A triangle has vertices (3,5), (5,2), and (2,0). Is the triangle a right triangle?

A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for

kherson [118]

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

a)

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

b)

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

6 0

3 years ago

By using a number line, arrange each of the each of the following in descending order (a) 4 29upon 33, -2.365,5.5,-3 upon 4 (b)

Sergeeva-Olga [200]

The arrangement of the numbers in descending order (largest to smallest) are as follows;

a). 5.5, 4, 29/33, -3/4, -2.365
b). 10, 5.855, 5/8, 1/2 -2π, -8

<h3>What is the arrangement of the numbers in descending order in each case?</h3>

It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.

Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.

Read more on number line;

brainly.com/question/4619309

#SPJ1

6 0

1 year ago

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c

svp [43]

Answer:

0.2839 = 28.93%

Step-by-step explanation:

In order to find find the probability that one car chosen at random will have less than 68.5 tons of coal, we have to find z

Le x be tons of coal in a car

Z = (x – mean)/standard deviation

Z = (x – μ)/ σ

P (x<68.5) = P(z < (68.5-69)/0.9)

P (x<68.5) = P(z < -0.5555)

Then we use the z table to find the area under the curve.

P (x<68.5) = 0.2893

5 0

3 years ago

Point P is the center of the circle below. What is the exact area

Ber [7]

Answer:

192π unit²

Step-by-step explanation:

Given that :

Radius = 24

Area of circle = πr²

Area = π*24²

Area = 576π in²

The Shaded area is 120°

Entire Circumference = 360°

Hence, shaded area = 120°/ 360° = 1/ 3 of the area

1/3 * 576π in²

= 192π unit²

5 0

2 years ago

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