A population of rabbits increases 30.8% each year. If the rabbit population is currently 75,
how many years will it take for the rabbit population to reach 5,400?

Answer:   [tex]\frac{10}{\sqrt{3}}[/tex]

This is equivalent to [tex]\frac{10\sqrt{3}}{3}[/tex]

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

Explanation:

To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.

This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.

The expression [tex]\frac{10}{\sqrt{3}}[/tex] is the same as [tex]\frac{10\sqrt{3}}{3}[/tex] after we multiply top and bottom by sqrt(3) to rationalize the denominator.

Side notes:

Uh oh, looks like you need the graph to answer this question! If you post the graph then I can answer in numbers but for now, I'll try to explain:

1) I assume the graph looks like a dome shape, so based on that, where the line comes back down and hits the bottom line on which x value is larger will be whose stone hit the water second and what time will be what x value represents the time it hit the water.

2) look at the highest value on the purple graph and that is the maximum height (the y value of that point) and the x value of that highest point will be the time it took for the stone to reach its maximum height.

3) based on this question, the graph should start not on the 0 but at a point on the y axis, so whoever's starting y value is higher will be this answer and what that is will be the number answer to the what was it part.

Hope this helps and if you post the graph then I can do more! :)

Given:

The expression is:

[tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex]

To find:

The integration of the given expression.

Solution:

We need to find the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex].

Let us consider,

[tex]I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx[/tex]

[tex]I=\int \dfrac{2\sin^2x}{2\cos^2x}dx[/tex]         [tex][\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x][/tex]

[tex]I=\int \dfrac{\sin^2x}{\cos^2x}dx[/tex]

[tex]I=\int \tan^2xdx[/tex]                      [tex]\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right][/tex]

It can be written as:

[tex]I=\int (\sec^2x-1)dx[/tex]             [tex][\because 1+\tan^2 \theta =\sec^2 \theta][/tex]

[tex]I=\int \sec^2xdx-\int 1dx[/tex]

[tex]I=\tan x-x+C[/tex]

Therefore, the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex] is [tex]I=\tan x-x+C[/tex].

Answer:

(x-4)(x+4)

Step-by-step explanation:

x^2 - 64 = x^2 - 4^2 = (x-4)(x+4)

Answer:

1215

Step-by-step explanation:

If you have a 25% or 1/4 increase, this would mean that you divided the total number of students and add the quotient to the main thing.

So: 972 divided by 1/4 = 972/4 = 243.

972 + 243 = 1215.

Answer:

1215 Students

Step-by-step explanation:

25% is equal to 1/4 correct? (It is :D) So divide 972/4 to know what 25% of the school's population is. 972/4 = 243. So then 243 is 25% of the students. To get the 25% increase add 972 (for the students that will be back next year) and 243 (for the new students). I may have explained this in a really detailed way but it isn't that hard when you think about it!

1. 972/4 (to find 25%)

2. 25% = 243

3. 974 + 243 (old + new)

4. 1215 Students

Answer: B

I took the edge test

Step-by-step explanation:

The location of the complex number 5 - 2i will be (5, -2) which is point D. Then the correct option is D.

The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.

The complex number is given below.

⇒ 5 - 2i

The real part represents the x-axis and the imaginary part represents the y-axis. Then the location of the complex number is written as,

⇒ (5, -2)

The location of the complex number 5 - 2i will be (5, -2) which is point D. Then the correct option is D.

More about the complex number link is given below.

https://brainly.com/question/10251853

#SPJ7

Answer: the answer should be 10%

Step-by-step explanation:

Answer:

10% is correct!

Answer:

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

Option "D"

Step-by-step explanation:

Given:

24 bran muffins required = 2.25 cups of flour

Find:

Number of cups water require for 30 muffins

Computation:

Assume;

Number of cups water require for 30 muffins = x

So,

24 / 2.25 = 30 / x

x = [30 × 2.25] / 24

x = 67.65 / 24

x = 2.8187

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

y = -49

multiply 7 on both sides

-7*7 = y/7*7

-49 = y

Answer:

y = -49

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-7 = y/7

Step 2: Solve for y

Answer:

see below

Step-by-step explanation:   5 25  14 02

herb garden is 1/8 The area of her vegetable garden

herb garden is 6 square feet

vegetable garden = ???

herb garden / vegetable garden  =   1/8      solve for vegetable garden

herb garden × 8  =  vegetable garden

       6 ft² ×  8  =  __________ ft²      

Answer:

3/6=4/8

Step-by-step explanation:

2/6=3/8

2*4 6*4=8/24

3*3 8*3=9/24

2/6 does not equal 3/8

3/6=4/8

3*4 6*4= 12/24

4*3 8*3=12/24

3/6=4/8 is true

Points J, K and M form a triangle.

In this triangle you are given the angles for JKM (50) and KJM (60)

The 3 inside angles of a triangle need to equal 180.

The third angle JMK would be 180 minus the two given angles:

JMK = 180 - 50 - 60 = 70

JMK = 70 degrees

all of the above which is e

Answer:

X>Dy+c

Step-by-step explanation:

I did this question before

Step-by-step explanation:

add 3

x = - 7___________..........

Answer:

She arrived home in December

Step-by-step explanation:

Add 14 months to October

Answer:

she returned home in December just add 14 months to October

Answer:

(-4, 7)

Step-by-step explanation:

It would be the exact opposite of point R because it was rotated about 180 degrees from it's original location

Answer:

"0.0041" is the right answer.

