MATHEMATICS HIGH SCHOOL

A 5-column table with 4 rows. The columns are labeled sock 2 and the rows are labeled sock 1. Column 1 contains entries blank, b, b, w, w. Column 2 contains entries b, (b, b), (b, b), (w, b), (w, b). Column 3 contains entries b, (b, b), (b, b), (w, b), (w, b). Column 4 contains entries w, (b, w), (b, w), (w, w), (w, w). Column 5 contains entries w, (b, w), (b, w), (w, w), (w, w).A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.

If the first sock is not replaced, how many possible outcomes are there?

How many of these outcomes contain a matching pair of socks?

Answers

Answer 1

Answer:

Answer:If the first sock is not replaced, how many possible outcomes are there? 12

How many of these outcomes contain a matching pair of socks? 4

Step-by-step explanation:

Answer 2

Answer:

Answer:

the first one is 12 and the last one is 4

Step-by-step explanation:

i got i right

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Can someone help me in this trig question, please? thanks A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

brainly.com/question/11001232

$\bf \textit{the position of the rider is clearly }20cos\left( (5\pi )/(12) \right)~~,~~20sin\left( (5\pi )/(12) \right)\n\n-------------------------------\n\n\cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4}\n\n\n\textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\n\n-------------------------------$

$\bf \textit{Sum and Difference Identities}\n\nsin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\n\ncos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n-------------------------------\n\ncos\left( (\pi )/(6)+(\pi )/(4) \right)=cos\left( (\pi )/(6)\right)cos\left((\pi )/(4) \right)-sin\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf cos\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}-\cfrac{1}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(6)}{4}-\cfrac{√(2)}{4}\implies \boxed{\cfrac{√(6)-√(2)}{4}}\n\n\nsin\left( (\pi )/(6)+(\pi )/(4) \right)=sin\left( (\pi )/(6)\right)cos\left( (\pi )/(4) \right)+cos\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf sin\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{1}{2}\cdot \cfrac{√(2)}{2}+\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(2)}{4}+\cfrac{√(6)}{4}\implies \boxed{\cfrac{√(2)+√(6)}{4}}\n\n-------------------------------\n\n20\left( \cfrac{√(6)-√(2)}{4} \right)\implies 5(-√(2)+√(6))\n\n\n20\left( \cfrac{√(2)+√(6)}{4} \right)\implies 5(√(2)+√(6))$

Under a dilation, the point (2, 6) is moved to (6, 18). What is the scale factor of the dilation?

Answers

Answer-3

2*3=6

6*3=18

-Steel jelly

Answer: The scale factor of the dilation =3

Step-by-step explanation:

We know that if we transform point (x,y) by using dilation with scale factor k then the coordinate of the image will be (kx,ky).

Given: under a dilation, the point (2, 6) is moved to (6, 18)

Here (x,y)=(2,6) and (kx,ky)=(6,18)

$\n\Rightarrow\ x=2\ and\ kx=6\n\Rightarrow\ k(2)=6\n\Rightarrow\ k=3$

Hence, the scale factor for the given dilation= 3.

If f(x) = 4x − 6 and g(x) = 6x − 4, what is f · g?

Answers

Answer:

f · g = 24x² - 52x + 24

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Expand by FOIL
Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4x - 6

g(x) = 6x - 4

Step 2: Find f · g

Substitute in function values: f · g = (4x - 6)(6x - 4)
Expand [FOIL]: f · g = 24x² - 16x - 36x + 24
[Subtraction] Combine like terms: f · g = 24x² - 52x + 24

A set of equations is given below:Equation C: y = 2x + 6
Equation D: y = 2x + 2

Which of the following best describes the solution to the given set of equations? (5 points)

One solution
Two solutions
No solution
Infinitely many solutions

Answers

y=2x+6

y=2x+2

Solve y=2x+6 for y

Substitute 2x+6 for y in y=2x+2

y=2x+2

2x+6=2x+2

Add -2x to both sides

2x+6-2x= 2x+2-2x

6=2

Add -6 to both sides

6-6=2-6

0=-4

No Solution

Answer:

both have a slope of 2 yet have different y intercepts meaning on a graph they never collide therefore there are no solutions.

What is the perimeter of triangle ABC with vertices A(-1,-2), B(2,-6), and C(-3,-6)?

Answers

find the distance between the points and that is perimiter

find
A to B
B to C
C to A
we need the distance formula
D= $\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}$
where D is the distance between points (x1,y1) and (x2,y2)

A to B
(-1,-2) to (2,-6)
D= $\sqrt{(2-(-1))^(2)+(-6-(-2))^(2)}$ =5

B to C
(2,-6) to (-3,-6)
since the y value stayed the same, find the distance betwen the x values
2 to -3 is distance of 5

C to A
(-3,-6) to (-1,-2)
D= $\sqrt{(-1-(-3))^(2)+(-2-(-6))^(2)}$ =2√5

add everybody

5+5+2√5=10+2√5 units

Give an example of a relation that is NOT a function and explain why it is not a function.I do not understand how to do this...please help its algebra.

Answers

The desired example is this: x=y^2
Because for each x>0 we have two different possible y values which means it is not a function anymore. a function should only maximum 1 y value for each x value.

You can see the above relation has multiple possible values for y because if we take x=1 then y can be -1 or 1.

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