Five Card Draw is one of most basic forms of poker, and it's the kind of poker you're used to seeing in movies and on TV. This game has been around for a long time, and has been played in countless home games and card rooms across the nation. Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players, then a round of betting occurs. Some combinations of five-card hand have special names such as full house, royal flush, four of a kind, etc. Let`s find some 5-card combinations. Order of the drawn card does not matter. a) A flush is a poker hand, where all five cards are of the same suit, but not in sequence. Compute the number of a 5-card poker hands containing all diamonds.

Answer:

D. 1/2

Step-by-step explanation:

Coin tosses are independent.  Past results don't affect future probabilities.  So the probability of getting heads on the fourth toss is still 1/2.

Answer:

D. 1/2

Step-by-step explanation:

Flipping coin is an INDEPENDENT event, meaning that if you flip a coin before, it is NOT going to affect the outcome of the next coin flipping

Since a coin has 2 sides, so the probability is 1/2

Answer:

  "unchanged"

Step-by-step explanation:

Congruence transformations (translation, rotation, reflection) do not change lengths, angles, area (of 2D figures), or volume (of 3D figures). The area would remain unchanged.

Answer:

Assumption: [tex]f(x)[/tex] is defined for all [tex]x\in \mathbb{R}[/tex] (all real values of [tex]x[/tex].)

Step-by-step explanation:

Evaluating [tex]f(x)[/tex] for a root of this function shall give zero.

Equate [tex]f(x)[/tex] and zero [tex]0[/tex] to find the root(s) of [tex]f(x)[/tex].

[tex]f(x) =0[/tex].

[tex](x - 6) \cdot 2 \cdot (x + 2) \cdot 2 = 0[/tex].

Multiply both sides by 1/4:

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0\times\frac{1}{4} = 0[/tex].

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0[/tex].

This polynomial has two factors:

Apply the factor theorem:

Answer:

X=6 , X = -2

Step-by-step explanation:

For any polynomial given in factorised form , the roots are determined as explained below:

Suppose we have a polynomial

(x-m)(x-n)(x+p)(x-q)

The roots of above polynomial will be m,n,-p, and q

Also if we have same factors more than once , there will be duplicate roots.

Example

(x-m)^2(x-n)(x+p)^2

For above polynomial

There will be total 5 roots . Out of which 2(m and -p) of them will be repeated. x=m , x=n , x =-p

Hence in our problem

The roots of f(x)= (x-6)^2(x+2)^2 are

x=6 And x=-2

Answer with explanation:

Let me answer this question by taking two decimals less than 1.

A= 0.50

B= 0.25

→A × B

= 0.50 × 0.25

=0.125

It is less than both A and B.

→→A=0.99

B= 0.1

→C=A × B

= 0.99 × 0.1

=0.099

It is less than both A and B.

So, We can say with surety, that if take two decimals ,both less than 1, the product of these two decimals will be  less than each of the original decimals.

General Rule

→A =0. p ,

→ B=0. 0 q,

Product of , A × B, gives a number in which  there will be three digits after decimal which will be always less than both A and B as in A, there is one digit after decimal, and in B there are two digits after decimal.

Answer: 0.07

Step-by-step explanation:

Given: Mean : [tex]\mu = 82[/tex]

Standard deviation : [tex]\sigma = 13[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 80

[tex]z=\dfrac{80-82}{13}=−0.15384615384\approx-1.5[/tex]

The P Value =[tex]P(z<-1.5)=0.0668072\approx0.07[/tex]

Hence, the  probability that a randomly selected score was less than 80 =0.07

Answer:

[tex](x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Step-by-step explanation:

The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2[/tex]

From the info, we can say:

a = 4

b = 3

c = 5

r = [tex]\sqrt{6}[/tex]

Plugging into formula we get the equation:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(\sqrt{6} )^{2} \\(x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Remember to use

Answer:

The last option is correct

Step-by-step explanation:

Hope this helps!

