A six sided cube is rolled. What is the probability of getting a 3 and then a 4, givrn the first number rolled was 3.

Answer:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Step-by-step explanation:

We have the function:

[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]

And we want to determine the intervals for which the function is increasing or decreasing.

We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.

To find the critical points, we need to find the first derivative and then solve for the x. So:

[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]

Differentiate:

[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]

Set the derivative equal to 0 and solve for x:

[tex]0=3x^2-11x-4[/tex]

Factor:

[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]

Zero Product Property:

[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]

Therefore, our critical points are -1/3 and 4.

We can thus sketch the following number line:

<————-(-1/3)——————————————(4)—————>

Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.

For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:

[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]

The result is positive.

Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).

For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:

[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]

The result is negative.

Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).

And finally, for greater than 4, we can use 5:

[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]

The result is positive.

Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.

Therefore:

[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]

In interval notation:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Answer:

40

Step-by-step explanation:

Answer:

He kept 7/12 of the box.

Step-by-step explanation:

We add and convert both 1/6 and 1/4 because we cant add fractions with unlike denominators.

1/6 = 2/12  | 1/4 = 3/12

then add.

2/12 + 3/12 = 5/12.

we subtract this from a whole, which is 12/12.

12/12 - 5/12 = 7/12

he keeps 7/12 of the box

hope this helped!

Answer:

= 3.9 candy per pound

Step-by-step explanation:

This is a fraction equal to

7.8 candy ÷ 2 pounds

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2

7.8 candy        ÷ 2

________

2 pounds ÷ 2

=  

3.9 candy

_______

1 pound

=  

3.9 candy

_______

pound

= 3.9 candy per pound

Answer:

its 6 units

Step-by-step explanation:

Answer:

Square root of 20

I really hope i'm right sorry in advanced if i'm not

Answer:

Um threre is no blanks or there is no question.

Step-by-step explanation:

Answer:

x = 33.13 units

Step-by-step explanation:

Let the altitude of the triangle be h units.

[tex] \sin 65 \degree = \frac{h}{31} \\ \\ 0.906307787 = \frac{h}{31} \\ \\ h = 0.906307787 \times 31 \\ \\ h = 28.0955414 \\ \\ \cos \: 32 \degree = \frac{h}{x} \\ \\ 0.8480480962 = \frac{28.0955414}{x} \\ \\ x = \frac{28.0955414}{0.8480480962} \\ \\ x = 33.1296556 \\ \\ x \approx 33.13 \: units[/tex]

Answer:

Step-by-step explanation:

Step 1

Find the length of vertical line segment, lets call it h. Use function cos

Step 2

Find x using another function, sin

Not sure what you mean but will be explaining about y = 0 and x =0 anyway.

So for x = 0, that means the value of x is 0.

y = -2(0)+8

y=0+8

y=8

So when x = 0, the value of y is 8 (y = 8) or we can write (0,8)

For y = 0, that means the value of y is 0.

0=-2x+8

-8=-2x

-2x=-8

x=4

So when y = 0, x = 4. We can write as (4,0)

Answer:

y=-6x-8

Step-by-step explanation:

well first of all the line passes through (0,-8) ehich would give you a y-int of -8, to find the slope of y=mx+b you could do rise/run. fi you found a point and counted down to another point it'd be -6, then count the run it'd be 1, -6/1 equals -6

Answer:

The slope is 3/2

Answer:

timeline

Step-by-step explanation:

the table shows the same time I don't have your phone you u you y you can get a hold of y have a lot to do it you got a

The domain and range provides a definition for a graph

Part A: The graph represents a function because a vertical line drawn from the horizontal crosses the graph only once

Part B. Domain: 0 ≤ t ≤ 30

Range: 7000 < f(t) ≤ 9,300

Reason:

Part A: The reason why the graph represents a function is that a function is a one to one relationship that maps each element of the set known as the domain to exactly one element of the set which is the range of the function

Therefore, a vertical line drawn on the graph of a function crosses the graph only once, such that one input cannot have two outputs

Which gives that the graph is a function, given that all the vertical lines from the horizontal axis crosses the graph f(t) at exactly one point

Part B

Domain:

The domain of a function are the possible input values of the function

In the graph, the possible values of the time, t are; 0 ≤ t ≤ 30

The domain of the function is 0 ≤ t ≤ 30

Range:

The range of a function are the possible output values of the function

The range of the given function f(t) are; from approximately 7,000 feet to approximately 9,000 feet, which gives;

The range of the function: 7000 < f(t) ≤ 9,300

Learn more here:

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Answer:

theres no image

Step-by-step explanation:

Answer:

to create an equation that is parallel to a line, you keep the slope or rate of change the same, all you do is change the y intercept. so you have to keep

y = 2x, but then you can add any number to the end.

