There is a bag of marbles that contain 5 blue, 6 red, 3 black, and 2 yellow marbles. What is the probability that you select a black marble

(1)

(a) Use the fact that [tex]\sqrt{x^2} = |x|[/tex] for all [tex]x[/tex]. Since [tex]x\to+\infty[/tex], we have [tex]x>0[/tex] and [tex]|x| = x[/tex].

[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ x \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= \frac{\sqrt9}1 = \boxed{3}[/tex]

(b) This time [tex]x\to-\infty[/tex], so [tex]x < 0[/tex] and [tex]|x| = -x[/tex].

[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ \boxed{-x} \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= (-1) \times \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= -\frac{\sqrt9}1 = \boxed{-3}[/tex]

(c) We immediately have

[tex]\displaystyle \lim_{x\to\infty} (x - \sqrt x) = \boxed{\infty}[/tex]

since [tex]x > \sqrt x[/tex] for all [tex]x > 1[/tex].

(d) Introduce a difference of squares by factoring in the limand's conjugate. The rest mirrors what we did in (a)/(b).

[tex]\displaystyle \lim_{x\to\infty} \left(\sqrt{x^2 + 12x} - x\right) = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x} - x\right) \left(\sqrt{x^2+12x} + x\right)}{\sqrt{x^2 + 12x} + x} \\\\ = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x}\right)^2 - x^2}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12x}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12}{\sqrt{1 + \frac{12}x} + 1} = \frac{12}{\sqrt1 + 1} = \boxed{6}[/tex]

(e) Divide through by the highest-degree exponential term.

[tex]\displaystyle \lim_{x\to\infty} \frac{12e^{2x} - 3e^{3x}}{2e^{2x} + 4e^{3x}} = \lim_{x\to\infty} \frac{12e^{-x} - 3}{2e^{-x} + 4} = \frac{0 - 3}{0 + 4} = \boxed{-\frac34}[/tex]

(2) By definition of the derivative, we have

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]

For [tex]f(x) = \sqrt{x^2+1}[/tex], the limit becomes

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\sqrt{(x+h)^2+1} - \sqrt{x^2+1}}h[/tex]

Factor in the conjugate.

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1} - \sqrt{x^2+1}\right) \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1}\right)^2 - \left(\sqrt{x^2+1}\right)^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\bigg((x+h)^2+1\bigg) - (x^2+1)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2xh + h^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2x + h}{\sqrt{(x+h)^2+1} + \sqrt{x^2+1}}[/tex]

[tex]\implies \boxed{f'(x) = \displaystyle \lim_{h\to0} \frac{x}{\sqrt{x^2+1}}}[/tex]

(3) The tangent line to

[tex]y = \frac1{x^2+1}[/tex]

at the point (2, 1/5) has slope equal to the derivative [tex]\frac{dy}{dx}[/tex] when [tex]x = 2[/tex]. Compute the derivative; since [tex]y = \frac1{f(x)^2}[/tex] where [tex]f(x)[/tex] is the function from the previous problem, using the chain rule gives

[tex]y = \dfrac1{f(x)^2} \implies \dfrac{dy}{dx} = -\dfrac{2f'(x)}{f(x)^3} = -\dfrac{2 \times \frac{x}{\sqrt{x^2+1}}}{\left(\sqrt{x^2+1}\right)^3} \\\\ \implies \dfrac{dy}{dx} = -\dfrac{2x}{(x^2+1)^2}[/tex]

The tangent line at (2, 1/5) then has slope

[tex]\dfrac{dy}{dx}\bigg|_{x=2} = -\dfrac{2\times2}{(2^2+1)^2} = -\dfrac4{25}[/tex]

Using the point-slope formula, the equation of the tangent line is

[tex]y - \dfrac15 = -\dfrac4{25} (x - 2) \implies \boxed{y = -\dfrac{4x - 13}{25}}[/tex]

Mark as brainliest :)

9514 1404 393

Answer:

Step-by-step explanation:

Jarvis is paid for 1 1/2 times the number of hours he worked on Saturday. So, for the 5 hours he worked, he is paid for ...

  5 × 1 1/2 = 7 1/2 hours . . . . paid on Saturday

Jarvis is paid for 1 3/4 times the number of hours he worked on Sunday, So, for the 2 hours he worked, he is paid for ...

