On James’s MP3 player, he has 12 sad songs and 40 upbeat songs that he wants to put into playlists. He wants to have the same number of sad songs and upbeat songs in each playlist. What is the maximum number of playlists that he can create?

Answer:

[tex]cos\theta = -\frac{12}{37}[/tex]

Step-by-step explanation:

Given

[tex]tan\theta = \frac{35}{12}[/tex]

Quadrant: 3rd

Required

Determine [tex]cos\theta[/tex]

This question will be solved using the Pythagoras theorem

[tex]Hyp^2 = Adj^2 + Opp^2[/tex]

The tangent of an angle is calculated as thus;

[tex]tan\theta = \frac{Opp}{Adj}[/tex]

Comparing

[tex]tan\theta = \frac{35}{12}[/tex] to [tex]tan\theta = \frac{Opp}{Adj}[/tex]

We can conclude that

[tex]Opp = 35[/tex]    [tex]Adj = 12[/tex]

Substitute these values in the Pythagoras formula

[tex]Hyp^2 = 35^2 + 12^2[/tex]

[tex]Hyp^2 = 1225 + 144[/tex]

[tex]Hyp^2 = 1369[/tex]

Square root of both sides

[tex]Hyp = \sqrt{1369}[/tex]

[tex]Hyp = 37[/tex]

SInce [tex]\theta[/tex] is in the 3rd quadrant, then

[tex]cos\theta = -\frac{Adj}{Hyp}[/tex]

Where [tex]Adj = 12[/tex] and [tex]Hyp = 37[/tex]

[tex]cos\theta = -\frac{12}{37}[/tex]

Answer:

8400/2 then simplify

Step-by-step explanation:

Answer:

y = 5x - 800

Step-by-step explanation:

If x represents the number of pages typed, 5x will represent how much money he earns from typing them, since he gets $5 per page.

Then, 800 needs to be subtracted from this because he spent $800 on the computer.

So, the equation will be y = 5x - 800 to represent his profit.

Answer:

y. 100

------ = -------

600. 120

120y= 60000

y = 60000÷ 120

= $500

Step-by-step explanation:

a =

a = 3

3,6 = and c =

olů

what is this please write this clearly

Answer:

D.

Step-by-step explanation:

The domain remains the same [a, b) and the range  is [mc + n,md + n).

Answer:

C

Step-by-step explanation:

The solution is Option C

The common ratio of the geometric sequence is -1/3

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric sequence be represented by A

Now , the value of A is

A = 18 , -6 , 2 , -2/3

Let the first term of the geometric sequence be = a₁

The value of a₁ = 18

Let the second term of the geometric sequence be = a₂

The value of a₂ = -6

And , the common ratio r is given by the formula

Common ratio r = second term / first term

Substituting the values in the equation , we get

Common ratio r = -6/18

On simplifying the equation , we get

Common ratio r = -1/3

Therefore , the ratio is -1/3

Hence , The common ratio of the geometric sequence is -1/3

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Answer:

Step-by-step explanation:

The sum of all exterior angles of any regular polygon is 360°.

= [tex]\frac{360}{57} \\\\= 120/19\\or\:6.315[/tex]

The number of sides should be a natural number not in fraction or decimal

Step-by-step explanation:

Hey, there!!

The given points are A(5,1) and B(-3,-5)

We have, distance formulae for AB is,

[tex]ab = \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

[tex]ab = \sqrt{( { - 3 - 5)}^{2} + ( { - 5 - 1)}^{2} } [/tex]

[tex]ab = \sqrt{( { - 8)}^{2} + ( { - 6)}^{2} } [/tex]

[tex]ab = \sqrt{64 + 36} [/tex]

[tex]ab = \sqrt{100} [/tex]

Therefore, the distance between AB points is 10 units.

Hope it helps...

Answer:

For Example say a number is in scientific form, 4.10x10^5, to write this in standard form you can either do 10^5=100,000x4.10=410,000, or you could simply take 4.10 and move the decimal place 5 places to the right, and you would get the same answer, 410,000.

Step-by-step explanation:

Answer:

-45

Step-by-step explanation:

The question is asking for the sum of the sequence. Therefore, there is no such thing as a "radians" answer.

When you evaluate the sum, you should get -45 as your answer. To find so, you simply plug in 1 as n and other numbers then add the result.

