Given a deck of 52 cards 3 are dealt without replacement let the first card be the queen of hearts and the second card be queen of diamonds is the probability of drawing the two cards independent? Explain

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

the outcome of the first event affects the second.

you cannot get the queen of hearts the first time and the queen of hearts the second time so these are dependent events.

flipping a coin is an example of an independent event

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Which of the following is equivalent to -(5/12) ?A. -5/-12 B. 5/12 C. 12/-5 D. -5/12

PREGUNTA 5Una fábrica produce 300 rodamientos de apoyo a un costo de 3200 dólares, pero si produce 700 el costo es de $4800. Si se sabe que la relación del costo (C) y el número de rodamientos de apoyo (x) es lineal, obtenga una fórmula que exprese esta relación y calcule el costo de producir 950 rodamientos de apoyo.

Answers

Answer:

C = 4x + 2000 es la ecuación

El costo de los rodamientos de soporte 950 es de $ 5,800

Step-by-step explanation:

Esperamos una gráfica lineal de costo contra el número de rodamiento de respaldo.

Un punto en este diagrama tendrá una representación como (número de demoras, costo)

Ahora, a partir de la pregunta, podemos identificar dos puntos; (300,3200) y (700,4800)

Generalmente, la ecuación de una línea recta tiene la forma

y = mx + c

donde m es la pendiente y c es la intersección en y

Lo que esto significa en esta línea es que tenemos dos cosas para calcular, que es la pendiente de la línea y la intersección de la línea. Usando los dos puntos podemos calcular estos.

matemáticamente, la pendiente se puede calcular como;

tenemos m = (4800-3200) / (700-300) = 1600/400 = 4

Como conocemos la pendiente, el modelo lineal ahora se convierte en

y = 4x + c

Para obtener el valor de la intersección con el eje y, podemos usar cualquiera de los dos puntos. Digamos que queremos usar el primer punto (300,3200)

3200 = 4 (300) + c

3200 = 1,200 + c

c = 3200-1200

c = 2000

Así la ecuación se convierte

y = 4x + 2000

Ahora usemos los parámetros definidos en la pregunta, tenemos;

C = 4x + 2000

donde C es el costo yx es el número de rodamientos de soporte

Ahora queremos calcular el costo de 950 rodamientos

Simplemente usamos la ecuación que hemos modelado donde en este punto, x = 950

C = 4 (950) + 2000

C = $ 5,800

transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.

Answers

$The\ vertex\ form\ of\ y=ax^2+bx+c:y=a(x-h)^2+k\n\nwhere\ h=(-b)/(2a)\ and\ k=f(h)=(-(b^2-4ac))/(4a)\n-----------------------------\n\ny=-2x^2-12x-10\n\na=-2;\ b=-12;\ c=-10\n\nh=(-(-12))/(2(-2))=(12)/(-4)=-3\n\nk=f(-3)=-2(-3)^2-12(-3)-10=-2\cdot9+36-10=-18+26=8\n\ntherefore:y=-2(x-(-3))^2+8\to\boxed{y=-2(x+3)^2+8}\leftarrow The\ vertex\ form$

$y-intercept\to f(0)=-2(0^2)-12(0)-10=\boxed{-10}\leftarrow y-intercept$

$x-intercept\ if\ y=0\n\n-2x^2-12x-10=0\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\nx^2+6x+5=0\nx^2+x+5x+5=0\nx(x+1)+5(x+1)=0\n(x+1)(x+5)=0\iff x+1=0\ or\ x+5=0\n\n\boxed{x=-1\ or\ x=-5}\leftarrow x-intercept$

y=-2x^2-12x-10
to find the x value of the vertex find the axis of symmetry which is
-b/2a
=12/2(-2)
=-3
to find the y value of the vertex sub the axis of symmetry back into the original equation.
y=-2(-3)^2-12(-3)-10
y=8
vertex=(-3,8)
to put it into vertex form use y=a(x-h)^2 +k where h and k are the x and y values of the vertex respectively.

y=-2(x--3)^2 +8
y=-2(x+3)^2+8

to find the x intercept let y=0

-2x^2-12x-10=0
x^2+6x+5=0
use quad formula and you will get
x=-5 and -1

to find the y intercept let x=0

y= -2(0)^2-12(0)-10
y=-10

How can i simplify √320x³

Answers

Answer:

8x * sqrt(5x)

Step-by-step explanation:

Factor 320 into its prime factors: (2^6) * 5

To simplify sqrt we extract factors which are squares and the rest remain inside the root: (2^6) will be extracted (2^6=64) and 5 will remain inside

Take sqrt of factors being extracted: sqrt64= 8

Now it looks like this: 8 * sqrt(5x^3)

SQRT(x^3) is the same as x * SQRT(x)

Therefore, sqrt (320x^3)= 8x*sqrt(5x)

What is the volume of a sphere with a diameter of 11ft? Round your answer to the nearest cubic foot. 2786 cubic feet 5572 cubic feet 8359 cubic feet 6193 cubic feet

Answers

Answer:

The volume of the sphere is $697\ ft^(3)$

Step-by-step explanation:

we know that

The volume of the sphere is equal to

$V=(4)/(3)\pi r^(3)$

we have

$r=11/2=5.5\ ft$ -----> the radius is half the diameter

assume

$}\pi=3.14$

substitute

$V=(4)/(3)(3.14)(5.5)^(3)=697\ ft^(3)$

Which of the following expressions represents "twelve diminished by six times a number"?a. 12 - 6n
b. 6n - 12
c. 12n - 6 User: The coefficient of 9(14)P is

Answers

Answer:

The answer is the option A

$12-6n$

Step-by-step explanation:

Let

n------> the number

we know that

The expression "twelve diminished by six times a number" is equivalent to say "Subtract six times a number from twelve"

The algebraic expression is equal to

$12-6n$

the number is n. 12 is what is being diminished (made smaller), so something is subtracted. 6 times a number is 6n

12 - 6n, so a

Alfonzo is building a deck on his house. He was originally going to make it a square with a side length of x x feet. Alfonzo decides to make it a rectangular deck, with 1 foot added to one pair of opposite sides (now the width) and 2 feet added to the other pair of opposite sides (now the length). Part A Determine the expressions for the length and width of the new deck in terms of x x , the length of the sides of the original deck.

Answers

The length and width of the new deck in terms of x x are (x + 2) feet and (x + 1) feet respectively.

Step-by-step explanation:

Step 1:

The side length of the original deck in the shape of a square was x feet.

Since it was a square, all the sides would measure x feet.

Now, the square deck is converted into a rectangular deck.

Step 2:

The side length of the original deck was x feet. 1 foot of deck is added to the side length and it is made into the width of the rectangular deck.

So the width of the new deck is (x + 1) feet.

The side length of the original deck was x feet. 2 feet of deck is added to the side length and it is made into the length of the rectangular deck.

So the length of the new deck is (x + 2) feet.

So the length of the new deck is (x + 2) feet and its width is (x + 1) feet.

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