Answer:

4/7 < 6/9. Hope this helps

Answer:

f(t)=9,220,000(0.888)^t

Step-by-step explanation:

We use 9,220,000 as our base because this is where the decay begins. To get the correct amount of decay, we need to subtract 11.2% from 1, or 100%. We get 88.8% so we turn this into a decimal by dividing by 100 and getting 0.888. We put this to the power of t to represent the decay because it has to be an exponent to be exponential decay, not linear decay. f(t) is not necessary, you could also use y. Hope this helps :)

The probability that both firms offer Peter a job is 6%.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

let X be the probability that Peter would receive offer from the accounting firm.

and, Y be the probability that Peter would receive offer from the consulting firm.

We have P(X) = 30% and P(Y) = 20%.

Now we want to find  P(X∪Y)  = ?

We know that

P(A∩B) = P(A) × P(B

             = 30% x 20%

             = 0.30 x 0.20

             = 0.06

             = 6%

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To find the probability that both an accounting firm and a consulting firm offer Peter a job, we multiply the individual probabilities of him receiving an offer from each firm. This results in a 6% chance that Peter will receive job offers from both firms.

The question asks about calculating the probability that Peter receives job offers from both an accounting firm and a consulting firm. Since the events are independent, the probability that both events occur is the product of their individual probabilities.

To compute the probability that both firms offer him a job, we multiply the probability of receiving an offer from the accounting firm (30%) by the probability of receiving an offer from the consulting firm (20%):

Probability(Both offers) = Probability(Accounting offer)  times Probability(Consulting offer)

Probability(Both offers) = 0.30  times 0.20

Probability(Both offers) = 0.06 or 6%

Therefore, the probability that both firms offer Peter a job is 6%.

Answer:

{P|P < -3 or P > 3}

Step-by-step explanation:

When we remove the absolute value bars, we take the positive value, and then flip the inequality and take the negative.  Since the original equation is a greater than, we use the or

p > 3   or    p < -3

Answer:

[tex]\large\boxed{\{P\ |\ P<-3\ or\ P>3\}}[/tex]

Step-by-step explanation:

[tex]\text{The absolute value:}\\\\|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right[/tex]

[tex]|P|>3\iff P>3\ or\ P<-3[/tex]

The cost of toolset before the discount was applied is:

                    Rs.  521.5189

It is given that:

A tool set has been discounted down to a price of Rs 412.00.

The percent discount that is provided to us is: 21%

Let the actual price of toolset be: Rs. x

This means that:

[tex]x-21\%\ of x=412\\\\i.e.\\\\x-0.21x=412\\\\i.e.\\\\(1-0.21)x=412\\\\i.e.\\\\0.79x=412\\\\i.e.\\\\x=\dfrac{412}{0.79}\\\\x=521.5189[/tex]

   Hence, the actual price of toolset i.e. cost before discount is:

                        Rs.   521.5189

To find the original price of the toolset before the discount was applied, we can set up an equation and solve for the original price. The original price of the toolset was R520.89.

To find the original price of the toolbox, we need to first calculate the amount of the discount. The discount given is 21%. Let's say the original price of the toolbox is P. We can calculate the amount of the discount by multiplying the original price by the discount percentage:

Discount = P * 21% = P * 0.21

The discounted price is given as R412.00. So we can set up the equation:

Original price - Discount = Discounted price

P - P * 0.21 = R412.00

We can now solve for P:

P(1 - 0.21) = R412.00

0.79P = R412.00

P = R412.00 / 0.79

P = R520.89

Therefore, the original price of the toolset before the discount was applied was R520.89.

Answer:  The mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.

Step-by-step explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

[tex]\text{Mean=}\dfrac{m+n}{2}\\\\\text{Variance}=\dfrac{(n-m)^2}{12}[/tex]

Given : [tex]m=625\ \ \ n=655[/tex]

[tex]\text{Then, Mean=}\dfrac{625+655}{2}=642.5\\\\\text{Variance}=\dfrac{(655-625)^2}{12}=75[/tex]

Hence, the mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.

Answer:

Max = 86; min = 36.54

Step-by-step explanation:

[tex]f(x) = x^{2} + \dfrac{85}{x}[/tex]

Step 1. Find the critical points.

(a) Take the derivative of the function.