Step-by-step explanation:

According to the question,

The total possible number of tickets will be:

= [tex]6^5[/tex]

= [tex]7776[/tex]

here,

The total even numbers are:

= [tex]2[/tex]

i.e., (2, 4)

now,

With even numbers, the total number of tickets are:

= [tex]2^5[/tex]

= [tex]32[/tex]

hence,

The probability will be:

= [tex]\frac{32}{7776}[/tex]

= [tex]0.0041[/tex]

The probability is the ratio of the favorable event to the total number of events. Then the probability is 0.0041.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. I

At a carnival entrance, tickets are assigned seven-digit numbers using the digits 0-5.

If one ticket number is chosen randomly for a prize.

Then the probability that every number on the ticket is even will be

The total possible number of tickets will be

⇒ 6⁵ = 7776

The total even numbers will be

⇒ 2 {2, 4}

With even numbers, the total number of tickets will be

⇒ 2⁵ = 32

Then the probability will be

[tex]\rm P = \dfrac{32}{7776}\\\\P= 0.0041[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

B(3/4*1/2)

Step-by-step explanation:

So lets see, we have:

3/4 divded by 2

Any whole number, such as 2, will have a denominator like this:

2/1

So we can rewrite this as:

3/4 divided by 2/1

Now, we can actually rewrite this division as multipication. To do this, you must flip the dividing fraction, which was 2/1.

So now it is 1.2:

3/4*1/2

Looking at the anwers, this should be the seocnd one down.

Hope this helps!

Answer:

Step-by-step explanation:

x/y=y/x

4.5/3=24/y

do cross multiplication

24*3=y*4.5

72=4.5y

72/4.5=y

16=y

Answer:

1:

p-r/6=-6-(-6)/6=-6+1=-5

2:

p-(m-n)= -1-(-4-4)=-1-(-8)=-1+8=7

3:

(z+y)/2)3=(-5-4)/3=-9/3=-3

4:

m/6-n=6/6-6=1-6=-5

5:

k³-h=3³-(-2)=27+2=29

6:

p-(p-(m-3))=5-(5-(4-3))=5-(5-1)=5-4=1

7:

(k)(k-j)+3=(5)(5-5)+3=5*0+3=3

8.

p²/6-q=6²/6-4=6-4=2

9;

zx+3³=6*4+3³=24+27=51.

10:

y+z-(y-x)=5+4-(5-2)=9-3=6

Some basic rules:

+. +. +=+

+. * +=+

+. ÷ +=+

+. - +=+

and

+. +. -=add and put sigh of greater one.

-. * +=-sigh

-÷-=+sigh

- - -=add and put - sigh

Y =k√x

12 = 3k

k = 4

now X = 1\2

y = 4√1/2

y = 2√2

Answer:

y = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given y is directly proportional to [tex]\sqrt{x}[/tex] then the equation relating them is

y = k[tex]\sqrt{x}[/tex] ← k is the constant of variation

To find k use the condition when x = 9, y = 12

12 = k[tex]\sqrt{9}[/tex] = 3k ( divide both sides by 3 )

4 = k

y = 4[tex]\sqrt{x}[/tex] ← equation of variation

When x = [tex]\frac{1}{2}[/tex] , then

y = 4[tex]\sqrt{\frac{1}{2} }[/tex] = 4 × [tex]\frac{1}{\sqrt{2} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

y = [tex]\frac{4}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{4\sqrt{2} }{2}[/tex] = 2[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

[tex]sin^2\theta+cos^2\theta=1~=>sin\theta=\pm\sqrt{1-cos^2\theta}\\\\cos\theta=\frac{\sqrt{2}}{2}[/tex]

we'll took the negative solucion of sin because sin is negative in IV cuadrant

[tex]sin\theta=-\sqrt{1-(\frac{\sqrt{2}}{2})^2}=-\frac{1}{\sqrt{2}}=-\frac{\sqrt{2}}{2}[/tex]

[tex]tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]  => [tex]tan\theta=-1[/tex]

so, the right option is the last one

Answer:

2 / 7

Step-by-step explanation:

Coin flipped 3 times has following outcomes, of heads 'H' & Tails 'T'

HHH , TTT , HTT, THT , TTH , THH , HTH , HHT  = total outcomes

P (A) = 2 consecutive heads , P (B) = atleast one tail

P (A) = 2 outcomes ( HHH , HHT , THH ) / total 8 outcomes = 3 / 8

P (B) = 7 outcomes (all except HHH) / total 8 outcomes = 7 / 8

P (A | B) = P ( A ∩ B ) / P (B)

P ( A ∩ B ) = P ( 2 consecutive heads & atleast one tail) / Total outcomes =   2 outcomes ( HHT , THH ) / total 8 outcomes = 2 / 8

So, P (A | B) = ( 2 / 8 ) /  ( 7 / 8 ) = 2 / 7

Answer:

the answer is in the picture

Answer:

[tex]\frac{z^{2} }{25}[/tex]

Step-by-step explanation:

In order to write the expression in the form of [tex]\frac{z^{2} }{k}[/tex] we simply have to open up the brackets. We do that the following way...

[tex](\frac{z}{5} )^{2} =( \frac{z}{5} )( \frac{z}{5}) = \frac{z^{2} }{25}[/tex]

Answer:

w+76=180(being supplementary angle)

w=180-76

w=104