Researchers capture and mark 43 squirrels in a park. The next week, researchers capture 50 squirrels and 38 of them are marked from the previous month. Estimate the squirrel population in the park.

Answer:

Trig identities

[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

[tex]\sin(\thet2\theta)=2 \sin(\theta)\cos(\theta)[/tex]

[tex]\begin{aligned}\cos(\thet2\theta) & =1-2\sin^2(\theta)\\2\sin^2(\theta) & = 1-\cos(2\theta) \end{aligned}[/tex]

Solution

[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

[tex]\textsf{Multiply by}\:\dfrac{2\sin(\theta)}{2\sin(\theta)}:[/tex]

[tex]\begin{aligned}\implies \tan(\theta) & =\dfrac{\sin(\theta)}{\cos(\theta)} \times \dfrac{2\sin(\theta)}{2\sin(\theta)}\\\\ & =\dfrac{2\sin^2(\theta)}{2\sin(\theta)\cos(\theta)}\\\\ & = \dfrac{1-\cos(2\theta)}{\sin(2\theta)}\end{aligned}[/tex]

Therefore,

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

There are 288  outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

The outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.

The number of  outcomes is created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time is;

[tex]\rm Outcome=4\times 6\times 12\\\\Outcomes =288[/tex]

Hence, there are 288  outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.

Learn more about combination here;

https://brainly.com/question/12428942

#SPJ2

Step-by-step explanation:

It depends on your function. It also depends on if you want an overestimate, or underestimate. Riemann sums are used to approximate integrals by summing the area of 'n' amount of rectangles.

Using scientific notation, considering that Thailand has the larger population, the power of 10 that should be on the label is of 7.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

In this b is the power of 10 and the base a is in the following interval:

[tex]a \in [1, 10)[/tex].

In this problem, considering that both Thailand and Peru population's have exponent 7, and Panama's population is of [tex]4 \times 10^6 = 0.4 \times 10^7[/tex], the power of 10 that should be on the label is of 7.

More can be learned about scientific notation at https://brainly.com/question/26482653

#1

Not divide we multiply

#2

Yes

#3

Yes it's reverse of first one

Answer:

False

True

True

Step-by-step explanation:

[tex]\textsf{Product Rule}:\quad \log_n(x)+\log_n(y)=\log_n(xy)[/tex]

When condensing a logarithm using the product rule, you combine the answers by multiplying them.

[tex]\textsf{Power Rule}:\quad a \log_n(x)=\log_n(x)^a[/tex]

When condensing a logarithm using the power rule, you move the front number to become the exponent on the log.

[tex]\textsf{Quotient Rule}:\quad \log_n(x)+\log_n(y)=\log_n\left(\dfrac{x}{y}\right)[/tex]

When condensing a logarithm using the the quotient rule, you combine the answers by dividing them.

Using the combination formula, it is found that such a committee can be formed in 342,700,125,300 ways.

The order in which the people are selected is not important, hence, the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 11 people are taken from a set of 60, hence:

[tex]C_{60,11} = \frac{60!}{11!49!} = 342700125300[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&65\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&6\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+65t+6[/tex]

Check the picture below, the maximum occurs at the vertex of the parabolic path, so

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+65}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 65}{2(-16)}~~~~ ,~~~~ 6-\cfrac{ (65)^2}{4(-16)}\right)\implies \left(\cfrac{65}{32}~~,~~6+\cfrac{4225}{32} \right) \\\\\\ \left(\cfrac{65}{32}~~,~~\cfrac{4609}{32} \right) \implies \stackrel{maximum~height}{(2.03125~~,~~\stackrel{\downarrow }{72.015625})}[/tex]

Answer:

5.5 sq units

Step-by-step explanation:

Find the square around the red shape and subtract out the white parts.

Square = 4x4 = 16

Triangles subtracted -

1x1/2

1x1/2

3x4/2

3x1/2

Total subtracted = -8.5

Squares subtracted

1x1

1x1

Total subtracted = -2

16 - 10.5 = 5.5

Answer:

Option C

Step-by-step explanation:

[tex]\boxed{Log \ \dfrac{a}{b}=log \ a - log \ b}\\\\\boxed{(log \ a)^b=b*log \ a}[/tex]

[tex]\sf log_w \ \dfrac{(x^{2}-6)^4}{\sqrt[3]{x^2+8} }=log_w \ (x^2-6)^4 - log_w(x^2+8)^{\frac{1}{3}}[/tex]

                       [tex]\sf = 4*log_w \ (x^2 -6) - \dfrac{1}{3}log_w \ (x^2 + 8)[/tex]

Answer:

Ans of No.3

C 40÷(x+4)

Step-by-step explanation:

question 40÷(4+x)

ans nothing changed but x move to front of 4 and 4 move behind of x

Answer:

Area: 10.7521 cm

Circumference: 11.62389 cm

________________________________________________________

Area, A, will equal the formula of [tex]\pi r^2[/tex], so we must find the value and split that up. Diameter, d is equal to 2r. Let's solve.

[tex]A = \pi r^2[/tex]

[tex]d = 2r[/tex]

Now, make an equation combining like terms.