[tex]f'(x) = 2x - \dfrac{85}{x^{2}}[/tex]

Set it to zero and solve.

[tex]\begin{array}{rcl}2x - \dfrac{85}{x^{2}} & = & 0\\\\2x^{3} - 85 & = & 0\\2x^{3} & = & 85\\\\x^{3} & = &\dfrac{85}{2}\\\\x & = & \sqrt [3]{\dfrac{85}{2}}\\\\& \approx & 3.490\\\end{array}\[/tex]

(b) Calculate ƒ(x) at the critical point.  

[tex]f(3.490) = 3.490^{2} + \dfrac{85}{3.490} = 12.18 + 24.36 = 36.54[/tex]

Step 2. Calculate ƒ(x) at the endpoints of the interval

[tex]f(1) = 1^{2} + \dfrac{85}{1} = 1 + 85 = 86\\\\f(5) = 5^{2} + \dfrac{85}{5} = 25 + 17 = 42[/tex]

Step 3.Identify the maxima and minima.

ƒ(x) achieves its absolute maximum of 86 at x = 1 and its absolute minimum of 36.54 at x = 3.490

The figure below shows the graph of ƒ(x) from x = 1 to x = 5.

The maximum and minimum values of the mathematical function f(x) = x^2 + 85/x on the interval [1, 5] occur at the endpoints with the maximum being 86 at x=1 and minimum being 37 at x=5.

To find the maximum and minimum values of the function f(x) = x2 + 85/x over the interval [1, 5], we first find the critical points in that interval. The critical points occur where the derivative of the function is zero or undefined. The derivative of the function f(x) is 2x - 85/x2 and it is undefined at x = 0 and becomes 0 at x = sqrt (42.5).

Since x = 0 is not in our interval, we disregard it. The value x = sqrt (42.5) is also outside our interval [1, 5], so we disregard this too.

Therefore, the maximum and minimum values of the function on the interval [1, 5] occur at the endpoints. We substitute these endpoint values into the function:

Therefore, the maximum value is 86 and the minimum value is 37, at x equals 1 and 5, respectively.

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Answer:

[tex]\boxed{\text{\$581.25; \$81.25}}[/tex]

Step-by-step explanation:

The formula for the total accrued amount is

A = P(1 + rt)

Data:

P = $500

r = 6.5 % = 0.065

t = 30 mo

Calculations:

(a) Convert months to years

t = 30 mo × (1 yr/12 mo) = 2.5 yr

(b) Calculate the accrued amount

A = 500(1 + 0.065 × 2.5)

  = 500(1 + 0.1625)

  = 500 × 1.1625

  = 581.25

[tex]\text{Dasha will have to pay back }\boxed{\textbf{\$581.25}}[/tex]

(c) Calculate the accumulated interest

[tex]\begin{array}{rcl}A & = & P + I\\581.25 & = & 500 + I\\I & = & 81.25\\\end{array}\\\text{The accumulated interest is }\boxed{\textbf{\$81.25}}[/tex]

Answer:

The population standard deviation is not known.

90% Confidence interval by T₁₀-distribution: (38.3, 53.7).

Step-by-step explanation:

The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus [tex]11 - 1 = 10[/tex].

Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,

Look up the t-score of the upper end on an inverse t-table. Focus on the entry with

[tex]t \approx 1.812[/tex].

This value can also be found with technology.

The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:

[tex]\displaystyle t \cdot \frac{s_{n-1}}{\sqrt{n}}[/tex],

where

For this confidence interval:

Hence the width of the 90% confidence interval is

[tex]\displaystyle 1.812 \times \frac{14}{\sqrt{10}} \approx 7.65[/tex].

The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:

[tex](38.3, 53.7)[/tex].

[tex]6\cdot7\cdot5=210[/tex]

210 days

If a set [tex]A[/tex] contains [tex]n[/tex] elements, then the number of subsets of this set is [tex]|\mathcal{P}(A)|=2^n[/tex].

[tex]A=\{4,5,6\}\\|A|=3[/tex]

[tex]|\mathcal{P}(A)|=2^3=8[/tex]

Answer:

B. The expected value of the sample mean is equal to the population mean.

Step-by-step explanation:

The expected value of the sample mean is equal to the population mean  is NOT a property of the sampling distribution of the sample.

