MATHEMATICS HIGH SCHOOL

A random walk on the 2-dimensional integer lattice begins at the origin. At each step, the walker moves one unit either left, right, or up, each with probability 1/3. (No downward steps ever.)A walk is a success if it reaches the point (1, 1).

What is the probability of success?

Answers

Answer 1
Answer: The 9 combinations that exist for two movements:

R,R
R,L
R,U *
L,R
L,L
L,U
U,R *
U,L
U,U

Walker would only be able to make it to (1,1) with only 2 of these combinations.

So if he were only allowed to make two movements, his chances of arriving at (1,1) would be 2/9.

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Simplify the following expression: 6(5 - 3x) - 5(3x + 2) �� 20 - 33x �� 40 + 33x
�� 20 + 33x �� 40 - 33x

Answers

Answer:20-33x

Step-by-step explanation:

Solve each equation for the indicated variable. u = -3a - 3 , for a

Answers

Answer:

a = (u + 3)/(-3)

Step-by-step explanation:

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 3 to both sides of the equation:

u = -3a - 3

u (+3) = -3a - 3 (+3)

u + 3 = -3a

Next, divide -3 from both sides of the equation:

(u + 3)/-3 = (-3a)/-3

a = (u + 3)/-3

a = (u + 3)/(-3)  is your answer.

~

Write a function rule that represents the sentence
y is 5 less than the product of 4 and x.

Answers

y=5-4x
since less than is subtraction
is means equals 
and product means you have to multiply the numbers

Final answer:

The function rule to represent the given sentence is y = 4x - 5.

Explanation:

To write a function rule that represents the sentence 'y is 5 less than the product of 4 and x,' we can use algebraic notation. The word 'less than' indicates a subtraction operation, so we can represent it as y = 4x - 5. In this function rule, 4x represents the product of 4 and x, and subtracting 5 from it gives us y.

Learn more about Function rule for subtraction here:

brainly.com/question/8131685

#SPJ3

Find three consecutive odd integers such that the sum of the smallest and four times the largest is 61. Please list the numbers from least to greatest with just a space in between

Answers

Answer:

9,11,13

Step-by-step explanation:

Given: sum of the smallest integer and four times the largest integer out of three consecutive odd integers is 61

To list: numbers from least to greatest

Solution:

Let the three consecutive odd integers be x,x+2,x+4.

According to question,

x+4(x+4)=61\nx+4x+16=61\n5x=61-16\n5x=45\nx=9

So, the integers are x=9,x+2=9+2=11,x+4=9+4=13

Numbers from least to the greatest: 9,11,13

Alessandro wrote the quadratic equation –6 = x2 + 4x – 1 in standard form. What is the value of c in his new equation?

Answers

The standard form of a quadratic equation is Ax^2 + Bx + C = 0. So for –6 = x^2 + 4x – 1 to be in its standard form, we can move -6 to the other side of the equation and have x^2 + 4x + (-1 +6) = 0 x^2 + 4x + 5 = 0 So, from the standard form, the value of of C is 5.

Answer:

Step-by-step explanation:

What is the measure of angle ABC?

Angle ABC=___ degrees

Answers

Answer:

60°

Step-by-step explanation:

measure of angle ACB = 180-135= 45

then the required angle = 180-(45+75) = 60°

I hope that was helpful
Angle ABC = 60 degrees!
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