You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. what is the minimum number of cards you must pick in order to guarantee that you geta)two pair (for example, two kings or two 5s)b)three of a kind (for example, three 7s)

Answers

Answer 1

Final answer:

To guarantee two pairs, a player must pick at least 14 cards from a deck of 52 playing cards without replacement. For three of a kind, a minimum of 16 cards is required. This is an example of sampling without replacement, where each selection affects subsequent draws.

Explanation:

To determine the minimum number of cards one must pick from a standard deck of 52 playing cards to guarantee getting two pairs, consider the worst-case scenario where you pick one card of each rank before getting any pair. Since there are 13 different ranks, picking 13 single cards wouldn't guarantee a pair, but the 14th card will definitely match one of the previously drawn ranks, thus forming a pair. To ensure two pairs, you could go through another 13 cards without getting a match to your first pair, so the 15th card would be the second pair. Therefore, you must pick at least 14 cards to guarantee two pairs.

For three of a kind, you pick sequentially from the different ranks. After picking one card of each of the 13 ranks, the 14th card will form a pair, and the 15th card could potentially be of a new rank. However, the 16th card drawn must either create a pair with another rank or a 'three of a kind' with the rank that already has two. Thus, the minimum number of cards one must pick to guarantee a three of a kind is 16.

In sampling without replacement, drawn cards are not returned to the deck, making each draw dependent on the previous ones. This contrasts with sampling with replacement, where each draw is independent since cards are returned to the deck and reshuffled after each pick.

Related Questions

0.063 written as fraction or a mixed number

Answers

63/1000 as a fraction

What is 35 divided by 768 plz I am really stuck on this one and need some improvement

Answers

35/ 768 = 0.04557

rounded up will be 0.05

hope this helps

The sum of two consecutive even integers is 138. Write an equation and solve

Answers

x+(x+2)=138
2x+2=138
2x=136
x=68
Final answers: 68,70

Final answer:

The two consecutive even integers that sum to 138 are 68 and 70. The equation n + (n + 2) = 138 was used to determine these integers.

Explanation:

The problem is asking for two consecutive even integers whose sum is 138. Let's denote the first integer as n (where n is an even number). As the problem says the numbers are consecutive even integers, we know the next number must be n + 2.

We can form an equation based on the information given. The sum of these two integers is equal to 138, so:

n + (n + 2) = 138

If we simplify the equation, it becomes:

2n + 2 = 138By subtracting 2 from both sides, 2n = 136We then divide both sides by 2 to get n = 68

Therefore, the two consecutive numbers are 68 and 70 as they add up to 138.

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Which of the following fractions is an equivalent fraction in lowest terms to the fraction ? -276/-540

A. 23/45
B. -23/45
C. 69/135
D. -69/135

Answers

23/45 would be the most simplified form of 276/540

[tex]\bf \cfrac{-276}{-540}\quad \begin{cases} 276=2\cdot 2\cdot 3\cdot 23\\ 540={2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5 \end{cases}\implies \cfrac{\underline{-2\cdot 2\cdot 3}\cdot 23}{\underline{-2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5} \\\\\\ \cfrac{23}{3\cdot 3\cdot 5}\implies \cfrac{23}{45}[/tex]

Perry has an opportunity to put $2291 into an investment with an APR of 7.6%. How long will it take his investment to double?

Answers

2×2291=2291 (1+0.076)^t==> 2=(1+0.076)^t
Solve for t
Log (2)=t×log (1.076)
T=log (2)÷log (1.076)
T=9.46 years round your answer to get 9 years

solve these equations fast.

(6 + 3i)(6 − 3i) =

(4 − 5i)(4 + 5i) =

(−3 + 8i)(−3 − 8i) =

Answers

(6 + 3i)(6 − 3i) = 45
(4 − 5i)(4 + 5i) = 41
(−3 + 8i)(−3 − 8i) = 73

Answer:

The correct answers are 45,41,73

Step-by-step explanation:

solve x2-8+41=0 for x

Answers

No real solutions or i square root 33

I'm taking x2 is x^2 or x squared

i stands for imaginary number

[tex]Problem: x^2-8+41= 0 \\ x^2+ 33 = ? \\ = 0 - 33 = (-33) \\ The Value Of 'x' is -33 \\ x= \sqrt{-33} [/tex] [tex]There \\ are \\ NO \\ Solution \\ in \\ this \\ equation! [/tex] [tex]Good Luck! [/tex]