[tex]A = \frac{1}{4} \pi d^2[/tex]

This equation means to multiply those terms together. Since the diameter is 3.7, d is 3.7

[tex]\frac{1}{4} * \pi * 3.7 = 10.8(estimate)~cm[/tex]

Let's move on to circumference. On we go!

________________________________________________________

With circumference, it is very similar to what you just did to find area(A). You must again, set up these terms and make an equation out of them. C(circumference) is going to be equal to [tex]\pi r[/tex], notice how it does not say squared([tex]^2[/tex]) at the end now.

[tex]C = \pi r[/tex]

And diameter, you guessed it, will be 2r.

[tex]d = 2r[/tex]

Now, combine the like terms into an equation.

[tex]C = \pi d[/tex] pi times diameter(3.7)

[tex]\pi * d(3.7) = 11.6~cm[/tex]

Now that the problem is done, we move on to review.

________________________________________________________

We learned how to solve for circumference and area using diameter.

________________________________________________________

Feel free to ask in the comments.

Answer:

[tex]-13x-23[/tex]

Step-by-step explanation:

Given sequence:  [tex]x-9, -x-11, -3x-13[/tex]

Therefore,

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

(where a is the first term and d is the common difference)

To find the common difference, subtract a term from the next term:

[tex]\begin{aligned}d & =a_2-a_1\\ & =(-x-11)-(x-9)\\ & = -x-11-x+9\\ & = -2x-2\end{aligned}[/tex]

Therefore,

[tex]a_n & =(x-9)+(n-1)(-2x-2)[/tex]

To find the 6th term, input n = 6 into the equation:

[tex]\begin{aligned}\implies a_6 & =(x-9)+(6-1)(-2x-2)\\ & = (x-9)+7(-2x-2)\\ & = x-9-14x-14\\ & = -13x-23\end{aligned}[/tex]

[tex]3x {}^{2} + 15x = 18[/tex]

[tex]x {}^{2} + 5x = 6[/tex]

[tex]x {}^{2} + 5x - 6 = 0[/tex]

[tex]let \: \alpha \: and \: \beta \: be \: the \: roots[/tex]

Answer:

B 37.5%

Step-by-step explanation:

Answer:

They are all real numbers.

Option (2) and (5) I think is correct. x = -5 and x = 3

Step-by-step explanation:

Answer: Option (2) and (5) is correct. ... We have to find the solution of the given equation (x + 5)(x – 3) = 0 and choose the correct option from the given·

Answer:

option (C) 2

Step-by-step explanation:

because 2 is a prime number and also an even integer.

(NOTE: 0 and 1 are not prime numbers and also 0 is an even numbers while 1 is a prime number).

Hope this helps.

Good luck .

1 yellow heart = 4

5 yellow hearts = 20

1 pink triangle = 4

5 pink triangles = 20

hope it helps...!!!

Answer:

0

Step-by-step explanation:

because when you square a number, you multiply it by itself. So, you would do 0 x 0 = 0

Hope this helps!

- profparis

Answer:

0

Step-by-step explanation:

0^2 = 0*0

Zero times zero is still zero

Hope this helps!

Answer:

-1,572,864

Step-by-step explanation:

r = - 4

6  - 24  96  - 384  ......

6 * r^9 = a10 = -1572864

Answer:

3 sqrt 5     ( or  6.7082039    as posted in earlier A )

Step-by-step explanation:

sqrt ( 5) ( 5-2)   = 3sqrt 5

Answer:

The answer is given in the picture

Answer:

31.4 m

Step-by-step explanation:

The formula for the circumference of a circle is c=dπ, so we can substitute our diameter and 3.14 for pi.
c=(10)(3.14)

c=31.4

So the diameter is 31.4 meters.

Answer:

It's 13<26

Step-by-step explanation:

Using the interpretation of a confidence interval, it is found that the correct option is:

x% confidence interval:

Hence, the correct option is:

You can learn more about the interpretation of a confidence interval at

https://brainly.com/question/25822483

Answer:

This tree has one line of symmetry.

Answer:

43cm²

Step-by-step explanation:

let's first consider the area of a square.

the area is L² which means all sides are equal so we take the length times the breadth which is both equal because like we said all sides are equal.

so to find the side of the square using the area, we take the square root of both of the area.

[tex] \sqrt{25} = 5[/tex]

and also

[tex] \sqrt{18} = 4.2[/tex]

so we have the height of the triangle as 5cm and the base is 4.2cm.

now, from the triangle, since we have two sides and it's a right-angled, we can use Pythagoras' formula.

[tex] \sqrt{ {5}^{2} + {4.2}^{2} } = 6.53cm[/tex]

so the side 6.53cm is also the same side as the largest triangle. Since it's a square, all sides are equal. So we find the area of the largest triangle by using the formula

Area = L²

Area = 6.53²

Area = 42.6cm

the nearest cm square

Area = 43cm²

Check the picture below.

Answer:

1.8 seconds

Step-by-step explanation:

Answer: 1 5/12

Step-by-step explanation:

Divide 17 by 12

Answer:

1 and 5/12

Step-by-step explanation:

Step 1: Find the whole number

Step 2: Get the new numerator

Step 3: Our mixed fraction

Step 4: Simplifying our fraction