A team of 22 soccer players needs to choose 3 players to fill water bottles. How many different groups can be made?

the discrete compounding formula is f = p * (1 + r) ^ n

f is the future value

p is the present value

r is the interest rate per time period

n is then number of time periods

in your problem, you are given:

f = what you want to find

p = 5000

r = 30% per year / 100 = .3 per year (percent / 100 = rate).

n = 3 years

if you compound annually, the formula becomes:

f = 5000 * (1 + .3) ^ 3 = 10985

if you compound quarterly, the formula becomes:

f = 5000 * (1 + .3 / 4) ^ (3 * 4) = 11908.898

if you compound monthly, the formula becomes:

f = 5000 * (1 + .3 / 12) ^ (3 * 12) = 12162.67658

if you compound continuously, a different formula is used.

that formula is f = p * e ^ (r * n)

f is the future value

p is the present value

e is the scientific constant of 2.718281828.......

r is the interest rate per time period

n is the number of time periods.

with this formula, you leave the time periods in terms of years.

it will make no difference what time periods and compounding periods you use, the answer will be the same.

most of the time you will just give it the interest rate per year and the number of years.

the reason is as follows:

r * n = .3 * 3 = .9 when giving it rate and time in terms of years.

r * n = .3 / 4 * 3 * 4 = .9 when giving it rate and time in terms of quarters.

r * n = .3 / 12 * 3 * 12 = .9 when giving it rate and time in terms of months.

in your problem, the formula becomes f = 5000 * e ^ (.3 * 3) = 12298.01556.

the more compounding periods per year, the higher the future value.

the highest is when you compound continuously.

this is apparent from the data.

Answer:

Step-by-step explanation:

I assume that you mean 4⅛ batches, not 41/8 batches.

4⅛ batches × (¾ stick)/batch = 33/8 batches × (¾ stick)/batch

= 99/32 sticks

= 3 and 3/32 sticks

Answer:

102 km/hr

90 km/hr

Step-by-step explanation:

Given that :

Total distance = 576

Time taken = 3 hours

Bus A :

Speed = x

Bus B :

Speed = x - 12

Recall :

Distance = speed * time

Hence,

Distance covered by A + Distance covered by B = total distance covered

(x * 3) + ((x - 12) * 3) = 576

3x + 3x - 36 = 576

6x = 576 + 36

6x = 612

x = 612 / 6

x = 102

Speed of faster bus, x = 102 km/h

Speed of slower bus, x - 12 = (102 - 12) = 90 km/hr

Answer: m = 1/2

Step-by-step explanation: To find the slope of the line, we would first put the equation in y = mx + b form to get y by itself on the left side.

So divide both sides by 2 to get y = 1/2x - 4.

Now the slope is the coefficient of the x term which is 1/2.

This is a positive slope.

We know the formula

[tex]\boxed{\displaystyle\int x^ndx=\dfrac{x^{n+1}}{n+1}+c}[/tex]

[tex]\\ \displaystyle\longmapsto \int (1+3x+2y)dx[/tex]

[tex]\\ \displaystyle\longmapsto \dfrac{3x^{1+1}}{1+1}+\dfrac{2y^{1+1}}{1+1}+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{3x^2}{2}+\dfrac{2y^2}{2}+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{3x^2}{2}+y^2+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{3x^2+2y^2+2}{2}[/tex]

Answer:

[tex]\\\int _{\:}^{\:}\int _{\:}^{\:}\:1+3x+2y\:dxdy=Cy+\frac{3x^2}{2}y+xy+xy^2+C[/tex]

Step-by-step explanation:

[tex]\\\int _{\:}^{\:}\int _{\:}^{\:}\:1+3x+2y\:dxdy[/tex]

[tex]\int _{\:}^{\:}\left(1+3x+2y\right)\:dx\:=x+2yx\:+\frac{3x^2}{2}+C[/tex]

[tex]=\int \left(x+2yx+\frac{3x^2}{2}+C\right)dy[/tex]

[tex]=Cy+\frac{3x^2}{2}y+xy+xy^2+C[/tex]

Answer:

below

Step-by-step explanation:

the is the procedure above

Answer:

[tex]\boxed {\boxed {\sf (B. \ -4, 3)}}[/tex]

Step-by-step explanation:

We are given 2 equations and asked to solve the system of equations using the substitution method.

The 2 equations are:

[tex]y= -5x-17 \\-3x-3y= 3[/tex]

The first equation is already solved for y, so we can substitute -5x-17 (the expression that y is equal to) into the second equation.

[tex]-3x-3(-5x-17)=3[/tex]

Solve for x by isolating the variable. First, distribute the -3. Multiply each term in parentheses by -3.

[tex]-3x + [ (-3*-5x ) \ + \ (-3* -17)][/tex]

[tex]-3x + [15x + 51]= 3[/tex]

[tex]-3x+15x+51=3[/tex]

Combine like terms. -3x and 15x can be added because both terms contain the variable x.

