A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?

a)0.09%
b) 6.25%
c)13%
d)52%

Answer:

[tex]\frac{4}{17}-\frac{19}{34}i[/tex]

Step-by-step explanation:

1. Approach

To divide complex numbers, first one must set the problem up as a fraction. The one will multiply the fraction by the complex conjugate. A complex conjugate is a complex number with the imaginary part multiplied by negative one. Since a number over itself equals one, this will ensure that the expression remains true. When one multiplies by the complex conjugate, the difference of squares property complex into play, therefore the denominator simplifies down to a real number (remember one can simplify the powers of (i)). Now all one has to do is divide each element in the complex number in the numerator by the real number in the denominator. If it does not divide evenly, one can just simply the fraction.

2. Solving

Set up as a fraction

[tex]\frac{3-4i}{8+2i}[/tex]

Multiply by the complex conjugate

[tex]\frac{3-4i}{8+2i}*\frac{8-2i}{8-2i}[/tex]

Simplify

[tex]\frac{(3-4i)(8-2i)}{(8+2i)(8-2i)}[/tex]

[tex]\frac{24-6i-32i+8i^{2}}{64-4i^{2}}[/tex]

[tex]\frac{24-6i-32i-8}{64-4(-1)}[/tex]

[tex]\frac{16-38i}{64+4}[/tex]

[tex]\frac{16-38i}{68}[/tex]

[tex]\frac{8-19i}{34}[/tex]

Answer:

? = 18

Step-by-step explanation:

Answer:

? = 18

Step-by-step explanation:

d^?/d^11 = d^7

d^? = d^11*d^7

d^? = d^(11+7)

d^? = d^18

? = 18

Answer:

It has side lengths of 3 and 13

Step-by-step explanation:

If it has an area of 39, then let the sides be x and y: thus we get the two relationships:

xy=39

2(x+y)=32

From the second equation, you get x+y=16. Now, rearrange to get y=16-x. You can now plug this into the first equation:

x(16-x)=39 -> 16x-x^2=39 -> x^2-16x+39=0 -> (x-3)(x-13)=0

This implies that x=3, or x=13, which further implies that the side lengths must be 3 and 13.

Answer:

This is an experiment with blocking ( B )

Step-by-step explanation:

The best way to describe this experiment is an experiment with blocking this is because the Type of surface where the tape is been tested can be considered a  blocking variable while the weights can be considered  as treatments

A blocking variable is a variable used in experiment which is not of primary interest to the experiment  observer ( I.e. The tape is supposed to hold on all types of surfaces and not just on Aluminum and wood surface )

Answer:

Step-by-step explanation:

1.

Igneous rock can change into sedimentary rock or into metamorphic rock. ... Igneous rock forms when magma cools and makes crystals. Magma is a hot liquid made of melted minerals. The minerals can form crystals when they cool.

2. The three processes that change one rock to another are crystallization, metamorphism, and erosion, and sedimentation. Any rock can transform into any other rock by passing through one or more of these processes.

3. The three types of metamorphism are Contact, Regional, and Dynamic metamorphism. Contact Metamorphism occurs when magma comes in contact with an already existing body of rock.

Answer:

2,700 units

Step-by-step explanation:

Answer:

I think it is B because it makes sense and I have done algebra before.

i dont know that so u answer it

Answer:

1/3

Step-by-step explanation:

The answer is 1/3 to find out how look at the picture above!

Hello!

The common denominator is 100.

~Sophia

Answer:

The correct answer is 40

Step-by-step explanation:

I took the quiz

Answer:

(7)(7)(1)=49 mm^3

Step-by-step explanation:

Answer:

49mm³

Step-by-step explanation:

[tex]v = 7mm \times 7mm \times 1mm = 49m {m}^{3} [/tex]

Answer:

NO

step by step

the answer is no

Answer:31/28

Step-by-step explanation:

Answer:

1 3/28

Step-by-step explanation:

Answer:

2,3,5

Step-by-step explanation:

Answer:

2, 3 and 5 are the prime numbers

Step-by-step:

The speed is the distance covered by an object at a particular time. The time it will take for Steven to cover a distance of 2.6 miles is 22.75 minutes.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

Speed = Distance / Time

Given that it takes Steven 12.25 minutes to run 1.4 miles. Therefore, the rate or speed at which Steven runs is,

Speed = Distance / Time

Speed of Steve = 1.4 miles / 12.25 minutes

Now, if at the same rate Steven runs, then the time it will take for Steven to run a distance of 2.6 miles is,

Speed = Distance / Time

Time = Distance / Speed

Time = 2.6 miles / (1.4 miles / 12.25 minutes)

Time = (2.6 miles × 12.25 minutes)/1.4 miles

Time = 22.75 minutes

Hence, the time it will take for Steven to cover a distance of 2.6 miles is 22.75 minutes.

Learn more about Speed here:

https://brainly.com/question/15100898

#SPJ2

Answer:

Y = 6X-5

Step-by-step explanation:

substitute the value of slope and Y intercept in the standard equation Y = MX + B

where M is the slope and b is the y-intercept

Answer:

-3

Step-by-step explanation:

An even number of negative numbers will give a positive answer. An odd number of negative numbers will give a negative answer.

13-16, 16 is larger than 13 so it's negative

Answer:

C

Step-by-step explanation:

the domain would be all positive real numbers, including zero

Answer:

length = 15 in

width = 10 in

Step-by-step explanation:

let '3x' = length

let '2x' = width

A = l x w

150 = 3x(2x)

150 = 6x²

x² = 150/6

x² = 25

x = [tex]\sqrt{25}[/tex]

x = 5

Length = 3(5) = 15 in

Width = 2(5) = 10 in

Answer:

C:      t= x1`-x2`/√p^q^(1/n1 +1/n2)

0.7−0.6/(0.65)(0.35)√(1/50+1/60)

Step-by-step explanation:

The options given are

A

35−36/ 35/√50+3660

B

35−36/0.7/√50+0.660

C

0.7−0.6/(0.65)(0.35)√(1/50+1/60)

D

0.7−0.6/(0.7)(0.6)/√(1/50+1/60)

E

0.7−0.6/(0.7)(0.6)/√150+160

↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔

This is a test hypothesis about difference of  means between two proportions.

The test statistic used is

t= x1`-x2`/√p^q^(1/n1 +1/n2)

x1`= 35/50= 0.7

x2`= 36/60= 0.6

so

x1`-x2`

= 35/50-36/60

= 0.7-0.6

p^= 35+36/50+60= 71/110= 0.645= 0.65

q^= 1-p^= 1-0.65= 0.35

p^q^= (0.65) (0.35)

n1= 50 and n2= 60

therefore √1/n1 +1/n2= √1/50+1/60

Now Putting the values in the test statistics we get

t= x1`-x2`/√p^q^(1/n1 +1/n2)

0.7−0.6/√(0.65)(0.35)(1/50+1/60)

Hence C is the correct option

Using the z-distribution, it is found that the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts is given by:

[tex]z = \frac{0.1 - 0}{0.0906}[/tex]

At the null hypothesis, it is tested if there is no difference between the proportions, that is, the subtraction is zero, hence:

[tex]H_0: p_A - p_B = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference between the proportions, that is, the subtraction is not zero, hence:

[tex]H_1: p_A - p_B \neq 0[/tex]

First, we find the mean and the standard error for each proportion:

[tex]p_A = \frac{35}{50} = 0.7[/tex]

[tex]s_A = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648[/tex]

[tex]p_B = \frac{36}{60} = 0.6[/tex]

[tex]s_B = \sqrt{\frac{0.6(0.4)}{60}} = 0.0633[/tex]

Then, for the difference:

[tex]\overline{p} = p_A - p_B = 0.7 - 0.6 = 0.1[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0648^2 + 0.0633^2} = 0.0906[/tex]

It is given by:

[tex]z = \frac{\overline{p} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{0.1 - 0}{0.0906}[/tex]

To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918

Answer:

$1,482 is the 10th percentile.

Step-by-step explanation:

xth percentile:

If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.

In this question:

10 computers, the 10th percentile is the value that is larger than 10% of the prices.

The prices, sorted in an increasing way, are:

$1,127, $1,482, ...

Computers at a price of $1,482 have larger prices than 10% of the population, so $1,482 is the 10th percentile.

Answer:

For ABC A= (-3,3) B= (0.2) and C= (-3,1)

For DFE D= (0,6) F= (2,6) and E= (2,3)

Step-by-step explanation:

I believe tha name of a sequence of transformation will be translation and the Reflection

Hope this Helped

Answer:

12.5 inches

Step-by-step explanation:

To best find this answer, we should set up a proportion. Our first fraction is practically given to us in the problem, and would look like this:

[tex]\frac{2in}{24mi}[/tex]

Next, we need to set up our second fraction. An important thing to make sure of is that the 150 is on the same side as the 24 since they are both miles. Here is what the final equation should look like:

[tex]\frac{2in}{24mi} = \frac{x}{150mi}[/tex]

To solve, just cross multiply and divide! First, multiply 2 by 150, giving you 300. Next, just divide the 300 by the remaining 24, giving you a final answer of 12.5 inches. Here's what the final calculations look like:

2in X 150mi = 300

300 / 24mi = 12.5in

Answer:

12.5 inches is your answer

Answer:

there is no pics any problem?

Answer:16km/hr

Explanation:

48km/3hr= 16km/hr

Answer:

b and c

Step-by-step explanation:

Answer:

her brother is 15 years old

Step-by-step explanation:

let 'b' = her brother's age

Harriet is 3 years old but Harriet is also '1/3b - 2'

3 = 1/3b - 2

5 = 1/3b

b = 5(3) or 15