Charlie wants to solve the equation -1/4(x-1) =2/3 x +2. Which step would not be an appropriate first step for Charlie to take to solve for x?

The value of vehicle after 15 years is $12,846.98 when purchased at $32500 and with rate of depreciation 6%.

The depreciation rate is the percentage at which an asset depreciates over its anticipated useful life. It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expense over the course of the asset's useful life.

Here,

The value of vehicle=$32500

rate of depreciation=6% per year

time period=15 years

The percent value of vehicle=100-6=94%

Therefore to find the value in 15 years we multiply 32500 by 0.94 raised to the 15th power.

The value of vehicle after 15 years=$12,846.98

After 15 years, a vehicle that cost $32,500 and had a 6% depreciation rate is worth $12,846.98.

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The value of the test statistic is 2.59.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

Here, the percentage of residents favored construction is 34%.

[tex]p\leq 0.31\\p > 0.31[/tex]

The test statistics is given by,

[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]

Here n=1600, P=0.34 and p=0.31,

Putting the values,

[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]

Test Statistics = 2.59

Therefore, the value of test statistics is 2.59.

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Answer:

Line 1 is considered perpendicular

Line 2 is considered parallel

Line 3 is also parallel

Step-by-step explanation:

This should be right if this is the rest to your problem:

1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)

2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)

3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)

Answer:

y = [tex]\frac{1}{3}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line

In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.

A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.

Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.

Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.

We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.

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Answer: $2738.02

Step-by-step explanation:

1) (3000x0.97) = 2910  } Year 1

2) (2910x0.97) = 2822.7  } Year 2

3) (2822.7x0.97) = 2738.019  } Year 3

If Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. The appropriate financial professional for Rod is: a. Discount broker.

A Discount broker can be defined as a type of broker which gives out discount to investor to offers lesser commission fees or rate to investors

Discount broker tend to as well help to handle  the buying and selling of stocks and they as well rendered different services to investors. Most investors tend to make use of discount broker instead of full service broker because of the lower commission fees that discount brokers often charge.

Based on the given scenario i will recommend Rod to make use of discount broker as they are professional financial assistance when it comes to buying and selling of stocks.

Therefore the correct option is A.

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The complete question is:

Rod is looking for professional financial assistance. Rod has a solid grasp of how investing works, but needs a way to handle the actual buying and selling of stocks. Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. Recommend an appropriate financial professional for Rod.

a.Discount broker

b.Full-service broker

c.Financial planner

d.Investment Advisor

The equivalents of the functions are f(x)+g(x) = -2x²-x+6, g(x) - f(x) =   -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given: f(x)  = 3x + 2, g(x) = -2x²-2x+4 and h(x) = 3x²-4x

To solve this problem, just substitute the value of the function and perform the necessary operations on them.

f(x)+g(x)  = (3x+2) + (-2x²-2x+4)

            =  3x+2-2x²-2x+4

           =  -2x²-x+6

g(x) - f(x) = (-2x²-2x+4) - (3x+2)

              =  -2x²-2x+4-3x-2

             =   -2x²-5x+2

f(x).g(x)  = (3x+2)(-2x²-2x+4)

             = -6x³-6x²+12x -4x²-4x+8

            =  -6x³-10x²+8x+8            

h(x) - f(x) = (3x²-4x) - (3x + 2)

             = 3x²-4x-3x-2

             = 3x²-7x-2

f( x) . h(x) = (3x + 2)(3x²-4x)

              = 9x³-12x²+6x²-8x

              = 9x³-6x²-8x

f(x)+g(x)+h(x) = (3x + 2) + (-2x²-2x+4) + (3x²-4x)

                    = 3x+2-2x²-2x+4+3x²-4x

                    = x²-3x+6

Therefore, the equivalents are f(x)+g(x) = -2x²-x+6, g(x) - f(x) =   -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6. You should match them accordingly

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Answer:

-3,-2,-1,0,1

Step-by-step explanation:

Just replace x with the x value to find the y value

y=x-1

y=-2-1

y=-3

Y=-1-1

y=-2

y=0-1

y=-1

y=1-1

y=0

y=2-1

y=1

hopes this helps please mark brainliest

The expression that represents the area of the triangle is given as follows:

A = (c - a)[8 - (c - a)]/4.

The area of a triangle is obtained as half the multiplication between the base b and the height h, that is:

A = 1/2 x b x h.

