Ask question

Ask question

All categories

10 days ago

8

Patrick has 4 green hats, 3 blue hats, and 1 orange hat. If he selects a hat at random, what is the probability of selecting a g

reen hat?

1 answer:

Svet_ta [4.3K]10 days ago

5 0

Answer:

1/2

Step-by-step explanation:

To determine the total count of hats:

4 green hats + 3 blue hats + 1 orange hat = 8 hats

The probability of selecting a green hat is calculated as:

P(green hat) = number of green hats / total number of hats

= 4 / 8

= 1/2

You might be interested in

There is an integer n such that 2n2 − 5n + 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n2

Leona [4187]

Response:

n = 0 or 3

Detailed explanation:

2n² - 5n + 2

2n² - 4n - n + 2

2n(n - 2) -1(n - 2)

(n - 2)(2n - 1)

A prime number is defined as one that can only be divided by itself and 1

Setting n-2 = 1 gives n = 3

Setting 2n-1 = 1 gives n = 0

7 0

15 days ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

Inessa [3926]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

5 0

1 day ago

Read 2 more answers

Liam cuts a 48-inch piece of string into two pieces. One piece is 12 inches longer than the other. If s represents the length of

Inessa [3926]

Answer:

Here is the solution to the entire assessment: https://school.ckseattle.org/documents/2019/2/8_2_The_Pythagorean_Theorem_and_Its_Converse.pdf

Step-by-step explanation:

4 0

3 days ago

Which table represents a linear function? A, B, C, D

tester [3938]

Answer:

Table B demonstrates a linear function.

Step-by-step explanation:

The reason Table B is classified as a linear function is that for each increment of one in x, y increases by a consistent rate of 4.

5 0

15 days ago

Read 2 more answers

Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc

Leona [4187]

To address this problem, let's start by formulating the general motion equation along the vertical direction.

This gives us:

$h = \frac {1} {2} gt ^ 2 + vo * t + h0$

Where,

g: gravitational acceleration
vo: initial velocity
h0: starting height

For the first individual:

$h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21$

For the second individual:

$h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50$

When both individuals reach the identical altitude, the following holds:

$h1 = h2\\$

$\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50$

Rearranging results in:

$\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50$

$\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21$

$\frac {19} {12} * t = 29$

Solving for time:

$t = 29 (\frac {12} {19})\\t = 18.31s$

Result:

The two window washers reach the same height after 18.31 seconds.

6 0

16 days ago

Read 2 more answers