7.5}{20}$

$\frac{x}{8}=\frac{7.5}{20} \\20x=7.5*8\\20x=60\\x=\frac{60}{20}\\ x=3$

So, value of x = 3

Keywords: Ratio and Proportions

Learn more about Ratio and Proportions at:

#learnwithBrainly

7 0

2 years ago

(x - 6) (X - 4) =<br> How do I solve this?

Vedmedyk [2.9K]

Answer: x^2 -10x + 24

Step-by-step explanation:

(x-6) (x-4)

= x^2 - 6x - 4x + 24

= x^2 -10x + 24

5 0

2 years ago

Read 2 more answers

A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and

nasty-shy [4]

Answer:

correct option is C) 2.8

Step-by-step explanation:

given data

string vibrates form = 8 loops

in water loop formed = 10 loops

solution

we consider mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = $\rho$

case (1)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

so here

$l = \frac{8 \lambda _1}{2}$ ..............1

$l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}$

and we know velocity is express as

velocity = frequency × wavelength .....................2

$\sqrt{\frac{Tension}{mass\ per\ unit \length }}$ = f × $\lambda_1$

here tension = mg

so

$\sqrt{\frac{mg}{\mu}}$ = f × $\lambda_1$ ..........................3

and

case (2)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

$l = \frac{10 \lambda _1}{2}$ ..............4

$l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}$

when block is immersed

equilibrium eq will be

Tenion + force of buoyancy = mg

T + v × $\rho$ × g = mg

and

T = v × $\rho$ - v × $\rho$ × g

from equation 2

f × $\lambda_2$ = f × $\frac{1}{5}$

$\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}$ .......................5

now we divide eq 5 by the eq 3

$\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}$

solve irt we get

$1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}$

so

relative density $\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}$

relative density = 2.78 ≈ 2.8

so correct option is C) 2.8

3 0

3 years ago