Which expressions represent 5 less than the quotient of X and 4.

From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21

ankoles [38]

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:

We are going to take 4 of the 5 even numbers in the box so we have

$5C4=5$

Case 2: When all 4 numbers are odd:

We are going to take 4 of the 5 odd numbers in the box, so we have

$5C4=5$

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

$5C2 * 5C2$

Remember that we obtain the probability from

$\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}$

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:

We are taking 4 of the 10 cards:

$10C_4=210$

Hence we have that the probability that their sum is even

$\frac{5+5+100}{210}=\frac{11}{21}$

8 0

3 years ago

Determine ƒ(a + h) for ƒ(x) = 2x3.

Kazeer [188]

F(a+h)=2(a+h)³=2(a³+3a²h+3h²a+h³)
the second choice is the correct answer.

4 0

3 years ago

At what value of x does the graph of the following function F(x) have a

tankabanditka [31]

Given:

The function is

$F(x)=\dfrac{1}{x+2}$

To find:

The vertical asymptote of the given function.

Solution:

Vertical asymptote are the vertical line passes thought the values for which the function is not defined.

To find the vertical asymptote, equate the denominator equal to 0.

We have,

$F(x)=\dfrac{1}{x+2}$

Denominator is (x+2).

$x+2=0$

$x=-2$

The vertical asymptote is $x=-2$ .

Therefore, the correct option is B.

8 0

2 years ago

Read 2 more answers

Find the derivative of

kirill [66]

Answer:

$\displaystyle y'(1, \frac{3}{2}) = -3$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \frac{3}{2x^2}$

$\displaystyle \text{Point} \ (1, \frac{3}{2})$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y = \frac{3}{2}x^{-2}$
Basic Power Rule: $\displaystyle y' = -2 \cdot \frac{3}{2}x^{-2 - 1}$
Simplify: $\displaystyle y' = -3x^{-3}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{-3}{x^3}$

Step 3: Solve

Substitute in coordinate [Derivative]: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1^3}$
Evaluate exponents: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1}$
Divide: $\displaystyle y'(1, \frac{3}{2}) = -3$