Rock climbing. I am out rock climbing, and the rock face has 4 easy, 7 challenging, and 3 extreme routes to get to the top. The routes are poorly marked, so I just choose one at random, with all routes equally likely. What is the probability that I do not choose an extreme route

Answer:

1,159 pieces of mail

Step-by-step explanation:

From the information given, you can write an inequality that indicates that the price of sending each piece of mail without the permit is higher than the price of purchasing the bulk-mail permit and then, you can solve for x that is the number of pieces of mail:

0.44x>0.276x+190

0.44x-0.276x>190

0.164x>190

x>190/0.164

x>1,158.5

According to this, the organization needs to send 1,159 pieces of mail in a year to make it cheaper to use a bulk-mail permit.

The general form of a solution of the differential equation is already provided for us:

[tex]y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},[/tex]

where [tex]c_1, c_2 \in \mathbb{R}[/tex]. We now want to find a solution [tex]y[/tex] such that [tex]y(-1)=3[/tex] and [tex]y'(-1)=-3[/tex]. Therefore, all we need to do is find the constants [tex]c_1[/tex] and [tex]c_2[/tex] that satisfy the initial conditions. For the first condition, we have:[tex]y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.[/tex]

For the second condition, we need to find the derivative [tex]y'[/tex] first. In this case, we have:

[tex]y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.[/tex]

Therefore:

[tex]y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.[/tex]

This means that we must solve the following system of equations:

[tex]\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.[/tex]

If we add the equations above, we get:

[tex]\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.[/tex]

If we now substitute [tex]c_1 = 0[/tex] into either of the equations in the system, we get:

[tex]c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}[/tex]

This means that the solution obeying the initial conditions is:

[tex]\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.[/tex]

Indeed, we can see that:

[tex]y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3[/tex]

[tex]y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,[/tex]

which do correspond to the desired initial conditions.

Answer:

12

Step-by-step explanation:

4+4+4=12

The ratio of number of girls and boys in a class of 30 students is 7:8

The ratio of number of girls and boys if 5 new boys admit in the class.

Let the number of students be x.

According to the question,

7x + 8x = 30

or, 15x = 30

or, x = [tex] \large {\tt {\frac{30}{15}}} [/tex]

or, x = 2

7x = 7(2) = 14

8x = 8(2) = 16

There were 14 boys and 16 girls in the school.

After admitting 5 new boys, we get

14 + 5 = 19

The ratio of number of girls and boys now is 16:19.

16:19

Answer:

The width of the frame is 3 inches

Step-by-step explanation:

We are told that the inner rectangle is 10 inches by 16 inches.

It means the outer rectangle has to be (L = 10 + 2x) by (W = 16 + 2x),

Where x represents the width of the frame.

The perimeter of the frame is given by; p = 2L + 2W

p = 2(10+2x) + 2(16+2x)

We are given perimeter, P = 76

Thus;

2(10 + 2x) + 2(16 + 2x) = 76

Divide both sides by 2 to give;

(10+2x) + (16+2x) = 38

(10+16) + (2x+2x) = 38

4x = 38 - 26

4x = 12

x = 12/4 = 3

The width of the frame is x = 3 inches

Answer: 4 + (-n) and -n+4

==========================================================

Explanation:

Adding a negative is the same as subtracting. For example, 10-7 = 10+(-7)

So that's why 4-n is the same as 4 + (-n)

---------

Then we go from 4 + (-n) to -n+4 because we can add two items in any order.

Example: 2+3 = 3+2 = 5

Answer:

D

Step-by-step explanation:

An exponential model is appropriate because the relationship between period and the log of subscribers is roughly linear and the residual plot shows no distinct pattern.

Answer:

its D

Step-by-step explanation:

By the chain rule,

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}[/tex]

It looks like we're given

[tex]\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}[/tex]

where a and b are presumably constant.