[tex]12x+51=3[/tex]

51 is being added to 12x. The inverse operation of addition is subtraction. Subtract 51 from both sides of the equation.

[tex]12x+51-51=3-51[/tex]

[tex]12x= -48[/tex]

x is being multiplied by 12. The inverse operation of multiplication is division. Divide both sides by 12.

[tex]\frac {12x}{12}= \frac{-48}{12}[/tex]

[tex]x= -4[/tex]

Now that we have solved for x, we must find y. We know that x is equal to -4, so we can substitute -4 in for x in the first equation.

[tex]y= -5x-17[/tex]

[tex]y= -5(-4)-17[/tex]

Multiply.

[tex]y=20-17[/tex]

Subtract.

[tex]y=3[/tex]

Coordinate points are written as (x, y), so the solution to this system of equations is (-4, 3)

Answer:

An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.

Answer:

first option f(x) -> negative infinity

Step-by-step explanation:

the other answer is sadly wrong.

there is a "-" in front of the expression.

-2x³ had two parts

-2, which is multiplied to x³

now x³ goes to (positive) infinity for x going to (positive) infinity.

but because this is multiplied by a negative value (-2), all the functional values for positive x are negative.

therefore, the function goes to negative infinity for x going to (positive) infinity.

The end behavior of f(x) as x goes to infinity is (a) f(x) → negative infinity

The function is given as:

f(x) = -2x^3

Next, we plot the graph of the function (see attachment)

From the graph, we can see that as the x values increase to infinity, the function values approaches negative infinity

Hence, the end behavior of f(x) as x goes to infinity is (a) f(x) → negative infinity

Read more about end behavior at:

https://brainly.com/question/11275875

9514 1404 393

Answer:

  8x -24 = 9y

Step-by-step explanation:

We assume your equation is ...

  2/3x -2 = 3/4y

__

Fractions can be eliminated by multiplying the equation by the least common denominator of the fractions.

  LCM(3, 4) = 12

Multiplying the equation by 12 gives you ...

  12(2/3x -2) = 12(3/4y)

  8x -24 = 9y

Answer:

1364

Step-by-step explanation:

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364

a1+a2 = a3, a2+a3=a4 etcetera..

1+3 =4

3+4 =7

4+7=11

.

.

a13+a14 = a15

521+843 = 1364

so, 1364 is the answer

Answer:

[tex]P(t) = 100e^{0.0251t}[/tex]

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

[tex]P(t) = P(0)e^{kt}[/tex]

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that [tex]P(0) = 100[/tex]. So

[tex]P(t) = 100e^{kt}[/tex]

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that [tex]P(60) = 450[/tex], and we use this to find k. So

[tex]450 = 100e^{60k}[/tex]

[tex]e^{60k} = 4.5[/tex]

[tex]\ln{e^{60k}} = \ln{4.5}[/tex]

[tex]60k = \ln{4.5}[/tex]

[tex]k = \frac{\ln{4.5}}{60}[/tex]

[tex]k = 0.0251[/tex]

So

[tex]P(t) = 100e^{0.0251t}[/tex]

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

[tex]200 = 100e^{0.0251t}[/tex]

[tex]e^{0.0251t} = 2[/tex]

[tex]\ln{e^{0.0251t}} = \ln{2}[/tex]

[tex]0.0251t = \ln{2}[/tex]

[tex]t = \frac{\ln{2}}{0.0251}[/tex]

[tex]t = 27.65[/tex]

The doubling time is of 27.65 minutes.

Answer:

13.5

Step-by-step explanation:

We can use a ratio to solve

2        3

---- = ------

11        3+x

Using cross products

2(3+x) = 3*11

Distribute

6+2x = 33

Subtract 6

6+2x-6 = 33-6

2x = 27

Divide by 2

2x/2 = 27/2

x = 13.5

Now we have to,

→ solve for x

Then use a ratio to solve,

→ 2/11 = 3/3+x

Now see the further steps,

→ 2(3+x) = 3 × 11

→ 6+2x = 33

→ 2x = 33-6

→ 2x = 27

→ x = 27/2

→ x = 13.5

Hence, 13.5 is value of x.

Answer:

[tex]\displaystyle 64[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Rule [Variable Direct Substitution Exponential]:                                         [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer: C. 64

Step-by-step explanation:

Edge 100%

• 2xy + x ² y' = 0

This DE is exact, since

∂(2xy)/∂y = 2x

∂(x ²)/∂x = 2x

are the same. Then there is a solution of the form f(x, y) = C such that

∂f/∂x = 2xy   ==>   f(x, y) = x ² y + g(y)

∂f/∂y = x ² = x ² + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x ² y = C

• sin(x) cos(y) + cos(x) sin(y) y' = 0

is also exact because

∂(sin(x) cos(y))/∂y = -sin(x) sin(y)

∂(cos(x) sin(y))/∂x = -sin(x) sin(y)

