Assuming a population of alpacas has been doubling every 5 years, and the current population is 2,000, what was the population 20 years ago? 8000 0 4000 O 1000 O 750 O 500 O 250 O 200 O 125

Answer:

What is meant by "Explain your answer?"

   On tests & problem sets students are often asked to explain the reasoning behind their answers. They are often frustrated and/or confused by “explain.” What & why are they supposed to explain? Here is one answer:

   It isn't enough to get the right answer -- you have to be able to explain how you got it. To be sure you get enough practice at explaining yourself, it pays to discuss the questions with your fellow students and/or to write out explanations of your reasoning. You need to both

           (1) Include the right facts, principles, etc., AND

           (2) Explain the logic that you used to solve the problem. How did you get from the facts to the answer?

   It is not sufficient to pile up unselected facts (even if they are correct), OR just to state the facts (even if they are the right ones), without explaining how they relate to the problem at hand, OR to just explain the logical train of thought (even if it is correct), without any specifics.

   That's what you shouldn't do. What should you aim for??

   Try to explain as if you were talking to a fellow student in the class who is generally intelligent, prepared, etc., but can't figure out this particular question.  In other words, explain your reasoning step by step.  Don't just repeat all the related facts in the book or notes--try to pick out the important, relevant points, put them in logical order, and explain (or diagram) how one leads to the next. (In other words, pretend you are writing a simple* answer key.)

*Note: The keys provided after each exam or problem set are usually quite complex and go beyond what we expect from an individual student. The posted keys tend to be so long and involved because they include not only correct answers (& explanations) but also explanations of common student misconceptions.

How to Get the Most out of Explaining

   When you explain things to yourself, or to others, try not to use pronouns. Use nouns instead. This may sound silly, but it really helps you to be sure that you understand what you are saying. If you use pronouns or vague terms you can fool yourself into thinking you understand when you really don't. An example: Suppose you say "The gene is transcribed and it goes to the cytoplasm and is translated, which uses tRNA and mRNA." What do you mean by it and/or which?  Is it the gene or the mRNA? Does which refer to translation or transcription? Sometimes you know, and you are just using shorthand. But sometimes you don't know, and you don't even realize it until you are forced to pick the right terms to replace "it" and "which."  So try to be as specific as possible instead of as vague and as general as possible. Being specific has multiple advantages. It helps you to learn, it helps listeners understand what you are saying, and it helps graders on exams know that you really understand what you are talking about.

If the measure of the sides of the square is 12 inches , then the maximum possible error for the square's area is 146.8944  .

In the question ,

it is given that ,

the measure of the length of the side of the square is = 12 inches ,

the possible error is = 1% ,

the error length of the side = 0.12 ,

the length of the side = 12.12 inches .

the area of the square ⇒ 12.12 × 12.12

= 146.8944   .

Therefore , the maximum possible error in the square's area is = 146.8944 .

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The square root of 89 is an irrational number with never-ending digits

Solution :

Real numbers :

Real numbers are the sets of rational numbers and irrational numbers taken together

Irrational numbers:

Irrational numbers are the set of all numbers that are not rational; they cannot be written as either a terminating or repeating decimal; they cannot be expressed as a fraction of two integers.

or,

The set of irrational numbers is the set of numbers that are not rational, are non repeating, and are non terminating. Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

1)65.555

Statement:65.555....is rational and a repeating decimal

2)-57

Statement: It is a negative integer.

3)\(\sqrt{89}\)

Statement:

Due to the nature of its non-repeating and non-terminating decimal expansion, the square root of 89 cannot be written in the form of p/q, hence, it is an irrational number.

The value of the square root of 89 in decimal form is 9.433981.. so on, The square root of a number can have two values, a positive and a negative value. So, √89=+9.433981. Hence, The square root of 89 is an irrational number with never-ending digits.

Step 1: Divide the number 89 by 9, (because 92 =81 is a perfect square number just less than 89).