Simplify this and show your work :

Answers

-2(x-3) = 5x+1

-2x +6 = 5x+1

subtract 5 x from each side

-7x+6 = 1

subtract 6 from each side

-7x = -5

divide both sides by -7

x = -5/-7 = 5/7

x = 5/7

Which expression is equivalent to the given expression? 100pts giveaway 3x(1.05) 3x + 3x + 3x 1.05x + 1.05x + 1.05x x + 3.15 1.05x + 3

Answers

17.2x+6.15
i am not sure but they may be right

I got, 17.35x+6.15

Btw you know it shows how many points your giving for the question

if x>2, then x^2-x-6/x^2-4=

Answers

consider the expression [tex] \frac{x^{2} -x-6}{ x^{2} -4} [/tex]

To factorize the expression in the denominator we use difference of squares: [tex]x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)[/tex]

To factorize [tex]x^{2} -x-6[/tex] we use the following method:

[tex]x^{2} -x-6=(x-a)(x-b)[/tex]

where a, b are 2 numbers such that a+b= -1, the coefficient of x,

and a*b= -6, the constant.

such 2 numbers can be easily checked to be -3 and 2

(-3*2=6, -3+2=-1)

So [tex]x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)[/tex]

[tex] \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2} [/tex]

[tex]\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}[/tex]

for x>2

[tex]\frac{1}{x+2}\ \textless \ \frac{1}{2+2}= \frac{1}{4} [/tex]

thus

for x>2,

[tex]1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4} [/tex]

Answer:

for x>2

[tex]\frac{x^{2} -x-6}{ x^{2} -4} = \frac{x+3}{x+2} \ \textless \ \frac{5}{4} [/tex], (but the expression is never 0)

What does the value of the GCF
represent?

Answers

GCF its full form is Greatest Common Factor.
It is found when we have two or more numbers and the largest factor are common in both the numbers.

The directions for mixing an insect spray say to use 1 1/2 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 3 4/5 gallons of water? First, estimate the answer to the application problem. Then find the exact answer.

Answers

1 1/2 oz to each gallon.
Total required for 3 4/5 gal is the product of 1 1/2 and 3 4/5, which is approximately 4*1 1/2 = 6 oz.

Exact answer
1 1/2 * 3 4/5
=3/2 * 19/5
=57/10
=5.7 oz

[tex]\bf \begin{array}{ccllll} chemical&water\ gallons\\ -----&-------\\ 1\frac{1}{2}&1\\\\ x&3\frac{4}{5} \end{array}\implies \cfrac{1\frac{1}{2}}{x}=\cfrac{1}{3\frac{4}{5}} \\\\\\ \cfrac{\frac{1\cdot 2+1}{2}}{x}=\cfrac{\frac{1}{1}}{\frac{3\cdot 5+4}{5}}\implies \cfrac{\frac{3}{2}}{\frac{x}{1}}=\cfrac{\frac{1}{1}}{\frac{19}{5}}\implies \cfrac{3}{2}\cdot \cfrac{1}{x}=\cfrac{1}{1}\cdot \cfrac{5}{19}\implies \cfrac{3}{2x}=\cfrac{5}{19}[/tex]

[tex]\bf 3\cdot 19=2x\cdot 5\implies 57=10x\implies \cfrac{57}{10}=x\implies \boxed{5\frac{7}{10}=x} \\\\\\ \cfrac{5\cdot 10+7}{10}\implies \cfrac{57}{10}[/tex]

Question 11(Multiple Choice Worth 5 points) (09.03 MC) A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below: Male Female Type A 55 75 Type B 48 22 Compare P(Male | Type A) with P(Male or Type A).

Answers

The solution would be like this for this specific problem:

[tex]\large P(F) \times P(B )= \frac {97} {200} \times \frac {70}{200} = \frac {97 \times 70} {200 \times 200} = 0.16975[/tex]

You need to compare the results of: P(female or type B) which is written in correct symbols as:

[tex]\large P (F\cup B) [/tex]

and P(female | given type B) which is written in correct symbols as:

[tex]\large P(FlB)

\large (F\cup B)=0.835 - 0.17 = 0.665

\large P (FlB) = 0.314

\large P (F \cup B) \ \textgreater \ P (F|B)[/tex]

So, the correct answer would be: P (Female or Type B) > P (Female | Type B).