For the triangle in this problem, the base is composed by these following vertices:

Hence the length of the base is of:

b = c - a.

The height is given by the difference between the y-coordinate of the vertex (b,4) and the midpoint of the base ac, hence:

h = 4 - (c - a)/2 = [8 - (c - a)]/2

Hence the area is given as follows:

A = 1/2 x (c - a) x [8 - (c - a)]/2

A = (c - a)[8 - (c - a)]/4.

The problem asks for which expression gives the area of the triangle with these vertices.

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Answer:

b)1.39

Step-by-step explanation:

i got it right on test

Answer:

other base = 16.3 yds

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the height between the parallel bases b₁ and b₂

given b₁ = 7 , h = 12 and A = 139.8 , then

[tex]\frac{1}{2}[/tex] × 12 × (7 + b₂ ) = 139.8

6(7 + b₂ ) = 139.8 ( divide both sides by 6 )

7 + b₂ = 23.3 ( subtract 7 from both sides )

b₂ = 16.3

the length of the other base is 16.3 yards

The image of (-1,7) after a reflection over the line y = x is (7, -1).

What is a line of reflection?

When reflecting a figure in a line or a point, the image and preimage coincide. A reflection converts each point in a figure from a point to an image via a set line. The reflection line is the name given to the fixed line.

Here, we have

Image : (-1.7)

Now,

Reflect over the line y = x:

When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.

Thus, the point (-1,7) maps to the point (7,-1) when reflected over y=x.

Hence, The image of (-1,7) after a reflection over the line y = x is (7, -1).

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The measure of < BAP in the figure of the circle is 30 degrees

< ACB covers same angle as < APB

therefore

< ACB = < BAP = 120

complete the line PB to form another radius. since radius of a circle are equal, an isosceles triangle is created

Isosceles triangle has a unique  property of 2 equal equal sides and equal base angles. one of the angles of the isosceles triangle is < BAP

solving with the new triangle APB

< BAP = < PBA (base angles of isosceles triangle)

< BAP + < PBA + 120 = 180

2 < BAP = 180 - 120

2 < BAP = 60

< BAP = 30 degrees

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Answer:

200 cm²

Step-by-step explanation:

Find the areas of all of the faces

17 × 2 = 34 (Top Face)

8 × 15 = 120 (Both Triangles)

15 × 3 = 30 (Bottom Face)

8 × 2 = 16 (Back Face)

Add them all together

120 + 34 + 30 + 16 = 200 cm²

The expression is x - a = 8.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Difference between two numbers is 8.

The lesser number is a.

let the another number be 'x'.

So, Difference between two numbers

x - a = 8

Hence, the expression is x - a = 8.

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1) Radius of the standard tank = 3 feet

2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.

3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.

4)Total volume of the tank is  36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet

5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.

6)Trails of values for r is 4 feet.

What do you mean by Volume?

A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.

What is radius?

A line segment connecting the circumference or boundary surface of a circle or sphere to its center.

Given that;

Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]

                                                [tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]

Volume of new tank = 2 x Volume of standard tank

                                  =  2 x 126π

                                  = 252π

But according to formula, volume of new tank will be;

[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]

where r = radius of new tank

[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]

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Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.

Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.

Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.

Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).

Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.

Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:

365 secοnds + 7.5x secοnds ≤ 875 secοnds

Subtracting 365 secοnds frοm bοth sides gives:

7.5x secοnds ≤ 510 secοnds

Dividing bοth sides by 7.5 gives:

x secοnds ≤ 68 secοnds

Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.

Therefοre, the answer is 68 secοnds.

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Option B is the correct choice.

Based on the findings, the following list compares the portfolios' overall performances, ranking them from best to worst:

Portfolios 2, 3, and 1, respectively.

The weighted average ROR is calculated by adding the rates of return on the portfolio's assets and the percentage of the portfolio that is invested in each investment.