The sum telescopes. Consider the N-th partial sum of the series,

[tex]S_N=\displaystyle\sum_{n=1}^N\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)[/tex]

[tex]S_N=\bigg(\tan^{-1}\sqrt1-\tan^{-1}\sqrt2\bigg)+\bigg(\tan^{-1}\sqrt2-\tan^{-1}\sqrt3\bigg)+\bigg(\tan^{-1}\sqrt3-\tan^{-1}\sqrt4\bigg)+\cdots+\bigg(\tan^{-1}\sqrt N-\tan^{-1}\sqrt{N+1}\bigg)[/tex]

Notice how [tex]\tan^{-1}\sqrt2[/tex] is added, then immediately subtracted. The same goes for [tex]\tan^{-1}\sqrt3[/tex], then [tex]\tan^{-1}\sqrt4[/tex], and so on, up to [tex]\tan^{-1}\sqrt N[/tex]. This leaves us with

[tex]S_N=\tan^{-1}\sqrt1-\tan^{-1}\sqrt{N+1}[/tex]

The value of the given sum is obtained as [tex]N\to\infty[/tex]. We get

[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\lim_{N\to\infty}S_N=\tan^{-1}1-\lim_{N\to\infty}\tan^{-1}\sqrt{N+1}[/tex]

To compute the limit, recall that [tex]\tan^{-1}x[/tex] has a range of [tex]\left(-\frac\pi2,\frac\pi2\right)[/tex]; in particular, [tex]\tan^{-1}x\to\frac\pi2[/tex] as [tex]x\to\infty[/tex]. So we have

[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\frac\pi4-\frac\pi2=\boxed{-\frac\pi4}[/tex]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.

(a) What are the individuals in this data set?

(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative?

Solution:

(a)

The term "individuals", in statistics, implies or denotes the objects or people included in a statistical study.

In this case it is provided that Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior.

So, the "individuals" in this data set are the monkeys.

(b)

Categorical variables belong to a certain category or label values. Such as gender of a person, state from which a person is from, color of the marble and so on.

Quantitative variables are those variables that assume numerical values and represent some sort of measurement. Such as height, weight, annual income of the people working at the same place and so on.

In this case the variables are:

Number of bananas the monkeys ate - Quantitative variable

Gender - Categorical variable

Age (in years) -  Quantitative variable

Specific breed of monkey - Categorical variable

The individuals in the data set refers to each monkey used in the experiment.

The variables in the experiment include :

Individuals used in a research refers to each species or subject used in the research finding.

DISCRETE variables involves variables whose values or numbers can be obtained by counting.while

CONTINUOUS variables include variable measure are obtained by measurement such as height and weight.

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Complete question :

Mr. Molesky observes a group of monkeys for 24 hours to learn about

their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.

(a) What are the individuals in this data set?

(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative(continuous), or quantitative(discrete), make sure tell me which one is continuous and which one is discrete

Answer:

45t = distance

Step-by-step explanation:

Distance = speed * time

Distance= 45 mph * t hours = 45t

Answer:

7560.

Step-by-step explanation:

There are 9 letters after the M consisting of  3 O's, 2 H's, 2 H's and 2 E's.

So the number of ways is   9! / (3!*2!*2!*2!)

= 362880 / (6*2*2*2)

= 362880 / 48

= 7560.

The number of ways the word MOSHOESHOE can be rearranged, if the letter M must always begin a word is 75,600 ways

Given:

MOSHOESHOE

n = total number of letters = 10

a = number of times O appears = 3

b = number of times S appears = 2

c = number of times E appears = 2

d = number of times H appears = 2

number of ways the word can be rearranged if M must always begin a word

= n! / (a! b! c! d!)

= 10! / (3!, 2!, 2!, 2!)

= (10 × 9 × 8 × 7 × 6 × 5 × 4× 3 × 2 × 1) / (3 × 2 × 1, 2 × 1, 2 × 1, 2 × 1)

= 3,628,800 / (6 × 2 × 2 × 2)

= 3,628,800 / 48

= 75,600 ways

Therefore, the number of ways the word can be rearranged if M must always begin a word is 75,600 ways

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Answer: sqrt(85)/2

Step-by-step explanation:

Remember that the length of the diameter is twice that of the radius.

The first step would be finding the distance between the two points using the distance formula[tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}[/tex].

The distance of diameter = [tex]\sqrt{85}[/tex]

The distance of the radius would be half that, so [tex]\frac{\sqrt{85}}{2}[/tex]

Answer:

1

Step-by-step explanation:

The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] so when you plug in all of the numbers to where they are supposed to be you would get [tex]\frac{1-3}{1-3}[/tex] which is [tex]\frac{-2}{-2}[/tex] which can be simplified to [tex]\frac{1}{1}[/tex] which is just 1 and that would be our answer

Answer:

5,170

Step-by-step explanation:use rounding number calculater for extra help

Answer:

u=(9-6w)÷-2

Step-by-step explanation:

Answer:

u = 3w - 4.5

Step-by-step explanation:

Step 1: -2u + 6w = 9 - Solve for u by isolating the variable u.

Step 2: Subtract 6w both sides

-2u = 9 - 6w

Step 3: Divide by -2 both sides

u = ( 9 - 6w ) / ( -2 )

u = 3w - 4.5

Have a good day!! :)

Step-by-step explanation:

I guess you mean 1cm:100000cm

Hence, for every 1 cm on the map 100000 cm is covered on the land.

Take the distance on the map for 20 km be x

Hence, 1:100000:: x: 2000000 cm

In order to solve this ratio, you must multiply the extremes and the moderates (nears).

