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3 years ago

13

A card is drawn from a standard deck of playing cards. what is the probability that the card is either a 9 or a 10? (express you

r answer as a decimal to the nearest thousandths.)

1 answer:

snow_lady [41]3 years ago

7 0

There are 52 cards in a standard deck, and 4 suits. There is one 9 per suit, so 4 cards, plus one 10 per suit, so 8 cards. 8 cards divided by 52 cards in a deck is 0.15384615 or 0.154.

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Find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°)

vazorg [7]

Answer:

-8i

Step-by-step explanation:

To multiply numbers is polar form

z1 = r1 ( cos theta 1 + i sin theta 1)

z2 = r2 ( cos theta 2 + i sin theta 2)

z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

z1 = 2(cos 70° + i sin 70°)

z2 = 4(cos 200+ i sin 200)

z1z2 = 2*4 (cos (70+200) + i sin (70+200)

z1z2 = 8 (cos(270) + i sin (270))

= 8 (0 + i (-1))

=-8i

5 0

4 years ago

Read 2 more answers

Which equation has the components of 0 = x2 – 9x – 20 inserted into the quadratic formula correctly?

Aneli [31]

Answer:

The required equation is $x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$ .

Step-by-step explanation:

If a quadratic equation is $ax^2+bx+c=0$ , then the quadratic formula is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given quadratic equation is

$x^2-9x-20=0$

Here, a=1, b=-9 and c=-20.

Substitute a=1, b=-9 and c=-20 in the above quadratic formula.

$x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$

Therefore the required equation is $x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-20)}}{2(1)}$ .

6 0

3 years ago

Read 3 more answers

5 ≤ - 3x- 3 ≤ 10 solve the inequality for x

kaheart [24]

Answer:

<h3> $- \frac{8}{3} \geqslant x \geqslant - \frac{13}{3}$ </h3>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

inequality
solving inequality
PEMDAS

<h3>given:</h3>

5 ≤ - 3x- 3 ≤ 10

<h3>to solve:</h3>

x

<h3>let's solve:</h3>

few notes about inequality

the direction of the inequality doesn't change if you

Add (or subtract) a number from both sides
Multiply (or divide) both sides by a positive number
Simplify a side

the direction of the inequality does change

if you

Multiply (or divide) both sides by a negative number
Swapping left and right hand sides

$step - 1 : difine$

$5 \leqslant - 3x - 3 \leqslant 10$

$step - 2 : \\ add \: 3 \: in \: each \: sides$

$5 + 3 \leqslant - 3x - 3 + 3 \leqslant 10 + 3$

$8 \leqslant - 3x \leqslant 13$

$step - 3 : \\ divide \: - 3\: from \: each \: sides \: \\ and \: swap \: the \: inequalily$

$\therefore - \frac{8}{3} \geqslant x \geqslant - \frac{13}{3}$

5 0

3 years ago

How many ways can a dozen books be placed on four distinguishable shelves if no two books are the same, and the positions of the

Jet001 [13]

Answer:

217945728000 ways

Step-by-step explanation:

Given

$Books = 12$ --- 1 dozen

$Shelf = 4$

The given condition implies that;

$Book\ 1 = 4$ ---- any of the 4 shelves

$Book\ 2 = 5$ --- any of the 4 shelves and either ways of book 1

$Book\ 3 = 6$ --- any of the 4 shelves and either ways of book 1 and 2

-----------------------

----------------

----------

<h2> $Book\ 12 = 15$ </h2><h2></h2>

So, the number of ways is:

$Ways = 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15$

$Ways = 217945728000$

5 0

3 years ago

The following are the ages (years) of 5 people in a room:

Nata [24]

Answer:

The age of the person who entered the room is 15

Step-by-step explanation:

Ages of 5 people in a room are:

17, 16, 15, 17, 22

A person enters room, the mean age of 6 people is 17.

We need to find the age of person who entered the room.

We know that: $Mean=\frac{Sum\:of\:all\:data\:values}{Number\:of\:data\:Values}$

Now, we have mean of 6 people that is 17

We know the age of 5 people while age of one person is unknown.

Let age of person which is unknown= x

So, we can write:

Sum of all data values = 17+16+ 15+ 17+ 22+x

where x is the age of person who enters the room.

Finding x

$Mean=\frac{Sum\:of\:all\:data\:values}{Number\:of\:data\:Values}\\17=\frac{17+16+ 15+ 17+ 22+x}{6}\\17=\frac{87+x}{6}\\17*6=87+x\\102=87+x\\x=102-87\\x=15$

So, we get the value of x: x=15

Therefore, the age of the person who entered the room is 15.

5 0

3 years ago