Answer:

The answer is P(Female or Type B) > P(Female | Type B)

Step-by-step explanation:

Just took the test.

Also check if you want the answer for males or females before you choose because they are completely different questions

6840 round to nearest hundredth

Answers

6800 is 6840 rounded to the nearest hundredth.

What are the coordinates of a point on the unit circle if the angle formed by the positive x-axis and the radius is 60?

Answers

Arc length equal to the radius of a circle

Elixir of acetaminophen contains 160 my per 5 milliliters. How much acetaminophen is needed to prepare 2 ounces of elixir?

Answers

60 milliliters is equal to two ounces.

Teachers of two history classes bought tickets to go on a field trip to a local museum. Mr. Lowe paid $115 for 4 adult tickets and 20 student tickets. Mrs. Tucker paid $135.25 for 5 adult tickets and 23 student tickets. Fill in the missing information in the system of equations for the situation. 4a + As = 115 5a + 23s = B

Answers

4a + 20s = 115
5a + 23s = 135.25

Answer with Step-by-step explanation:

Let a represents the cost of one adult ticket

and s represents the cost of one student ticket

Mr. Lowe paid $115 for 4 adult tickets and 20 student tickets.

i.e. 4a+20s=115

Mrs. Tucker paid $135.25 for 5 adult tickets and 23 student tickets.

i.e. 5a+23s=135.25

We get system of equations:

4a+20s=115

5a+23s=135.25

On comparing the above system with

4a + As = 115

5a + 23s = B

We get

A=20

and B=135.25

if you were to load 225 boxes onto a truck and the boxes are created with each crate containing 9 boxes how many crates would you need to load

Answers

You would need 25 Crates because 225 divided by 9 is 25.

225 / 9 = 25 (Total number of boxes / the number of boxes per crate)

You would need to load 25 crates

The primary goal of using correlational research is to

Answers

The Primary goal of using correlation research is to determine the nature and strength of the association between two measured variables.
Here you must know the terms correlation and variable. The term Correlation is simply defined as the relation between two variables. variables are factors that are liable to vary or change.

Final answer:

Correlational research is used to determine whether there's a relationship between two or more variables without establishing a cause-and-effect connection. It identifies how closely connected variables are by observing them as they naturally occur.

Explanation:

The primary goal of using correlational research is to determine whether a relationship exists between two or more variables, but without establishing a cause-and-effect connection. In this method, a researcher may observe variables as they naturally occur with no intervention or manipulation. By examining the degree to which these variables move together, the researcher can identify how closely connected they are. For example, in psychological studies, a correlational research might be used to investigate the relationship between study habits and academic performance. However, it's critical to note that correlation does not imply causation.

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Find the area of a regular hexagon with apothem 2√3 mm. Round to the nearest whole number.

Answers

Join the center of the hexagon with the 2 base angles.

An equilateral triangle, with side length x, is formed.

(remark: a regular hexagon is made up of 6 equilateral triangles with equal length)

The height [tex]2 \sqrt{3} [/tex] forms 2 congruent right triangles with :

hypotenuse= x, side_1=x/2, and side_2= [tex]2 \sqrt{3} [/tex].

From the pythagorean theorem we have:

[tex] x^{2} = ( \frac{x}{2} )^{2}+(2 \sqrt{3})^{2} [/tex]

[tex]x^{2} = \frac{ x^{2} }{4} +12[/tex]

[tex] \frac{3}{4} x^{2} =12[/tex]

[tex] x^{2} = \frac{12*4}{3}=4*4 [/tex]

thus, x=4.

The area of the triangle is 1/2 * 4 * [tex]2 \sqrt{3}[/tex]=6.93 (mm squared)

The area of the hexagon is 6* the area of the triangle = 42 (mm squared)

Answer: a. 42 (mm squared)

In the diagram, PN is the perpendicular bisector of AB and is also the angle bisector of

Answers

The perpendicular bisector is a line segment that is drawn from a vertex of an angle to the midpoint of another line segment creating a right triangle or a 90° angle in the process. Suppose AB is the base segment of the triangle, therefore the perpendicular sector is also the angle bisector of the other angle of the triangle, supposedly angle C. Angle bisector is a line segment that divides the angle into two equal parts. Imagine a line drawn from the top vertex C extended down to the midpoint of line AB. That is the perpendicular and angle bisector.

What are the orders of 3,7,9,11,13,17 and 19(mod20)?does 20 have primitive roots?

Answers

[tex]3\equiv3\mod{20}[/tex]
[tex]3^2\equiv9\mod{20}[/tex]
[tex]3^3\equiv27\equiv7\mod{20}[/tex]
[tex]3^4\equiv3\cdot3^3\equiv3\cdot7\equiv21\equiv1\mod{20}[/tex]

[tex]7\equiv7\mod{20}[/tex]
[tex]7^2\equiv49\equiv9\mod{20}[/tex]
[tex]7^3\equiv7\cdot7^2\equiv63\equiv3\mod{20}[/tex]
[tex]7^4\equiv7\cdot7^3\equiv21\equiv1\mod{20}[/tex]

[tex]9\equiv9\mod{20}[/tex]
[tex]9^2\equiv3^4\equiv1\mod{20}[/tex]

[tex]11\equiv11\mod{20}[/tex]
[tex]11^2\equiv121\equiv1\mod{20}[/tex]

[tex]13\equiv-7\equiv13\mod{20}[/tex]
[tex]13^2\equiv169\equiv9\mod{20}[/tex]
[tex]13^3\equiv13\cdot13^2\equiv(-7)9\equiv-63\equiv-3\mod{20}[/tex]
[tex]13^4\equiv13\cdot13^3\equiv(-7)(-3)\equiv21\equiv1\mod{20}[/tex]

[tex]17\equiv-3\equiv17\mod{20}[/tex]
[tex]17^2\equiv(-3)^2\equiv9\mod{20}[/tex]
[tex]17^3\equiv(-3)^3\equiv-27\equiv3\mod{20}[/tex]
[tex]17^4\equiv(-3)^4\equiv81\equiv1\mod{20}[/tex]

[tex]19\equiv-1\equiv19\mod{20}[/tex]
[tex]19^2\equiv19(-1)\equiv-19\equiv1\mod{20}[/tex]

Generally speaking, a number [tex]x[/tex] coprime to [tex]n[/tex] will be a primitive root of [tex]n[/tex] if we have [tex]x^n\equiv x\mod{n}[/tex], or [tex]x^{n-1}\equiv1\mod{n}[/tex]. In other words, if [tex]x[/tex] is of order [tex]n-1[/tex] modulo [tex]n[/tex], then [tex]x[/tex] is a primitive root of [tex]n[/tex].

Since none of these numbers has order 19, it follows that 20 does not have any primitive roots.

The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $25 item is $25.75, what is the total cost on a $60 item?

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{cost(c) is directly proportional to price(p)}\qquad c=kp \\\\\\ \textit{we also know that } \begin{cases} p=25\\ c=25.75 \end{cases}\implies 25.75=k25\implies \cfrac{25.75}{25}=k \\\\\\ 1.03=k\qquad thus\qquad \boxed{c=1.03p}\\\\ -------------------------------\\\\ \textit{what's \underline{c} when \underline{p} is 60?}\qquad c=1.03(60)[/tex]

Final answer:

The total cost of a $60 item including a 3% sales tax, which has been derived from a $25 item that costs $25.75 after tax, is $61.80.

Explanation:

The total cost of an item including sales tax is directly proportional to its price.

This means that the sales tax is a constant ratio to its price.

For a $25 item, the total cost (including sales tax) is $25.75. Therefore, the sales tax is $0.75. The tax rate is consequently $0.75/$25 = 0.03 or 3%. Now, if you want to find the total cost of a $60 item, you will apply this tax rate to the price.

Thus, the total cost including tax would be $60 + (3% of $60), or $60 + $1.80 = $61.80.

