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NARA [144]
3 years ago
13

The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your very impr

essive friend guessed right on 41 of those trials. What proportion of the cards would I expect my friend to guess correctly?
Mathematics
1 answer:
avanturin [10]3 years ago
3 0

Answer:

The proportion is \frac{41}{100} = 0.41 or 41%

Step-by-step explanation:

Hello!

The expected proportion is calculated as "the number the event of interest has occurred"(i.e. success) divided the total of trials.

In this case, your success is the number of times your friend guessed a card correctly in 100 trials.

The proportion is \frac{41}{100} = 0.41 or 41%

I hope it helps!

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90 Degree Rotation

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

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Main content

Rotations

Rotating shapes about the origin by multiples of 90°

Learn how to draw the image of a given shape under a given rotation about the origin by any multiple of 90°.

Introduction

In this article we will practice the art of rotating shapes. Mathematically speaking, we will learn how to draw the image of a given shape under a given rotation.

This article focuses on rotations by multiples of 90^\circ90∘90, degrees, both positive (counterclockwise) and negative (clockwise).

Part 1: Rotating points by 90^\circ90∘90, degrees, 180^\circ180∘180, degrees, and -90^\circ−90∘minus, 90, degrees

Let's study an example problem

We want to find the image A'A′A, prime of the point A(3,4)A(3,4)A, left parenthesis, 3, comma, 4, right parenthesis under a rotation by 90^\circ90∘90, degrees about the origin.

Let's start by visualizing the problem. Positive rotations are counterclockwise, so our rotation will look something like this:

yyxxA'A′\blueD{A(3,4)}A(3,4)

Cool, we estimated A'A′A, prime visually. But now we need to find exact coordinates. There are two ways to do this.

Solution method 1: The visual approach

We can imagine a rectangle that has one vertex at the origin and the opposite vertex at AAA.

\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}

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