Step 2: The divisor and the quotient need to be the same numbers; in this case, it is 9. Multiply the quotient and the divisor and subtract the result from 89.

Step 3: For the next divisor, add the previous divisor with the quotient. (9 + 9 = 18); place it as the new divisor with a blank on its right.

Step 4: Put a decimal after the quotient '9' and bring down two zeros to place it after 8 so that it becomes 800. (184 × 4 = 736). Subtract 736 from 800.(800 − 736 = 64)

Step 5: Bring down another pair of zeros and place it after 64, so that it becomes 6400. Take the new quotient 4 and add it to 184. (184 + 4 = 188)

Step 6: Repeating the above steps, we need to fill the blank with a number such that when the new divisor is multiplied by the new quotient, the product is less than or equal to the dividend 6400. (1883 × 3 = 5649)

Step 7: Write the same number after 4 in the quotient. Subtract 5649 from 6400. (6400 − 5649  = 751)

Step 8: Repeat the process until we get the remainder equal to zero. The square root of 89 up to two places is obtained as 9.43 by the long division method.

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i dont know ethrreer

Step-by-step explanation:

Answer:

Step-by-step explanation:The distributive property dictates that:

a(b + c) = ab + ac

Thus,

(0.7 x 0.7) + (0.7 x 0.9) + (0.7 x 0.2)

= 0.7(0.7 + 0.9 + 0.2)

follows the distributive property. The third option is correct.

Hey there! I'm happy to help!

When multiplying numbers with exponents, all you do is add the exponent numbers, so 5^12×5^8=5^20.

A is not equal to this.

B is also not equal to this. B is 25^20.

C is  wrong as well. It is 5^5.

This leaves us with D, which does evaluate to 5^20. If you raise a power to a power you multiply the exponent numbers, and 5(4)=20.

The answer is D. (5^5)^4.

Have a wonderful day! :D

5^12 * 5^8

5^12+8

5^20

The only option that is equal to that is D.

(5^5)^4

5^5*4

5^20

Best of Luck!

Answer:

K = infinite amount of solutions

Step-by-step explanation:

Step 1: Write out equation

4K - 32 = -32 + 4K

Step 2: Rearrange

4K - 32 = 4K - 32

Here we see that any value of x can be plugged in and would render the equation true. You can also look at it as 2 exact same lines, and when 2 lines are the same, they have infinite amount of solutions.

So K could equal -2, -4, 5, 7, 2935, or even 91235780271.

Hey there! I'm happy to help!

We want to figure out what K is equal to. Let's put all of the Ks on one side of the equation and the constants on the other side.

We subtract 4K from both sides.

4K-4K-32=-32

We combine like terms.

-32=-32

Add 32 to both sides.

0=0

Whenever you are solving an equation and end with a true equation like 0=0, it means that there are infinitely many solutions. This means you could use any number for K and the equation would work. Notice what the original equation is. 4K-32=-32+4K. It is literally the same thing on both sides, so any value for K would work.

Have a wonderful day! :D

Answer:

A = 34

B = 29.4

C = 58.8

D = 34

Answer:

option b is the correct answer

Answer:X=8

Step-by-step explanation:

Answer:

id say company a is a proportional relationship

Step-by-step explanation:

company a has a flat fee to start out with so no matter wat your paying $50 so yeah i think its company A hope this helps

Answer:

18

Step-by-step explanation:

Let x be the smaller number. The larger number would be...

x+7 as the question states their difference is 7.

We can use this to set up an equation:

x+x+7=43

Combine like terms

2x+7=43

Subtract 7 from both sides

2x=36

Divide both sides by 2

x=18

The smaller number is 18

The sum of all possible values of x is 19.4

The term median is referred by putting the numbers in increasing order and then taking the middle number if n is odd. where as If n is even then the median is the sum of two middle numbers divided by 2.

Here we have given that the median of 20, x, 15, 30, 25 is 0.4 less than the mean and we need to find the value of x.