For Portfolio 1:

Total Investment= $700 + $2575 + $220 + $1000 + $1430 = $5925

Therefore, total investment = $5,925

Weighted Average ROR= (-3.8% * $700) / $5925 + (2.1% * $2575) / $5925 + (11.3% * $220) / $5925 + (5.8% * $1000) / $5925 + (1.6% * $1430) / $5925

WAROR = (-0.0045) + 0.0091 + 0.0042 + 0.0098 + 0.0039 = 0.0225

Therefore, the Weighted Average ROR= 2.25% (third)

For Portfolio 2:

Total Investment = $1250 + $1700 + $1515 + $1345 + $1,675 = $7485

Therefore, Total Investment = $7,485

Weighted Average ROR = (-3.8% * $1250) / $7485 + (2.1% * $1700) / $7485 + (11.3% * $1515) / $7485 + (5.8% * $1345) / $7485 + (1.6% * $1,675) / $7485

= (-0.0063) + 0.0048 + 0.0229 + 0.0104 + 0.0036 = 0.0354

Therefore, the Weighted Average ROR = 3.54% (first)

For Portfolio 3:

Total Investment = $1025 + $500 + $790 + $250 + $2500 = $5065

Therefore, Total Investment = $5,065

Weighted Average ROR = (-3.8% * $1025) / $5065 + (2.1% * $500) / $5065 + (11.3% * $790) / $5065 + (5.8% * $250) / $5065 + (1.6% * $2,500) / $5065

= (-0.0077) + 0.0021 + 0.0176 + 0.0029 + 0.0079 = 0.0228

Therefore, Weighted Average ROR = 2.28% (second)

Therefore, the correct order of portfolios based on the performance from best to worst will be:

Portfolio 2, Portfolio 3, and Portfolio 1. (Option B)

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COMPLETE QUESTION:

ROR Portfolio 1 Portfolio 2 Portfolio 3 −3.8% $700 $1,250 $1,025 2.1% $2,575 $1,700 $500 11.3% $220 $1,515 $790 5.8% $1,000 $1,345 $250 1.6% $1,430 $1,675 $2,500 Using technology, calculate the weighted average of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?

A) Portfolio 1, Portfolio 3, Portfolio 2

B) Portfolio 2, Portfolio 3, Portfolio 1

C) Portfolio 1, Portfolio 2, Portfolio 3

D) Portfolio 3, Portfolio 2, Portfolio 1

Answer:36.1

Step-by-step explanation:

ixl

From the information, observe that the food and drug Administration is a US government agency that regulates food and drugs for customer safety.

One thing the FDA regulates is the allowable insect parts in various foods.

When wheat is ground into the flour, insects that were in the wheat are ground up as well.

The mean number of insect parts allowed in 100 grams of wheat flour is 75

The FDA takes a random sample of 35 bags of floor for evaluation and finds that their average of 80 insect parts per 100 grams with a standard deviation of 6.3

In this situation use t test for population mean because the population standard deviation is not known.

Hence, the correct option is (2).

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As per the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

As given in the question,

Given equation in inequality form is :

4x - 2y > 12

Simplify the given equation in intercept form we get,

2y < 4x -12

⇒ y < 2x -6

If we write this inequality in equation form we have,

y = 2x -6

slope of the line is 2

x -intercept is x = 3

y - intercept is y = -6

And in inequality form x > 3 and y < -6.

Therefore, for the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

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The diagonals of a square are equal to each other

Let ABCD be a square.

We need to prove that the diagonals are equal to each other

AC=BD and AC and BD bisect each other at right angles

(i) Considering the ΔABC and ΔBAD,

AB=AB ( common line)

BC=AD ( opppsite sides of a square)

∠ABC=∠BAD ( = 90° )

ΔABC≅ΔBAD( By SideAngleSide property)

AC=BD ( by CPCT).

(ii) Now in triangles ΔOAD and ΔOCB,

AD=CB ( opposite sides of a square)

∠OAD=∠OCB ( transversal AC )

∠ODA=∠OBC ( transversal BD )

ΔOAD≅ΔOCB (ASA property)

OA=OC ---------(i)

Similarly OB=OD ----------(ii)

From (i) and (ii)  we can conclude that AC and BD bisect each other.

Now in a ΔOBA and ΔODA,

OB=OD ( from (ii) )

BA=DA

OA=OA  ( common line )

ΔAOB=ΔAOD----(iii) ( by CPCT

∠AOB+∠AOD=180°  (linear pair)

2∠AOB=180°

∠AOB=∠AOD=90°

Therefore, it is proved that AC and BD bisect each other at right angles.

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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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The number of cell phone brands will be:

Samsung = 144

iPhone = 18

Motorola = 36

Huawei = 162

From the information, the business has 360 cell phones.