  2 × 1 3/4 = 3 1/2 hours . . . . paid on Sunday

The total of hours for which Jarvis is paid is ...

  7 1/2 + 3 1/2 = 11 hours . . . . paid for the weekend

At $9 per hour, the amount Jarvis is paid for the weekend is ...

  $9 × 11 = $99.00 . . . . weekend pay

y=mx+b

-3=3(3)+b

-3=9+b

-12=b

Answer: a

Step-by-step explanation:

Answer:

A robot can complete tasks in

hour. Each task takes the same amount of time.

a. How long does it take the robot to complete one task?

It takes one hour to complete one task.

b. How many tasks can the robot complete in one hour?

It complete only one task in one hour.

Answer:

C. 11 customers

Step-by-step explanation:

The pattern is that it rises or goes up by 2 in the y axis, it runs or goes to the right once in the x-axis.

Answer:

12 passengers can travel in Rs. 900.

Step-by-step explanation:

see the above attachment.

if you face any problem comment me, I am there for help.

hope this helps you.

9514 1404 393

Answer:

  D: 21

Step-by-step explanation:

The first term is (a1). The third term is (a1)r². The product of these terms is ...

  (a1)(a1)r² = ((a1)r)², the square of the second term.

The missing term is √(7·63) = √441 = 21.

_____

Additional comment

In consideration of the above, you can also see that the common ratio can be found from ...

  a3/a1 = ((a1)r²)/(a1) = r² = 63/7 = 9

Then the common ratio is r = √9 = 3, and the second term is 7·3 = 21.

Answer:

it will rotate 7.5 degrees

Step-by-step explanation:

Answer:

80 I believe

Step-by-step explanation:

Answer:

Define:

Domain is the set of values that you can input in a function

Range is the set of values that corresponds to the output of a function, the set of values corresponding to its results

The vertical line test is a simple test you can do with a graph to know if this graph correspond to a function or not: you have to draw a vertical line, parallel to the y-axis and if that line touch the graph in just one point, it is a function

What is the domain and range of each function?

Domain = {3, 5, 7, 8, 11}

Range = {6, 7, 9, 14}

Is each relation a function?

Yes

Answer:

my butt

Step-by-step explanation:

why well because when were dinosaurs created in 1957 and when they were alive they drove cars to school to learn about extra chromosomes and and then the meatore hit and created my butt.

I hope that helps if you need anymore help let me know :)

Answer:

The answer is 86° Fahrenheit.

Step-by-step explanation:

The equation for converting between Fahrenheit and Celsius is °F = 1.8 x °C + 32. So you would just plug 30 in for the °C.

°F = 1.8 x 30° + 32.

°F = 54 + 32

°F = 86°

Answer:

30ºC = 86ºF

Step-by-step explanation:

The temperature T in degrees Fahrenheit (ºF) is equal to 30 degrees Celsius (ºC) times 9/5 plus 32:

T(ºF) = 30ºC × 9/5 + 32 = 86ºF

An ogive graph serves as a graphical representation of the cumulative relative frequency distribution for quantitative variables. In other words, these graphs plot the percentile on the y-axis and the quantitative variable on the x-axis. An Ogive is connected to a point on the x-axis, that represents the actual upper limit of the last class, i.e.,( 80.5, 0) Take x-axis, 1 cm = 10 marks. Y-axis = 1 cm – 10 c.f. There are two types of ogives : Less than ogive : Plot the points with the upper limits of the class as abscissae and the corresponding less than cumulative frequencies as ordinates. Ogives are useful for determining the median, percentiles and five number summary of data. Remember that the median is simply the value in the middle when we order the data. A quartile is simply a quarter of the way from the beginning or the end of an ordered data set.

I know this is a lot but this will help you understand.

Answer:

hope i helped...if anythng not understood please write in the comments

Answer:

3y^5(2y^3+3)=−6y^8−9y^5

−2c^6(5c^3+6)=−10c^9−12c^6

are the correct equations.

Step-by-step explanation:

If you simply all these equations you will get following equations :

when bases are same and are in multiplication we add the exponents.