As per the given question we know that x is the whole number

And the given sequence is written as,

=> 20, x , 15, 30, 25

Here we also know that the median is less that the mean by 0.4.

In order to find the median, we have to arrange the given data,

=> 15, x, 20, 25, 30.

Then the value of x is calculated as,

=> 20 - 0.4

=> 19.4

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Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

Answer:

The formula to find the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.

Given that the radius of the cylinder is 2 inches and the height is 4 inches, we can substitute these values into the formula to find the volume:

V = πr²h

V = 3.14 x 2² x 4

V = 3.14 x 4 x 4

V = 50.24

Rounding this value to the nearest whole number, the volume of the cylinder is 50 in³.

The limit comparison test is used to determine if a series converges or diverges. If the series is positive and the limit of a_n divided by b_n equals L, then the series of b_n converges or diverges if and only if the series of a_n converges or diverges. The series converges, as the limit of the ratio is finite and positive.

To determine whether the series below converges or diverges,\(\[ \sum_{n=3}^{\infty} \frac{1}{n \sqrt{n^{2}-2}} \]\) let's use the limit comparison test. The series will converge if the limit comparison test passes, and it will diverge if it fails. Now we are going to learn about limit comparison test:If the series is positive and a_n, b_n are positive and the limit of a_n divided by b_n equals L (where L is a finite positive number), then the series of b_n converges or diverges if and only if the series of a_n converges or diverges.    

Thus, we're going to compare it to the series 1/n since that series converges (p-series with p=1)

.\($$\lim_{n \to \infty}\frac{\frac{1}{n\sqrt{n^2-2}}}{\frac{1}{n}}=\lim_{n \to \infty}\frac{1}{\sqrt{n^2-2}}=1$$\)

By the limit comparison test, the series converges, since the limit of the ratio is finite and positive. Hence, the answer is that the series converges.

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 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

Step-by-step explanation:

it's simple:

The face value of the discount note, to the nearest cent is calculated as: $11,617.74.

To find the face value of the discount note, we can use the formula:

Face Value = Proceeds / (1 - Discount Rate x Time)

Where the time is in years, so we need to convert 75 days to years by dividing by 365:

Time = 75 / 365 = 0.2055 years

Substituting the given values, we get:

Face Value = 11,450 / (1 - 0.0675 x 0.2055)

Face Value = 11,450 / 0.9861

Face Value = $11,617.74 (rounded to the nearest cent)

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The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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We can use the general form of a quadratic model:

We can find the parameters a, b and c by taking some pair of values from the table, like this:

Let's take the pair (0,0), if we replace these values for y and x into the above model we get:

Now let's take the pair (1, 2.4), by replacing these values into the above model for x and y, we get:

From this equation, we can solve for a to get:

By taking the pair (2, 9.4) we get:

We can replace the expression that we got previously a = 2.4 - b into the above equation to get:

From this expression, we can solve for b like this:

Now we can replace it into the equation a = 2.4 - b, then we get:

a = 2.4 - 0.1 = 2.3

Then we get the expression:

Now we just have to evaluate 10 km into the equation, then we get:

Then, the best prediction of the time required for the oil spill to reach a diameter of 10 km is 233 days

So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.

The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:

4(3x + 5y) = 4(17)

12x + 20y = 68

-3(4x + 4y) = -3(-13)

-12x - 12y = 39

then we can add these two equations:

12x + 20y = 68

-12x - 12y = 39

0 = 29

This is an impossible equation, which means that the system has no solution.

Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

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Teniendo en cuenta la regla de tres simple, el cartero reparte 64.200 cartas en un semestre.

La regla de tres es una forma de resolver problemas de proporcionalidad entre tres valores conocidos y un valor desconocido, estableciendo una relación de proporcionalidad entre todos ellos.

Es decir, lo que se pretende con ella es encontrar el cuarto término de una proporción conociendo los otros tres.