Recall that

[tex]\cos^2t=\dfrac{1+\cos(2t)}2[/tex]

[tex]\sin^2t=\dfrac{1-\cos(2t)}2[/tex]

so that

[tex]\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}[/tex]

Then we have

[tex]\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t[/tex]

[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}[/tex]

[tex]\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}[/tex]

where the last reduction follows from dividing through everything by [tex]\cos(2t)\cos^2t[/tex] and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

Answer

7 chocolates.

Step-by-step explanation:

42÷6=7

Answer:welll i think its 5

Step-by-step explanation:

Answer:21 obviously it’s actually (19) don’t tell anyone

Step-by-step explanation:

Though I prefer to eat fruit, I enjoy vegetables too.

A homophone is a word that is pronounced the same as another word but differs in meaning.

Homophones may consist of two or more words, although pairs are more common than three or more words that sound the same. Examples of homophones that have three words are to, too, and two, and their, there, and they're.

here, we have,

Though I prefer to eat fruit, I enjoy vegetables too.

A homophone is a word that is pronounced the same as another word but differs in meaning.

Learn more about homophones here

brainly.com/question/7449238

#SPJ7

Answer:

Hi there!

Your answers are:

1) 2^4 = 2×2×2×2 = 16

2) 2^3= 2×2×2= 8

3) 2^2 = 2×2 = 4

4) 2^1 = 2

5)2^0 = 1

6)2^ -1 = .5

7) 2^ -2 = .25

8) 2^ -3 = .125

9) 2^ -4= .0625

Hope this helps

Answer:

37

Step-by-step explanation:

Answer:

[tex] \boxed{\sf x\degree = 67\degree} [/tex]

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

So,

⇒ 43° + 70° + x° = 180°

43° + 70° = 113°:

⇒ 113° + x° = 180°

Substracting 113° from both sides:

⇒ 113° - 113° + x° = 180° - 113°

113° - 113° = 0°:

⇒ x° = 180° - 113°

180° - 113° = 67°:

⇒ x° = 67°

Answer:

w= 3 feet

h= 5 feet

Step-by-step explanation:

H=height; W=width=2H-7ft

W=2H-7ft

2H+4W=22ft Substitute for W

2H+4(2H-7ft)=22ft

2H+8H-28ft=22ft Add 28 ft to each side.

10H=50ft

H=5 ft ANSWER 1: The bookshelf is 5 feet high.

W=2H-7ft=2(5ft)-7ft=10ft-7ft=3ft

ANSWER 2: the bookshelf is 3 feet wide.

CHECK:

2H+4W=22ft

2(5ft)+4(3ft)=22ft

10ft+12ft=22ft

22ft=22ft

Hope this helps!

Answer:

Eight-hundred thousand plus six-thousand plus three hundred plus two  

The answer equals Eight-hundred six thousand three hundred two  

Hopefully this helps! Feel free to mark brainliest!

Answer:

eight-hundred six-thousand three-hundred and two

Step-by-step explanation:

[tex]800,000+6000+300+2[/tex] in word form

Let's separate everything.

[tex]800,000=[/tex] eight-hundred thousand

[tex]6,000=[/tex] six thousand

[tex]300=[/tex] three hundred

[tex]2=[/tex] two

So let's combine everything and make it proper.

Eight-hundred six-thousand three-hundred and two

Hope this helps!

Answer:

f'(1)=150ln(1.5)

Step-by-step explanation:

I'm not sure why you would need a table since the limit definition of a derivative (from what I'm remembering) gives you the exact formula anyway... so hopefully this at least helps point you in the right direction.

My work is in the attachment but I do want to address the elephant on the blackboard real quick.

You'll see that I got to the point where I isolated the h's and just stated the limit equaled the natural log of something out of nowhere. This is because, as far as I know, the way to show that is true is through the use of limits going to infinity. And I'm assuming that you haven't even begun to talk about infinite limits yet, so I'm gonna ask you to just trust that that is true. (Also the proof is a little long and could be a question on it's own tbh. There are actually other methods to take this derivative but they involve knowing other derivatives and that kinda spoils a question of this caliber.)

