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3 years ago

12

Find the distance between the points (0,2)and (-5,-9)The answer must be a whole number or a fully simplified radical expression

do not round up

1 answer:

LiRa [457]3 years ago

7 0

Answer:

d = $\sqrt{146}$

Step-by-step explanation:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(-5-0)^2+(-9-2)^2}\\d= \sqrt{(-5)^2+(-11)^2}\\d= \sqrt{25+121}\\d= \sqrt{146}$

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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

3 years ago

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime has coordinates of (–0. 25, 0. 5) after the triangle has

babunello [35]

The true statements about the dilation are as follows;

The scale factor is One-eighth

The coordinates of the C prime are (0.75, 0.5).

The coordinates of B prime are (–0.25, 1).

Given

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4).

If A prime has coordinates of (–0. 25, 0. 5) after the triangle has been dilated with a center of dilation about the origin.

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. If an object is transformed then all its points are also transformed. Types of transformation are reflection, dilation, rotation, and translation.

Dilation is the enlargement or reduction in the size of an object. If a point X(x, y) is dilated about the origin by a factor k, its new location is X'(kx, ky).

Triangle ABC with vertices at A(–2, 4), B(–2, 8), and C(6, 4) is dilated to give A'(-0.25, 0.5)

kA = A'

(-2k, 4k) = (-0.25, 0.5)

-2k = -0.25, hence k = 1/8

Therefore the scale factor is 1/8 (one- eight)

The new location of the vertices is B'(-0.25, 1), C'(0.75, 0.5)

To know more about Transformation click the link given below.

brainly.com/question/11709244

3 0

3 years ago

Can someone please help me with my math hw (1-11) thanks

uranmaximum [27]

1) 2 1/5
2) -1 1/4
3)1 5/8
4)19/30
5)2 1/6
6) ???
7)-8 5/24
8)???
9)6 11/15
10)???
11)???
I couldn’t see the ones with the ??? on them and also all you have to do to get the answer is find the LCD and combine

8 0

3 years ago

What is the volume of a hemisphere with a radius of 3.6m ,rounded to the nearest tenth of a cubic centimeter

Mrrafil [7]

Answer:

$V\approx 97.7\ m^3$

Step-by-step explanation:

-A hemisphere is equivalent to half of a sphere.

- The area of a sphere is given by the formula:

$V=\frac{4}{3}\pi r^3$

-Given that r=3.6m, the hemisphere's volume can be calculated as:

$V=\frac{4}{3}\pi r^3\\\\V_h=0.5\times \frac{4}{3}\pi r^3\\\\=0.5\times \frac{4}{3}\pi \times 3.6^3\\\\=97.7161\approx 97.7\ m^3$

Hence, the hemisphere's volume is approximately $97.7\ m^3$

6 0

3 years ago

PLEASE HELP FOR 50 POINTS

ra1l [238]

Answer:

what class are you in? if you have a book you can use this site called slader it gives you every answer for free and there is steps. HOPE THIS HELPS.

Step-by-step explanation:

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3 years ago