Si la relación entre las magnitudes es directa, es decir, cuando una magnitud aumenta, la otra también (o cuando una magnitud disminuye, la otra también), se debe aplicar la regla de tres directa.

Para resolver una regla de tres directa se debe seguir la siguiente fórmula, siendo a, b y c datos conocidos y x la variable a calcular:

a ⇒ b

c ⇒ x

Entonces: \(x=\frac{cxb}{a}\)

En este caso, se puede aplicar la regla de tres de la siguiente manera: Entonces, si el cartero en un mes reparte 10.700 cartas, ¿en 6 meses (un semestre) reparte cuántas cartas?

1 mes ⇒ 10.700 cartas

6 meses ⇒ ×

Entonces: \(cantidad de cartas=\frac{6 mesesx10.700 cartas}{1 mes}\)

Resolviendo:

cantidad de cartas= 64.200 cartas

En resumen, el cartero reparte 64.200 cartas en un semestre.

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Answer:

k

Step-by-step explanation:

The coordinate vector of p(t) = -5 - 7t - 8t^2 relative to the basis B = {1 + t^2, -2t - t^2, 1 + t + t^2} is [3, -7, -6].

To find the coordinate vector of p(t) relative to the basis B, we need to express p(t) as a linear combination of the basis vectors and find the coefficients.

We start by writing p(t) as a linear combination of the basis vectors:

p(t) = c1(1 + t^2) + c2(-2t - t^2) + c3(1 + t + t^2)

Expanding and collecting like terms, we have:

p(t) = (c1 - c2 + c3) + (c1 - 2c2 + c3)t + (c1 - c2 + c3)t^2

Comparing the coefficients of the polynomial terms on both sides, we get the following system of equations:

c1 - c2 + c3 = -5

c1 - 2c2 + c3 = -7

c1 - c2 + c3 = -8

Simplifying the system, we can see that the third equation is redundant as it is the same as the first equation. Thus, we have:

c1 - c2 + c3 = -5

c1 - 2c2 + c3 = -7

Solving this system of equations, we find that c1 = 3, c2 = -7, and c3 = -6.

Therefore, the coordinate vector of p(t) relative to the basis B is [3, -7, -6].

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The Equation of line is  y = 8x - 25

Equation of line: The general equation of a straight line is y = mx + b, where m is the gradient, and y = b is the  value where the line cuts the y - axis. This number b is called the intercept on the y - axis.

Equation of a line in slope - intercept form:

y = mx + b with m as the slope and b as the y - intercept.

To find the slope using two points (\(x_{1},y_{1}\)) and (\(x_{2},y_{2}\)):

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\) \(=\frac{7-(-1)}{4-3}\)

=8/1 = 8

Then, The equation will be y = 8x + b

and, to find b, plug in one of points:

7 = 8 × 4 + b

7 = 32 + b

b = - 25

y = 8x - 25

Hence, The Equation of line is  y = 8x - 25

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

no

no

yes

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

Use the distributive property to multiply  \(\frac{1}{2}\) by x - 6

-

Multiply \(\frac{1}{2} and -6\)

= \(\frac{-6}{2}\)

-

Divide −6 by 2 to get −3.

-

Add −3 and 12 to get 9.

-

Subtract \(\frac{3}{2} x\) from both sides

-

Combine \(\frac{1}{2} x\) and \(-\frac{3}{2} x\) to get -x

-x + 9 = -4

Subtract 9 from both sides.

-x = -4 - 9

Subtract 9 from −4 to get −13.

-x = -13

Multiply both sides by −1.

x=13

Answer:

X=13

Step-by-step explanation:

my explanation is above hope this helps.

Answer:

Step-by-step explanation:

3 = 307k

Answer:

Real, Rational

Step-by-step explanation:

The Set of integers includes zero, positive and negative numbers (not fractions)

Whole numbers include only zero and positive numbers.

Irrational numbers can't be expressed as a fraction; in fact, it's an infinite decimal.

So 0/3 is real and rational. Hope it helps!