1. Point A(3,7), Scale Factor (k) = 2<br> Find the Point A'(

A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to

Fantom [35]

A geometry program can show you the total displacement is about 10.14 miles.

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You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

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If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles

4 0

3 years ago

Suppose the waiting times in an emergency room are normally distributed with a mean (mean) of 40 and a standard deviation (sigma

kipiarov [429]

Answer:

0.68269

Step-by-step explanation:

When we are to find the z score for population where a random sample is picked, the z.score formula we use is

z = (x-μ)/Standard error, where

x is the raw score,

μ is the population mean

Standard error = σ/√n

σ is the population standard deviation

n = random number of samples

For : x = 38 minutes, μ = 40, σ = 10, n = 5

z = 38 - 40/10 /√25

= -2/10/5

= -2/2

= -1

Determining the probability value using z table

P(x = 38) = P(z = -1)

= 0.15866

For : x = 42 minutes, μ = 40, σ = 10, n = 25

z = 42 - 40/10 /√25

= 2/10/5

= 2/2

= 1

Determining the probability value using z table

P(x = 42) = P(z = 1)

= 0.84134

The probability that their average waiting time will be between 38 and 42 minutes is calculated as

P(-Z<x<Z)

= P(-1 < x < 1)

= P(z = 1) - P(z = -1)

= 0.84134 - 0.15866

= 0.68269

Therefore, the probability that their average waiting time will be between 38 and 42 minutes is 0.68269

3 0

4 years ago

3 part question-Show work for part a and part c

blagie [28]

Answer:

Step-by-step explanation:

Part A: You can only use Pythagorean's Theorem on a right triangle.

Part B: The side across from the right angle is the hypotenuse. It has a length of 15.

Part C: To find the missing side using Pythagorean's Theorem:

$a^2+11^2=15^2$ and

$a^2+121=225$ and

$a^2=104$ and

a = 10.20

5 0

3 years ago

Use the given diagram to answer the question.

Elanso [62]

Answer:

X Z Y

Step-by-step explanation:

The first Question is X

The second Question is Z

The third question is Y

5 0

3 years ago

Sam is building a new deck. His decking material is sold by the square foot. At a cost of $3.90 per square foot, how much will i

AVprozaik [17]

It would be =18*14*3.90=982.8

6 0

3 years ago

1. Point A(3,7), Scale Factor (k) = 2 Find the Point A'(