Samsung will be:

= Percentage × Total phone

= 40% × 360

= 0.4 × 360

= 144

iPhone = 5% × 360

= 0.05 × 360

= 18

Motorola = 10% × 360

= 0.1 × 360

= 36

Huawei = 45% × 360

= 0.45 × 360

= 162

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The size if the angle NOM is 54.

What is angle?

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

What is tangent of circle?

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.

Given,

M and N are points on a circle.

QMT is the tangent

O is the center.

angle NOM = 2 angle NLM

NOM = 2(27)

= 54.

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The probability that more boys than girls are chosen is 0.4731. So option b is correct.

Combination:

The act of combining or the state of being combined. A number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.

Here it is given that there are 18 boys and 19 girls and 5 students are chosen.

We have to find the probability that more boys than girls are chosen.

Probability = [tex]C^{5} _{18}[/tex] + [tex]C^{4}_{18} C^{1} _{19}[/tex] + [tex]C^{3} _{18} C^{2} _{19}[/tex] / [tex]C^{5}x_{37}[/tex]

                  = 8568 + 58140 + 139536 / 435897

                  ≈ 0.4731

Therefore the probability is 0.4731.

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Answer: 0.4754

A poker hand is a combination of 5 cards from the pack of 52 cards.

One hand full is said when we have 2 cards of the same rank.

In this question, we have to find the probability of 2 hands full of different ranks.

So,

We use the formula : C(n,k)=\frac{n!}{k!(n-k)!}

From permutations and combinations, since order doesn't exist.

From a suit of 13 cards any two cards are chosen:

C(13,2)=\frac{13!}{2!(13-2)!}

C(13,2)=\frac{13×12×11!}{2!11!}

C(13,2)=\frac{13×12!}{2!}

C(13,2)=156/2

C(13,2)=78

78 ways are there to choose for each of the pairs .

Now,

If one of the ranks is of any particular suit or maybe a face card out of which two of them are chosen.

C(4,2)=\frac{4!}{2!(4-2)!}

C(4,2)=6

And same for the other sets of cards of another pair.

We have 78×6×6= 2808 ways to pick the first 4 cards.

Now,

For the fifth card which can be any card except for the paired suit i.e, 13-2=11

There are 4 suits to pick from, 4×11= 44 cards to pick for the final card.

For the first card = 2080

For the fifth card= 44

Total number of two pair hands possible= 2080×44= 123,552

Out of:

C(52,5)=\frac{53!}{5!(52-5)!}

C(52,5)= 2,598,960

Probability of event= 123,552/2,598,960

= 0.4753901560624

Final answer= 0.4754

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The probability of being dealt a two-pair is 0.4754.

Given;

What is the likelihood of receiving a two-pair when dealing a five-card poker hand from a 52-card deck that has been properly shuffled?

We use combinations to solve the given case;

From each suit, any two cards are chosen,

C(13,2) = [tex]\frac{13!}{2!(13-2)!}[/tex]

           = [tex]\frac{13*12*11!}{2!11!}[/tex]

           = 156/2

           = 78

Hence, there are 78 ways to choose for each of the pairs.

Now,

If one of the ranks is a face card, two of them are chosen, or if one of the ranks is a certain suit.

C(4,2) = [tex]\frac{4!}{2!(4-2)!}[/tex]

          =6

Similar to the other sets of cards of another pair.

We have 78×6×6= 2808 ways to pick the first 4 cards.

Now,

The fifth card, which can be any card other than the paired suit, is dealt as follows: 13 - 2 = 11.

There are 44 cards total to choose from among the 4 suits, or 4 x 11.

2080 for the primary card.

44 for the fifth card.

Possible two-pair hands total 2080 x 44 = 123,552.

Then,

C(52,5) = [tex]\frac{53!}{5!(52-5)!}[/tex]

            = 2,598,960

Probability of event = Possible two-pair hands / Total outcome

                                 = 123,552 / 2,598,960

                                 = 0.47539

Hence, the probability of being dealt a two-pair is 0.4754.

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Answer:

Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating

Answer:

b.  12, 17, 23

Step-by-step explanation:

Look at the differences between the numbers.

Number   Difference

2                  

3                      1

5                      2

8                      3    The difference increase by 1 at each step.  The next 3 increase would be:

                        4

                        5

                        6

The next three numbers are:

12                       4

17                        5

23                       6

Answer:

b.

12, 17, 23

Step-by-step explanation: