Consider the quadratic expression given below.

What is the sample space for each one of the following statements? (7.5 points each)

photoshop1234 [79]

We can define the sample space for a given experiment as the set of all the possible outcomes for the experiment.

For example, tossing a coin has a space sample of 2 elements, tails and heads.

The spaces are:

a) {WW, BB, WBB, BWW, WBWW, BWBB,... }

b) { 1-2-3-4, 1-2-3-5,..., 7-6-5-4,...}

a) We can write one element in this sample space as:

WBB

This would mean that first we draw a white ball, then a black ball, and then the second black ball, thus we stop drawing.

<u>So all the elements in this set will have the form</u>

{WW, BB, WBB, BWW, WBWW, BWBB,... }

As we have infinite balls in the bag, we have infinite elements in this set.

b) Now we have only 10 balls numbered from 1 to 10, and we draw 4.

So each element in the sample space can be written as:

1-2-3-4

This element means:

"first we draw ball number 1, then ball number 2, then ball number 3, then ball number 4"

Then the sample space will have the form:

{ 1-2-3-4, 1-2-3-5,..., 7-6-5-4,...}

If you want to learn more, you can read:

brainly.com/question/23125812

6 0

2 years ago

1) 5(h + 9) = 55 Distribute _____ to everything in parentheses.

NikAS [45]

9 + h = 55/5
9 + h = 11
11 - 9 = h
2 = h

The opposite of addition is subtraction, Subtract 9 from both sides, The opposite of multiplication is division, divide both sides by 5 is the first step, and final answer is h = 2.

8 0

2 years ago

A triangle has 2 sides that equal 5 inches. The other side equals 4 inches

miskamm [114]

Answer:

Isosceles triangle

Step-by-step explanation:

It is assumed that the triangle is a right angle triangle, implying that Pythagoras theorem becomes applicable.

If the first side is represented by x and the second side by y,

x + y = 5

The hypotenuse is always the longest side hence it can be presumed to be 4 since both x and y cannot be more than 5.

Therefore using pythagoras equation:

hyp^2 = sqrt(opp^2 + adj^2)

this implies that

$4^{2} = \sqrt{x} (x^{2} +y^{2}$

therefore

16 = sqrt (x^2 + y^2) ----------------- (i)

since x + y = 5, y = 5 - x ------------------- (ii)

substituting (ii) into eqn (i)

16 = sqrt ( x^2 + (5-X)^2)

16 = sqrt( x^2 + 25 -10x + x^2)

16 = sqrt( x^2 + x^2 - 10x + 25)

16 = sqrt( 2x^2 - 10x + 25)

squaring both sides

256 = 2x^2 - 10x + 25

this can be refined as

2x^2 - 10x - 231 = 0

Solving using quadratic equation:

where a = 2, b = -10 and c = -231

x = 13.53 or -8.53.

Since x is a side of a triangle that cannot be negative,

x = 13.53 but x can never be greater than 5 since x + y = 5

This implies that the triangle is not a right angle triangle; it is most likely an isosceles triangle with two sides of equal length such that x = y = 2.5 inches while the longest side; the hypotenuse is 4 inches.

substituting for x in

4 0

2 years ago

Graph for f(x)=6^6 and f(x)=14^x

zlopas [31]

Graph Transformations

There are many times when you’ll know very well what the graph of a

particular function looks like, and you’ll want to know what the graph of a

very similar function looks like. In this chapter, we’ll discuss some ways to

draw graphs in these circumstances.

Transformations “after” the original function

Suppose you know what the graph of a function f(x) looks like. Suppose

d 2 R is some number that is greater than 0, and you are asked to graph the

function f(x) + d. The graph of the new function is easy to describe: just

take every point in the graph of f(x), and move it up a distance of d. That

is, if (a, b) is a point in the graph of f(x), then (a, b + d) is a point in the

graph of f(x) + d.

As an explanation for what’s written above: If (a, b) is a point in the graph

of f(x), then that means f(a) = b. Hence, f(a) + d = b + d, which is to say

that (a, b + d) is a point in the graph of f(x) + d.

The chart on the next page describes how to use the graph of f(x) to create

the graph of some similar functions. Throughout the chart, d > 0, c > 1, and

(a, b) is a point in the graph of f(x).

Notice that all of the “new functions” in the chart di↵er from f(x) by some

algebraic manipulation that happens after f plays its part as a function. For

example, first you put x into the function, then f(x) is what comes out. The

function has done its job. Only after f has done its job do you add d to get

the new function f(x) + d. 67Because all of the algebraic transformations occur after the function does

its job, all of the changes to points in the second column of the chart occur

in the second coordinate. Thus, all the changes in the graphs occur in the

vertical measurements of the graph.

New How points in graph of f(x) visual e↵ect

function become points of new graph

f(x) + d (a, b) 7! (a, b + d) shift up by d

f(x) Transformations before and after the original function

As long as there is only one type of operation involved “inside the function”

– either multiplication or addition – and only one type of operation involved

“outside of the function” – either multiplication or addition – you can apply

the rules from the two charts on page 68 and 70 to transform the graph of a

function.

Examples.

• Let’s look at the function • The graph of 2g(3x) is obtained from the graph of g(x) by shrinking

the horizontal coordinate by 1

3, and stretching the vertical coordinate by 2.

(You’d get the same answer here if you reversed the order of the transfor-

mations and stretched vertically by 2 before shrinking horizontally by 1

3. The

order isn’t important.)

74

7:—

(x) 4,

7c’

‘I

II

‘I’

-I

5 0

2 years ago

What is the answer a b or c

olganol [36]

I think it's B I might be wrong I hope it helped

7 0

3 years ago