This is about understanding properties of sampling distribution of sample mean.

Option A is not a Property of Sampling distribution of Sample mean.

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Answer: 4 units.

Step-by-step explanation:

Once each point is plotted, you get the rectangle attached.

You can observe in the figure that the base of the rectangle is its longer side.

 Since the length of the base of the rectangle goes from [tex]x=-1[/tex] to [tex]x=3[/tex], you can say that the lenght of the base is the difference between 3 and -1.

So, you need to subtract this two coordinates, getting that the lenght of the base of the rectangle attached is:

[tex]lenght_{(base)}=3-(-1)\\\\lenght_{(base)}=3+1\\\\lenght_{(base)}=4\ units[/tex]

Answer: 4 units

Step-by-step explanation:

Answer: 0.0051

Step-by-step explanation:

Given: Mean : [tex]\mu = 50\text{ inch}[/tex]

Standard deviation : [tex]\sigma =1.1\text{ inch}[/tex]

Sample size : [tex]n=8[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x= 51

[tex]z=\dfrac{51-50}{\dfrac{1.1}{\sqrt{8}}}=2.57129738613\approx2.57[/tex]

The P Value =[tex]P(Z>51)=P(z>2.57)=1-P(z<2.57)=1-0.994915=0.005085\approx0.0051[/tex]

Hence, the probability that the sample mean hardness for a random sample of 8 pins is at least 51 =0.0051

Answer:

  1.94%

Step-by-step explanation:

The desired percentage can be found using an appropriate calculator or spreadsheet. A nice on-line calculator is shown in the attachment.

Answer:

165 combinations possible

Step-by-step explanation:

This is a combination problem as opposed to a permutation, because the order in which we fill these positions is not important.  We are merely looking for how many ways each of these 11 people can be rearranged and matched up with different candidates, each in a different position each time.  The formula can be filled in as follows:

₁₁C₃ = [tex]\frac{11!}{3!(11-3)!}[/tex]

which simplifies to

₁₁C₃ = [tex]\frac{11*10*9*8!}{3*2*1(8!)}[/tex]

The factorial of 8 will cancel out in the numerator and the denominator, leaving you with

₁₁C₃ = [tex]\frac{990}{6}[/tex]

which is 165

Answer:

The probability of E and F is 0.367236 ≅ 0.367

Step-by-step explanation:

* Lets study the meaning independent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question  

- There are two events E and F

- E and F are independent

- P(E) = 0.404

- P(F) = 0.909

∵ Events E and F are independent

- To find P(E and F) find the product of P(E) and P(F)

∴ P (E and F) = P(E) · P(F)

∵ P(E) = 0.404

∵ P(F) = 0.909

∴ P(E and F) = (0.404) · (0.909) = 0.367236 ≅ 0.367

* The probability of E and F is 0.367236 ≅ 0.367

the probability that both event E and event F occur is 0.36.

When dealing with independent events, the probability of both events E and F occurring, denoted as P(E and F), is determined by multiplying the probability of event E by the probability of event F. In this case, since P(E)=0.4 and P(F)=0.9 and the events are independent, you calculate P(E and F) as follows:

P(E and F) = P(E)  × P(F) = 0.4 × 0.9 = 0.36.

Therefore, the probability that both event E and event F occur is 0.36.

Hence, the probability is:

               0.8846

D be the event that the card drawn is red.

and F denote the event that the card drawn is a face card.

We are asked to find:

P(D'∪F')

We know that D' denote the complement of event D

and F' denote the complement of event F.

Hence, we have:

[tex]P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)[/tex]

D∩F denote the event that the card is a red card and is a face card as well

Since there are 6 cards which are face as well as red cards out of a total of 52 cards.

Hence, we get:

[tex]P(D'\bigcup F')=1-\dfrac{6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{52-6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{46}{52}\\\\P(D'\bigcup F')=0.8846[/tex]

Answer:

y=131°

x=53°

Step-by-step explanation:

∠ ABD and ∠ BDC are supplementary.