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How do you change a ratio into a fraction baseballs to basketballs

Answers

[tex]\bf baseballs:basketballs\implies \cfrac{baseballs}{basketballs} \\\\\\ anything:whatever\implies\cfrac{anything}{whatever}[/tex]

if that's what you mean.

a=one half bh solve for b

Answers

A = [1/2] bh

1) Multiply both sides by 2 =>

2A = 2 * [1/2] bh

2A = [2/2]bh

2A = bh

2) Divide both sides by h =>

2A/h = bh / h

=> 2A/h = b

Answer: b = 2A/h

How are midsegments of trapezoids and triangles alike? How are they different?

Answers

similarity 1.

Midsegments of a triangle and a trapezoid are alike, because their endpoints, are the midpoints of the sides they touch.

similarity 2.
The length of the midsegment of a trapezoid is (large base+small base)/2

whereas, the length of a midsegment of a triangle is base/2.

difference 1:

Midsegments of triangles and trapezoids are different, because we can draw 3 of them in triangles, but only one in trapezoids.

(we can only join the midpoints of the nonparallel sides of a trapezoid to form its only midsegment.)

Final answer:

In both trapezoids and triangles, midsegments connect the midpoints of two sides. They are parallel to one side and their lengths are determined by the measurements of certain sides. The main difference lies in the number of midsegments each shape can have: a trapezoid can have only one, while a triangle can have three.

Explanation:

In both trapezoids and triangles, a midsegment is a line segment that connects the midpoints of two sides. The similarity between these midsegments lies in their properties. In both cases, the midsegments are parallel to one of the sides of the figure (the base for the trapezoids and the third side for the triangles) and their length is equivalent to the average of the two bases in a trapezoid and half the length of the base in a triangle.

However, the main difference between midsegments of trapezoids and triangles is the number of such segments each figure can have. A trapezoid has only one midsegment, that connects the midpoints of the non-parallel sides, while a triangle can have up to three midsegments, one for each side of the triangle.

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One survey estimates that, on average, the retail value of a mid-sized car decreases by 8% annually. If the retail value of a car is V dollars today, which expression represents the car’s value 1 year later?

A. 0.08V
B. 0.92V
C. 1.08V
D. V-0.08

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &V\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ t=\textit{elapsed time}\to &1\\ \end{cases} \\\\\\ A=V(1-0.08)^1\implies A=V(0.92)\implies A=0.92V[/tex]

Answer:

i ggot it right on test

Ineed help help me please

Answers

The symbol ₁₂P₉ represents the permutations of 9 quantities out of 12.
By definition,
[tex]_{12}P_{9} = \frac{12!}{(12-9)!} = \frac{12!}{3!} [/tex]

From the calculator,
12! = 479,001,600
3! = 6

Therefore
₁₂P₉ = 479001600/6 = 79,833,600

Answer: 79,833,600

Joe Popoff, a collection agent, collected 90% of a debt of $5,600.00 that had been overdue 90 days. This collection rate was 5% more than the average collection rate for that agenr. The agent charged 25% commission. What are the net proceeds?

Answers

You are given the debt collected by Joe Popoff with a 90% of a debt of $5,600.00 that had been overdue 90 days. This collection rate was 5% more than the average collection rate for that agent. The agent charged 25% commission. You are asked to find the net proceeds.

Amount collected
= $5,600 * 0.90
= $5,040

Commision
= $5,040 * 0.25
= $1,260

Net Proceeds
= $5,040 - $1,260
= $3,780

please help me!!!
The scale for the map of Missouri is 1 in = 30 mi. On the map, the distance from Springfield to Columbus is about 5.6 in. How far apart are the two cities? Round your answer to the nearest mile.

Answers

if 1 inch = 30 miles

thn multiply 30 x 5.6

30 x 5.6 = 168 miles apart

The actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

To find the actual distance between Springfield and Columbia, we can use the scale provided in the map.

Given that 1 inch on the map represents 30 miles in real life, and the distance on the map from Springfield to Columbia is 5.6 inches, we can use the following calculation to find the actual distance:

[tex]\[ \text{Actual distance} = \text{Map distance} \times \text{Scale factor} \][/tex]

[tex]\[ \text{Actual distance} = 5.6 \, \text{inches} \times 30 \, \text{miles/inch} \][/tex]

[tex]\[ \text{Actual distance} = 168 \, \text{miles} \][/tex]

So, the actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

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