−4b^4(5b^2+6)=−20b^6−24b^4

−5x^3(3x^3+2)=−15x^6−10x^3

−3y^5(2y^3+3)=−6y^8−9y^5

−2c^6(5c^3+6)=−10c^9−12c^6

so equation 3 and 4 are correct.

Answer:

1/64

Step-by-step explanation:

P(pick 3 consecutive spades with replacement of drawn cards) =

(13/52)(13/52)(13/52) =

(1/4)(1/4)(1/4) =

1/64

Answer:

Banks play an important role in the economy by offering a service for people wishing to save. Banks also play an important role in offering finance to businesses that wish to invest and expand. These loans and business investment are important for enabling economic growth.

The financial services sector is the primary driver of a nation's economy. It provides the free flow of capital and liquidity in the marketplace. When the sector is strong, the economy grows, and companies in this industry are better able to manage risk.

Step-by-step explanation:

Answer: 4

pls give brainliest

Answer:

[tex]\large\boxed{\tt-\frac{3}{4} x}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify the missing number for our equation.}[/tex]

[tex]\textsf{First, we should translate our \underline{word form} equation into \underline{numerical form}.}[/tex]

[tex]\tt \underset{-4}-4 \ \underset{\times}{times} \ \underset{?}{what} \ \underset{=}{equals} \ \underset{3x}{3x}?}[/tex]

[tex]\tt -4 \times \ ? = 3x[/tex]

[tex]\large\underline{\textsf{Identifying Ways of Solving;}}[/tex]

[tex]\textsf{We know that the unknown value is multiplied by -4 to equal 3x.}[/tex]

[tex]\textsf{-4 will equal the quotient of 3x and the unknown number.}[/tex]

[tex]\textsf{Hence, the unknown number will equal the quotient of 3x and 4.}[/tex]

[tex]\large\underline{\textsf{Solving For the Unknown Number;}}[/tex]

[tex]\tt \frac{3x}{-4} = Unknown \ Number[/tex]

[tex]\underline{\textsf{Multiply the Numerator and Denominator by the Reciprocal of -4;}}[/tex]

[tex]\textsf{The Reciprocal is a fraction where the numerator and denominator flip.}[/tex]

[tex]\tt Reciprocal \ of \ -4 \ is; -\frac{4}{1} \rightarrow \boxed{-\frac{1}{4}}[/tex]

[tex]\mathtt{ \frac{-\frac{1}{4} \times3x}{-\frac{1}{4} \times -4} \rightarrow \frac{\frac{-3}{4}x }{1} \rightarrow \large\boxed{\tt-\frac{3}{4} x}}[/tex]

can you help me this 4^x x ^8^x^+^1 = 2⁴

Answer:

Any expression that sums up to 96 is equivalent to 12+84.

Step-by-step explanation:

Since, you haven't provided any options.

12+84=96

Any expression that sums up to 96 is equivalent to 12+84.

Answer:

1/10

Step-by-step explanation:

The default placeholder value for tenths in math is 0.1, or 1/10. the first digit after the decimal point.

Answer:

[tex]y = \frac{1}{2} x - 1[/tex]

Explanation:

The first pic shows the line graphed, while the second pic shows how to turn the equation into proper slope-intercept form.

The only steps the second pic is missing however, is flipping the sides around to be better understood (optional), and more importantly subtracting 2 on both sides in order to move it to the other side, to get 2y = x - 2. And dividing the 2 on both sides to get y by its self, to get:

y = (x-2)/2 , or y = 1/2 x - 2/2 , which if you notice 2/2 makes it equal to one whole so your answer is y = 1/2 x - 1 .

If you like this answer can you please mark me brainliest? :)

Answer:

-9

Step-by-step explanation:

(-4-2*-1/2)3

(-4+1)3

-3*3

-9

Answer:

-27

Step-by-step explanation:

Hi there!

[tex](a-2b)^3[/tex]

Plug in the given information:

[tex](-4-2(\displaystyle -\frac{1}{2} ))^3\\\\(-4-(\displaystyle -\frac{2}{2} ))^3\\\\(-4+1)^3\\\\(-3)^3\\\\-27[/tex]

I hope this helps!

Answer:

7.083

Step-by-step explanation:

well there's the ones place, tenths, hundredths, and thousandths. easy math, unless i'm stoopid and this is wrong :D

Answer:

?

Step-by-step explanation: