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Five cards are drawn randomly from a standard deck of 52 cards
Determine the probability that exactly 3 of these cards are Aces. Write your answer in decimal form, rounded to 5 decimal
places
Answer

Answers

Answer 1

Answer:

there are 4 aces in the deck of 52 cards

so the probability to draw one ace is 4/52

if we draw an ace, there are 3 left in 51 cards.

so the next probability will be 3/51

we need to multiply probabilities to know how likely it is that this happens in a row.

for three in a row that's

[tex] \frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} [/tex]

rewritten its:

[tex] \frac{4 \times 3 \times 2}{52 \times 51 \times 50} [/tex]

we'll see soon why this is easier to write.

we also have to account for the two cards that are no aces. it doesn't matter if the first two cards are no aces, the last two, or any rodney. just the ammount of non-aces is important.

there are 48 non-aces in the deck.

so the probability to draw one of them in the first step is 48/52.

wich each draw the number of cards left in the deck decreases by 1. and depending what we draw, that ammount also decreases.

we draw 5 cards, so we know what the denominators will be. the numerator will be the rest-ammounts of each event, like shown in the complicated fraction above.

let's write it most easily as this:

[tex] \frac{4 \times 3 \times 2 \times 48 \times 47}{52 \times 51 \times 50 \times 49 \times 48} [/tex]

this scenario looks like it only describes 3 aces, then two non-aces, but the order of multiplication isn't important. you could put the 48 and 47 to the left, same solution. so this expression represents all permutations of "3 aces when drawing 5 cards", including the two cards that are not aces.

that's why writing it as one convoluted fraction is indeed better and simpler than many fraction multiplied in row.

time to grap a calculator.

our probability for the event is

54144 possible valid outcomes out of

311875200 possible combinations.

luckily the calculator can reduce that to a simpler form of

[tex] \frac{47}{270725} [/tex]

(reduced with 2^6*3^, big number, but tried it out by hand stacking up prime factors until hittinga prime in the numerator)

written as a readable kind of number you probably know and like it's

0.0001736079047

in decimal form. now rounded as asked for:

0.00017

(as percentage: 0.017%)

hope the way how we got here is somewhat clear. feel free to ask any questions.

kind regards

Alex


Related Questions

construct a scale of A-sharp major on a treble staff in ascending order only​

Answers

Answer: In the picture from the basic music theory website's page on a-sharp  major scale

Step-by-step explanation: music theory

How much in earning can PNG make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne ? (2 marks)​

Answers

Answer: K941,200,000

Step-by-step explanation:

From the question, we are to calculate the amount of earning that PNG can make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne.

This will be:

= Number of tonnes × Amount per ton

= 400000 × k2353

= K941,200,000

Therefore, the answer is K941,200,000

Write an explicit formula for an, the nth term of the sequence 63,21,7

Answers

Answer:

63/3=2121/3=77/3=7 -

3

How do I solve this and do the explanation of it

Answers

Answer:

180-66

114

hope it helps mark as brainlist

determine the general term of this sequence 2;10;18;26;.........;394​

Answers

Answer:

Tn=8n-6

Step-by-step explanation:

this is arithmetic sequence so first we check our difference by saying

T2-T1=T3-T2

10-2=18-10

so difference =8 nd a=2

Formula for arithmetic is Tn=a + (n-1)d

then substitute Tn=2 + (n-1)(8)

Tn=2 + 8n-8

Tn=8n-6

5)
I
6
50°
16x + 2
B) 9
A) -10
C) 4
D) 8

Answers

Answer:

c is answer

Step-by-step explanation:

c is ans because it is simple c only serves the need of questions and satisfy it

Answer:

D) 8

Step-by-step explanation:

Liner pair meaning that the angles have a sum of 180. So you add them together to get the equation 16x+52=180 an16x=128 and then you divide both sides by 16 to get x equal to 8. Hope I helped and post more questions :)

Công thức tính hiệu suất

Answers

Answer:

Công thức tính hiệu quả công việc là tỷ lệ giữa đầu ra và đầu vào được biểu thị bằng phần trăm. ... Công thức hiệu quả công việc là hiệu quả = đầu ra / đầu vào, và bạn có thể nhân kết quả với 100 để tính hiệu quả công việc theo tỷ lệ phần trăm.

What's the LCM of 16,24,40

Answers

Step-by-step explanation:

explanation is in the attachment

hope it is helpful to you

Complete the table of inputs and outputs for the given function. g(x) = 3 - 8x g() 0 -5 3 Reset​

Answers

Answer:

Step-by-step explanation:

simplify: 6x²+35x-6÷ 2x²-72

Answers

Step-by-step explanation:

this will be the answer of the question where quotient is 3 and the remainder is 35x + 210

Answer:

[tex]\frac{6x - 1}{2(x - 6)}[/tex]

Step-by-step explanation:

[tex]6x^2 + 35x - 6 \ \div \ 2x^2 - 7 2\\\\6x^2 + 36x - x - 6 \ \div \ 2(x^2 - 36)\\\\6x(x + 6) - 1(x + 6) \ \div \ 2(x^2 - 6^2)\\\\(6x - 1)(x + 6) \ \div \ 2(x- 6)(x+ 6) \ \ \ \ \ \ \ \ \ \ [ \ x^2 -a^2 = (x-a)(x+a) \ ]\\\\\frac{(6x - 1)(x + 6) }{2(x- 6)(x+ 6)} = \frac{6x - 1}{2(x-6)}[/tex]

What is the measure of each exterior angle of the right triangle?
x =
y =
z =

Answers

Answer:

x = 90

y = 134

z = 136

Step-by-step explanation:

Sum of interior angles of a triangle are 180

Linear angles are 180

So 180 - 90 = 90

180 - 44 = 136

180 - 90-44 = 46

180 - 46 = 134

when is 9+10 really equal to 21

Answers

Answer:

9 + 10 = 21

Step-by-step explanation:

9 + 10 = 21

Factor out 9 and 10

9 = 3 · 3   10 = 2 · 5

Next multiply 3 by 2

3 × 2 = 6

Then multiply 3 by 5

3 · 5 = 15

Finally add the products

15 + 6 = 21

It can never be equal to 21 because that’s not how math works

A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. A preliminary sample showed that 30.0% of the families in this sample own this company's product. The sample size that would limit the margin of error to be within 0.047 of the population proportion is:

Answers

Answer:

The sample size is of 366.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

A preliminary sample showed that 30.0% of the families in this sample own this company's product.

This means that [tex]\pi = 0.3[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The sample size that would limit the margin of error to be within 0.047 of the population proportion is:

This is n for which [tex]M = 0.047[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.047 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]

[tex]0.047\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.047}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.047})^2[/tex]

[tex]n = 365.2[/tex]

Rounding up:

The sample size is of 366.

Please answer this!!! WILL GIVE BRAINLIEST

Answers

Answer:

p > 9

Step-by-step explanation:

First let's note down-

George- has 23$

Total cost of m+p= more than $14

Second, let's subtract 23 and 14 to get what the glue costs.

23 - 14 = 9

So now we can cross out choice A and D.

Third, now earlier I said  more than $14, this is the key part to find what we are going to choose.

more than = >

now we just plug in the variable,

p > 9

Hope this helps!

Please reach out to me if you still don't understand :)

HELP PLEASE ASAP What is the product of any integer and -1?​

Answers

Answer:

A

Step-by-step explanation:

The product is opposite of the integer

For example

2 * -1 = -2

Which matrix represents the solution to the system of equations below?
2a+b+c=2
-a+ - =-4
a-25+2c=6
1
0
0
2
1
0
-2.
0
0
1
0
1
0
0
1
0
1
0
- 2
0
0
1
0
2
1
1
2.
-4

Answers

Answer:

The one that's include a rows 2 1 1 2

Answer:

A

Step-by-step explanation:

they wanted the reduced echelon form.

On Edge. btw

Rewrite the following subtraction problem as an addition problem.

Answers

Answer:

x+129=592

Step-by-step explanation:

add 129 to each side

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2 and a mean diameter of 200 inches.

If 83 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches? Round your answer to four decimal places.

Answers

Answer:

0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Standard deviation of 2 and a mean diameter of 200 inches.

This means that [tex]\sigma = 2, \mu = 200[/tex]

83 shafts

This means that [tex]n = 83, s = \frac{2}{\sqrt{83}}[/tex]

What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches?

Mean between 200 - 0.2 = 199.8 inches and 200 + 0.2 = 200.2 inches, which is the p-value of Z when X = 200.2 subtracted by the p-value of Z when X = 199.8.

X = 200.2

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

By the Central Limit Theorem

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

[tex]Z = \frac{200.2 - 200}{\frac{2}{\sqrt{83}}}[/tex]

[tex]Z = 0.91[/tex]

[tex]Z = 0.91[/tex] has a p-value of 0.8186

X = 199.8

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

[tex]Z = \frac{199.8 - 200}{\frac{2}{\sqrt{83}}}[/tex]

[tex]Z = -0.91[/tex]

[tex]Z = -0.91[/tex] has a p-value of 0.1814

0.8186 - 0.1814 = 0.6372

0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.

John throws a biased four-sided dice.
The probabilities of getting each number are summarised in the table below.
Number
1
2
3
4
Probability
0.2
x
0.2
0.2
Work out the probability that the dice lands on 2.

Answers

Answer:

0.4

Step-by-step explanation:

0.2+0.2+0.2=0.6

1.0-0.6=0.4

This isn't 0.2 like the others which is why it's a biased dice like it says.

Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)

Answers

Answer:

(a) [tex]A = A_0 * e^{kt}[/tex]

(b) There will be 1lb left after 14 hours

Step-by-step explanation:

Solving (a): The equation

Since the substance decomposes at a proportional rate, then it follows the following equation

[tex]A(t) = A_0 * e^{kt}[/tex]

Where

[tex]A_0 \to[/tex] Initial Amount

[tex]k \to[/tex] rate

[tex]t \to[/tex] time

[tex]A(t) \to[/tex] Amount at time t

Solving (b):

We have:

[tex]t = 4.6hr[/tex]

[tex]A_0 = 8[/tex]

[tex]A(4.6) = 4[/tex]

First, we calculate k using:

[tex]A(t) = A_0 * e^{kt}[/tex]

This gives:

[tex]A(4.6) = 8 * e^{k*4.6}[/tex]

Substitute: [tex]A(4.6) = 4[/tex]

[tex]4 = 8 * e^{k*4.6}[/tex]

Divide both sides by 4

[tex]0.5 = e^{k*4.6}[/tex]

Take natural logarithm of both sides

[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]

This gives:

[tex]-0.6931 = k*4.6[/tex]

Solve for k

[tex]k = \frac{-0.6931}{4.6}[/tex]

[tex]k = -0.1507[/tex]

So, we have:

[tex]A(t) = A_0 * e^{kt}[/tex]

[tex]A(t) = 8e^{-0.1507t}[/tex]

To calculate the time when 1 lb will remain, we have:

[tex]A(t) = 1[/tex]

So, the equation becomes

[tex]1= 8e^{-0.1507t}[/tex]

Divide both sides by 8

[tex]0.125= e^{-0.1507t}[/tex]

Take natural logarithm of both sides

[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]

[tex]-2.0794= -0.1507t[/tex]

Solve for t

[tex]t = \frac{-2.0794}{-0.1507}[/tex]

[tex]t = 13.7983[/tex]

[tex]t = 14[/tex] --- approximated

Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
x + y - z = -2
2x - y + 3z = 9
x - 4y - 2z = 1

Answers

Answer:

(x, y, z) =(1, -1,2)

Step-by-step explanation:

.............

HELP!!

What are extraneous solutions to rational and radical equations? How do they arise? How do we check if a solution is extraneous? Use these equations as examples to help you explain:

Answers

Answer:

In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. ... Squaring (or raising to any other even power) is a non-invertible operation. Solving equations involving square roots involves squaring both sides of an equation

Step-by-step explanation:

I hope this will help u

y=x+9x solve for x. Please and Thank you.

Answers

Answer:

x=y/10

Step-by-step explanation:

y=10x

y/10=x

x=y/10

Hope this is helpful

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: x = \frac{y}{10}}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]y = x + 9x\\[/tex]

[tex]➺ \: y = 10x\\[/tex]

[tex]➺ \: x = \frac{y}{10}\\ [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Can someone please answer this please

Answers

Answer: I don't know but i have the formula.

Step by Step: [tex]A=\frac{1}{2}b h[/tex]

Find cos 0.
53
45
28

Answers

the answer is A. 28/53

what do you call the middle value in the set of the data or quantities a mean b. median c.mode d.range​

Answers

Answer:

median is the middle value

mean is the average

mode is the one that occurs most

range is the highest number - lowest number

Marc is sending his sister a parcel through the post. the parcel weighs 2.451kg. round this to 1 decimal place​

Answers

Answer:

2.5 kg

Step-by-step explanation:

2.451

Find the number in the tenth place 4 and look one place to the right for the rounding digit 5.

Round up if this number is greater than or equal to 5 and round down if it is less than 5.

Simplify 3/4 X 14/ 15 .

Answers

the answer is 7/10 !!!!!!
The Answer is 7/10 ____

X^2+9x+20 divided by x+5

Answers

Answer:

 x ≠ -5

Step-by-step explanation:

The easiest way is to factor the numerator.

 

x2 + 9x + 20 = (x + 4)(x + 5)

 

Then

 

(x2 + 9x + 20)/(x + 5) = (x + 4)(x + 5) / (x + 5) = x + 4,

 

with the restriction that x ≠ -5

Whoever helps gets Brainliest!!! PLEASE HELP!!!

Answers

The slope of the line is 0
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