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2 years ago

If you have a 5 letters A,B,C,D,E and you can put them in any order how many ways can you place them

1 answer:

4 0

The first letter can be any one of 5. For each of those . . .
The second letter can be any one of the remaining 4. For each of those . . .
The third letter can be any one of the remaining 3. For each of those . . .
The fourth letter can be any one of the remaining 2. For either of those . . .
The fifth letter is the last remaining one.

Total number of possibilities = (5 x 4 x 3 x 2 x 1) =

 120 ways to line them up.

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their whole life on, to make sure that a lot of kids won't go through their
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Katie bought 2 one gallon bottles for a party. Her guest drank 5/4 gallons of juice. What is the fraction of juice leftover? Sho

frosja888 [35]

Answer:

3/4 gallons of juice

Step-by-step explanation:

Katie bought 2 one-gallon bottles for a party.

2 one-gallon bottles = 2-gallon bottles of juice

We are told that:

Her guest drank 5/4 gallons of juice.

The fraction of juice leftover is calculated as:

2 gallons of juice - 5/4 gallons of juice

2 - 5/4

Lowest Common Denominator = 4

2/1 - 5/4

= 8 - 5/4

= 3/4 gallons of juice

Therefore, the fraction of juice leftover is 3/4 gallons of juice

7 0

2 years ago

Please help :) i really need your help right now thank you

Nastasia [14]

The first one and the last one, the 2 middle ones are not corresponding

5 0

2 years ago

Determine the value of k

KATRIN_1 [288]

Answer:

$\displaystyle k = 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$