The sum of the supplementary angles =180 °

thus y-4+x=180...........i

x and 37° are complementary, that  is, they add up to 90°

Thus, x=90-37=53°

Using this value in equation 1 we obtain:

y-4°+53° =180°

y= 180°-53°+4°

y=131°

Answer:

x  = 53°

y = 131°

Step-by-step explanation:

From the figure we can see a right angled triangle.

AB∥CD

To find the value of x and y

Consider the large triangle, by using angle sum property we can write,

90 + 37 + x = 180

127 + x = 180

x = 180 - 127

x  = 53°

Since AB∥CD and BD is a traversal on these parallel lines.

Therefore <ABD and < CDB are supplementary

we have x  = 53°,

x + (y - 4) = 180

53 + y - 4 = 180

y = 180 - 49 = 131°

y = 131°

Answer:

[tex]\text{1) }0.1141814[/tex]

[tex]\text{2) }0.6193473[/tex]

[tex]\text{3) }0.2003702[/tex]

Step-by-step explanation:

[tex]\text{1) }P(-0.3203\leq Z \leq-0.0287)=P(Z\leq -0.0287)-P(Z\leq-0.3203)\\\\=0.4885519-0.3743705\\\\=0.1141814[/tex]

[tex]\text{2) }P( -0.5156 \leq Z \leq1.4215)=P(Z\leq 1.4215)-P(Z\leq -0.5156 )\\\\=0.9224142-0.3030669\\\\=0.6193473[/tex]

[tex]\text{3) }P(0.1269\leq Z \leq0.6772)=P(Z\leq 0.6772)-P(Z\leq-0.1269)\\\\=0.7508604- 0.5504902\\\\=0.2003702[/tex]

Answer:

[tex]y=x^2+2x-8[/tex]

Step-by-step explanation:

When you graph those points on a piece of graph paper it appears that the points are in the form of a positive x^2 parabola, which has the standard form

[tex]y=ax^2+bx+c[/tex]

We just need to solve for a, b, and c.  Easy.  We have 3 points from the table.  We will use all three of them to find the values of a, b, and c.

Use the points (0, -8), (2, 0), and (4, 16).  You can use any points, but I chose the one with an x value of 0 for a good reason, and chose the other 2 because I don't like too many negatives!

Use the first point in those above to solve for c:

[tex]-8=a(0)^2+b(0)+c[/tex]

From this you solve for c:  c = -8

Now use the next point along with the value of c to find another equation:

[tex]0=a(2)^2+b(2)-8[/tex] and

[tex]0=4a+2b-8[/tex] so

8 = 4a + 2b

That equation will be used again in a minute.

Use the last point to solve for yet another equation (stay with me...we are almost there!):

[tex]16=a(4)^2+b(4)-8[/tex] and

24 = 16a + 4b

Now we will use the method of elimination to solve for b:

8  =  4a  +  2b

24 = 16a + 4b

Multiply the first equation by -4 to eliminate the a terms:

-32 = -16a - 8b

24 = 16a + 4b

leaves you with

-4b = -8 and b = 2.  Now plug that back in to solve for a:

If 8 = 4a + 2b, then 8 = 4a + 2(2) and 8 = 4a + 4

4a = 4 and a = 1

Again, your equation is

[tex]y=x^2+2x-8[/tex]

Answer: 1527

Step-by-step explanation:

Given: Mean : [tex]\mu = 3234\text{ grams}[/tex]

Standard deviation : [tex]\sigma=871\text{ grams}/tex]

Sample size : [tex]n=1600[/tex]

The formula to calculate the z score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X=1492

[tex]z=\dfrac{1492-3234}{871}=-2[/tex]

The p-value of z =[tex]P(z<-2)=0.0227501[/tex]

For X=4976

[tex]z=\dfrac{4976-3234}{871}=2[/tex]

The p-value of z =[tex]P(z<2)=0.9772498[/tex]

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

[tex]P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997[/tex]

Now, the number  newborns who weighed between 1492 grams and 4976 grams will be :-

[tex]1600\times0.9544997=1527.19952\approx1527[/tex]