Answer:y = -0.6x + 5

Step-by-step explanation:

Answer:

yessir the one on top is right btw

Step-by-step explanation:

hope this helped

Answer:

$90

Step-by-step explanation:

70-25 = 45

45x2 = 90

Answer:

Linear

General Formulas and Concepts:

Types of Graphs

Step-by-step explanation:

Whenever the graph is a straight line (either a diagonal or a horizontal, NOT a vertical line), it will always be linear.

Answer:

2x^2-4x+1

Step-by-step explanation:

2(x-1)^2-1

2(x^2-2x+1)

2x^2-4x+2-1

2x^2-4x+1

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[tex]f(x) = 2 ({x - 1})^{2} - 1 [/tex]

[tex]f(x) = 2( {x}^{2} - 2x + 1) - 1[/tex]

[tex]f(x) = 2 {x}^{2} - 4x + 2 - 1 [/tex]

[tex]f(x) = 2 {x}^{2} - 4x + 1 [/tex]

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Answer:

B

Step-by-step explanation:

That's my guess.

Answer:

C

Step-by-step explanation:

140 ÷ 20 = 7

7 × 15 = 105

24

6 1/2

Answer:

if you have and piece of clothing that was left behind.

Step-by-step explanation:

Answer:

x=59

Step-by-step explanation:

The sum of the interior angles of a triangle add up to 180 degrees.  That means that (x+12)+(x)+(x-9)=180 degrees in total.  If we combine the like terms (combine the xs and regular constant values), the xs add up to 3x (x+x+x) and the regular constants add up to 3 (12+-9=3).  If we rewrite this in a more simplified form, we get 3x+3=180.  Subtract 3 on both sides to get 3x=177 because we want to isolate x.  3x=177 divide 3 on both sides and we get 59.  x=59

Answer:

1/5

Step-by-step explanation:

[tex]\frac{2-1}{3--2} = \frac{1}{5}[/tex]

Answer: 1/5

Step-by-step explanation: Following our hint,

let's start with the slope formula.

m = y₂ - y₁ / x₂ - x₁

We take the second y minus the first y over the second x minus the first x.

So we have m = 2 - 1 / 3 - (-2) or 1 / 5.

So our slope is 1/5.

Answer:

two sevenths

Step-by-step explanation:

Answer:

238

Step-by-step explanation:

juans has 10 more than kevin's, so you just subtract 10 from 248, getting 238

Answer:

[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]

Step-by-step explanation:

Recall that using the chain rule we can state:

[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt  and dx/dt,

Given that

[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]

And similarly:

[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]

now notice that we can find   [tex]cos(t) = \sqrt[3]{y}[/tex]  from the expression for y,

and   [tex]sin(t) = \sqrt[3]{x}[/tex]  from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]

Answer:

-6

Step-by-step explanation:

-10-(-4)=-1+4=-6

Hope this helps plz mark brainliest ;D

Answer:

7x+Y=-2

Step-by-step explanation:

(y-y1)=m(x-x1)

(Y+4)=-7(x-2)

Y+4=-7x+2

Y+7x=2-4

7x+Y=-2

Answer:

x <(with a line underneath the carrot) -11

Step-by-step explanation:

Hope this helps! Could not find the symbol.

The inequality for x which is less than or equal to -11 is written as x ≤ -11 or  x + 11 ≤ 0.

Inequality shows relation between two expression which are not equal to each others.

Let the required number is x.

In the given question,

Number x is less than or equal to -11.

The inequality for x which is less than or equal to -11 can be written as,

x ≤ -11

The inequality can be further simplified as,

⇒x + 11 ≤ 0

The inequality for x is x + 11 ≤ 0.

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