Then

∂f/∂x = sin(x) cos(y)   ==>   f(x, y) = -cos(x) cos(y) + g(y)

∂f/∂y = cos(x) sin(y) = cos(x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = -cos(x) cos(y) = C

• x ² + y ² - 2xyy' = 0

is not exact:

∂(x ² + y ²)/∂x = 2x

∂(-2xy)/∂y = -2x

So we look for an integrating factor µ(x, y) such that

µ (x ² + y ²) - 2µxyy' = 0

becomes exact, which would require that these be equal:

∂(µ (x ² + y ²))/∂y = (x ² + y ²) ∂µ/∂y + 2µy

∂(-2µxy)/∂x = -2xy ∂µ/∂x - 2µy

Observe that if µ(x, y) = µ(x), then ∂µ/∂y = 0 and ∂µ/∂x = dµ/dx, so we would have

2µy = -2xy dµ/dx - 2µy

==>   -2xy dµ/dx = 4µy

==>   dµ/µ = -2/x dx

Integrating both sides gives

∫ dµ/µ = ∫ -2/x dx   ==>   ln|µ| = -2 ln|x|   ==>   µ = 1/x ²

So in the modified DE, we have

(1 + y ²/x ²) - 2y/x y' = 0

which is now exact and ready to solve, since

∂(1 + y ²/x ²)/∂y = 2y/x ²

∂(-2y/x)/∂x = 2y/x ²

We get

∂f/∂x = 1 + y ²/x ²   ==>   f(x, y) = x - y ²/x + g(y)

∂f/∂y = -2y/x = -2y/x + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x - y ²/x = C

• exp(2x) (2 cos(y) - sin(y) y' ) = 0

is exact, since

∂(2 exp(2x) cos(y))/∂y = -2 exp(2x) sin(y)

∂(-exp(2x) sin(y))/∂x = -2 exp(2x) sin(y)

Then

∂f/∂x = 2 exp(2x) cos(y)   ==>   f(x, y) = exp(2x) cos(y) + g(y)

∂f/∂y = -exp(2x) sin(y) = -exp(2x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = exp(2x) cos(y) = C

Given that y = 0 when x = 0, we find that

C = exp(0) cos(0) = 1

so that the particular solution is

exp(2x) cos(y) = 1

Answer:

Step-by-step explanation:

We have two sides; the Adjacent and the Hypotnuse

Meaning we will use Cos

Cos = A/H

Cos X = 16/19

Use the inverse of Cos to find the angle

X = cos-1 (16/19)

X = 0.45499141546

X = 0.45

Answer:

???

Step-by-step explanation:

Answer:

D. 0.9938.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 115 and a standard deviation of 8.

This means that [tex]\mu = 115, \sigma = 8[/tex]

100 people are randomly selected

This means that [tex]n = 100, s = \frac{8}{\sqrt{100}} = 0.8[/tex]

Find the probability that their mean blood pressure will be less than 117.

This is the p-value of Z when X = 117, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{117 - 115}{0.8}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938, and thus, the correct answer is given by option D.

Answer:

Step-by-step explanation:

6 is the thousands place

0 (right next to it) is the 10 thousands place

9 is the hundred thousands place. There is only 1 nine present so the answer is unique.

Answer:

I think it's a function

Step-by-step explanation:

as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.

Answer:

yes

Step-by-step explanation:

it's a cubic function having maximum and minimum turning points

it has a point of inflation, y - intercept and x-intercept

Answer:

3x

Step-by-step explanation:

9x^2 ?6x

9x? 6x

÷3x. ÷3x

=3x and 2x

highest number is 3x

what we know?:

* scale factor of 1/4

* the point (4, -8)

all we have to do is put 4/4 (because we are dilating by 1/4)

4/4= 1

same for the other one: -8/4= -2

FINAL ANSWER: (1, -2)

Answer:

your laptop is nice really

Answer:

Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.

Traza 1

Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.

Traza 2

Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.

Traza 3

La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.

Traza 4

La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.

Traza 5

Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.

Traza 6

La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.

Traza 7

Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.

Traza 8

La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.

Traza 9

La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.

Traza 10

Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?

Traza 11

Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.

Traza 12

La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

Traza 13

La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

Traza 14

La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.

Traza 15

El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.

Traza 16

El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.

Traza 17

Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.

Traza 18

Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?

Traza 19

Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.

Traza 20

Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.

Traza 21

La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.

Traza 22

Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.

Traza 23

En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.

Traza 24

Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.

Traza 25

Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.

Traza 26

Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.

Traza 27

Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.

Traza 28

Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.

Traza 29

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

Traza 30

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

Traza 31

Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.

Traza 32

Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.

Traza 33

Step-by-step explanation:

Answer:

A= 84cm

Step-by-step explanation:

length x width= area

plug in the given information.

14cm x 6cm = A

A=84

with a length of 14cm and a width of 6cm multiply them for an area of 84cm.

Answer:

9999*999

Step-by-step explanation:

it 6 in the morning