Answer: (C). There are 200 animals, and the cost is $8,000 daily.

Step-by-step explanation: We already know (x) is the number of animals measured in hundreds and it would go on the x axis. And that would mean that (f) is going to be on the y axis. Go over on the x axis 2 then for the y axis go up 8 on the y axis and you would get (2,8)= (200 animals, $8,000 a day)

There are 200 animals, and the cost is $8,000 daily

Answer:

For revolution about the y-axis:

For revolution about the x-axis, swap x and y.

Step-by-step explanation:

The methods for computing the volume of revolution of  a plane figure are ...

The name of the method describes the shape of the differential of volume.

__

Cylindrical shell

For revolution about the y-axis, the differential of volume is a cylindrical shell of radius x, thickness dx, and height y2 -y1, where y2 = f2(x) and y1 = f1(x). (y2 > y1) Integration is over x.

  dV = 2π·x·(f2(x) -f1(x))·dx

For revolution about the x-axis, the variables x and y are interchanged.

__

Disk

For revolution about the y-axis, the differential of volume is a donut or disk of inner radius f1(y) = x1 and outer radius f2(y) = x2 (x1 ≤ x2). The thickness is dy. Integration is over y.

  dV = π·(f2(y)^2 -f1(y)^2)·dy

For revolution about the x-axis, the variables x and y are interchanged.

__

The preferred method is the one that gives simple integrable functions over a single range of integration. For some geometries, the integration range must be split, because the shape of the differential volume cannot be described by a simple rectangle whose length is the difference of functions of the integration variable.

When the differential of volume can be drawn either way, the choice of methods may be arbitrary. I usually choose the method that gives the simplest integrand.

_____

Additional comment

When the axis of revolution is something other than a coordinate axis, the radius of revolution becomes a different function than a simple x (or y). For example, if the axis of revolution is x=a, the radius of the cylindrical shell will be a-x (for x ≤ a) or x-a (for a ≤ x).

Here's an example of the use of the disk method.

https://brainly.com/question/17446389

Answer for 1.a is 6. 6 is in the thousands place.

Answer for 1.b is 9. 9 is in the thousandths place.

Answer:

acute

Step-by-step explanation:

its less then 90 degree

Answer:

Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.

Step-by-step explanation:

Note: This question is not complete as the bar chart is not included. The bar chart is therefore included before answering the question. Please, see the attached jpeg file for the bar chart.

The explanation to the answer is now given as follows:

From the bar chart, we have the number of hours each student spends working on the group project as follows:

Numbers of hours spent by Paloma = 21 hours

Numbers of hours spent by Adbul = 18 hours

Numbers of hours spent by Ben = 13 hours

Numbers of hours spent by Min = 22 hours

The number of hours each group spent working on the group project is calculated as follows:

Numbers of hours spent by Paloma and Abdul = Numbers of hours spent by Paloma + Numbers of hours spent by Paloma = 21 hours + 18 hours = 39 hours

Numbers of hours spent by Ben and Min = Numbers of hours spent by Ben + Numbers of hours spent by Min = 13 hours + 22 hours = 35 hours

Th number of hours Paloma and Abdul spend working on the project combined more than Ben and Min combined = Numbers of hours spent by Paloma and Abdul - Numbers of hours spent by Ben and Min = 39 hours - 35 hours = 4 hours

Therefore, Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.

Answer:

6.1021 6.109 6.12 6.2

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

According to order of operations (PEMDAS), you should multiply the numbers on the two sides of the addition sign first. So:

-4 x -5 = 20

and

2 x -3 = -6

Then you add those two numbers together:

-6 + 20 = -14

Answer:

No.

Step-by-step explanation:

8 doesn't equal 0 on the very right, which means it's not a solution to the equation.  So therefore, it is false based on the equation.

Answer:

1.   75 degrees

2.  105 degrees

3.  35 degrees

Step-by-step explanation:

Hope this helps! :)