Hence, 2000000×1=100000×x [1km=100000 cm]

Hence, 2000000= 100000x

Hence, x=2000000/100000 cm

Hence, x=20 cm

Hence, 20 cm on the map

Answer:

40.8696% increase (40.9%)

Answer:

{-5, -4, 0, 1, 2}

Step-by-step explanation:

The domain is the inputs or the x values

{-5, -4, 0, 1, 2}

Answer:

See below.

Step-by-step explanation:

The domain of a relation is all of the x-coordinates.

So we have the relation:

{(-5,4), (-4,2), (0,2), (1,3), (2,4)}

This means that the domain will be the following values:

{(-5,4), (-4,2), (0,2), (1,3), (2,4)}

So, our domain is:

[tex]\{-5, -4, 0, 1, 2\}[/tex]

Note that the domain is in ascending order.

Answer:

Answer is A the highest number we can get is 12 so its potion A

The both highest numbers are 6 and, 6 6 +6 is 12 so its 0

Answer:

Jeremy has 12 ways of painting his room.

He has 4 different wall colors and 3 different trim colors, so, if we want to know how many ways does he have to paint his room, we only need to multiply:

4 * 3 = 12

That's why he has 12 ways of painting his room. That's because for each of the 4 different wall colors, there are 3 trim colors he can use.

Answer: 12 different ways

Step-by-step explanation:

The question is asking for a combination of a wall color and a trim color because his room required one wall color and one trim color.

In this case, combination will be the number of first kind multiplies with the second kind. This is similar to sketching a tree diagram but instead, we will be using numerical method which will be quicker.

If you are still confused, I will provide some examples.

This also applies to your question. You have 4 different wall colors and 3 different trim colors.

4×3=12

You have 12 different ways to paint the room

Hope this helps!! :)

Please let me know if you have any question

Answer:

12.3

Step-by-step explanation:

Round it where you have 3 numbers that are not 0.

12.3456

round to the hundredths place

12.34 (round to 4)

12.3 (3 sigfigs)

Answer:

12.4

Step-by-step explanation:

12.3456

first you would round the 5 to a 6, the round the 4 to a 5, because the six is greater than five, than you would change the 3 to a 4, because the four that was changed to a five now is big enough to change the number.

The required g(5) is -9.

Function g(x) = -x-4. g(5) to determine.

The function is a type of mathematical sting that contains an algebraic link.

Here. g(x) = -x-4
     Put 5 in place of x.
         g(5) = -5-4
         g(5) = -9  

Thus, g(5) is -9

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Answer:

#1 true

#2 false

false

Step-by-step explanation:

Answer:

x=52

I think it is the answer

Answer:

The correct answer is rational.

Step-by-step explanation:

The diameter of the tree belongs to the subset of rational numbers.

Natural numbers are the numbers 1, 2, 3 4, etc. Since 18.5 has a fractional/decimal component, it is not considered a natural number.  Whole numbers include all of the natural numbers, as well as 0; therefore, 18.5 is not a whole number either.

Integers include all whole numbers as well as negative numbers, but the integer category still does not encompass numbers with a decimal component.  For this reason, 18.5 is not an integer either.

Therefore, the only subset of numbers that 18.5 can fall under is rational numbers.  A rational number is a number that can be represented as a fraction.  18.5 can be represented as 37/2 and is thus a rational number.

You can also refer to the infographic given in the question for further clarity on which subsets of numbers are more inclusive than others.

Hope this helps!

Answer:

Supongo que en realidad dice

"... Para llegar de la planta baja hasta el piso 9..."

Ok, el elevador comienza en el piso 0, y llega hasta el piso 9 después de 5 movimientos.

De estos 5 movimientos, 3 suben (los podemos definir como positivos)

y 2 bajan (los escribimos como negativos).

Entonces, comienzo en 0.

0 + A + B + C - D - E = 9.

ahí dice que:

"desde el piso 0, tengo 3 subidas y dos bajadas de tal forma que el resultado final es el piso 9"

Una expresión algebraica matemática consta de variables y constantes junto con operaciones algebraicas. Al resolver problemas de palabras algebraicas, es necesario que los problemas se traduzcan con precisión en ecuaciones y se resuelvan correctamente.

Dado que:

Para configurar una operación que indique el número de pisos que recorrió el ascensor con cada movimiento;

Vamos a considerar

∴

Así, la puesta a punto de la operación que indica el número de pisos que recorrió el ascensor con cada movimiento se puede deducir de la diferencia entre el movimiento de subida y bajada será igual a 9.

Por lo tanto, podemos concluir que la configuración de la operación es:

3a - 2b = 9

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Answer:

83 cm

Step-by-step explanation:

let's make an equation for this situation. The plant starts at 8 cm and grows 3 cm every week. If x represents time in weeks and y represents height in cm, then:

y = 8+3x

filling in 25 for x, we find that:

y = 8+75

y = 83 cm

Answer:83

Step-by-step explanation:

25 x 3 = 75

75 + 8 = 83