a lottery consists of selecting 5 numbers out of 45 numbers. you win $10 if exactly three of your 5 numbers are matched to the winning numbers chosen. what is the probability of winning the $10? round your answer to six decimal places.

Answer:

[tex]y=-\frac{2}{3}x-2[/tex]

Step-by-step explanation:

To find the equation in slope-intercept form, isolate [tex]y[/tex].

[tex]2x+3y=-6 \\ \\ 3y=-2x-6 \\ \\ y=-\frac{2}{3}x-2[/tex]

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 product of a number minus 17 and 5 are equivalent to: 5 (n - 17) .

X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.

the sum of a number less than 17 and five

If x is an ambiguous number,

The sign for minus is -

A number less than 17 is denoted by x-17.

The multiplication is the product.

Add x-17 and (x-17)5 to get the answer.

In this case, the expression is 5 (n - 17).

When two numbers are multiplied together, the outcome is known as the product.

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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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Answer:

x > 17

Step-by-step explanation:

x - 5 > 12 ( isolate x by adding 5 to both sides )

x > 17

-------------- from your comment

x - (- 5) > 12 , that is

x + 5 > 12 ( subtract 5 from both sides )

x > 7

The rewritten expression will be 4a³ and the value of this expression is -500.

Given in the question:

(2a⁴)² / a⁰a⁵

We know that

(xy)ⁿ = xⁿ × yⁿ ... (i)

We can use equation (i) for the next step of our given expression.

In the case of the numerator:

(2a⁴)² = 2² × a⁸ = 4a⁸

Now, we know, any number to the power of zero is 1.

So, for the denominator, we get:

a⁰a⁵ = 1 × a⁵ = a⁵

We know,

pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)

Using this equation, we can further simplify the given expression:

⇒ 4a⁸ / a⁵

⇒ 4 a⁽⁸ ⁻ ⁵⁾

⇒ 4 a ³ ... (iii)

Now, in the second part of the question, we need to find the value of the expression.

Given a = -5

Putting this value in equation (iii) we get:

4 a ³

⇒ 4 (-5) ³

⇒ 4 × (-125)

⇒ -500

Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.

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There are 56 ways to choose a committee of students.

What is Combination?

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

A committee of five be selected from eight students if two particular students are to be included.

Now,

Since, 2 members are must be included.

So, We have to choose 3 student from 8 student to form a committee.

Hence, The number of ways to choose 3 students from 8 students is,

= [tex]^{8} C_{3}[/tex]

= 8! / (8-3)! 3!

= 8! / 5! 3!

= 8 x 7 x 6 / 3 x 2

= 56

Thus, There are 56 ways to choose a committee of students.

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The perimeter of the floor in the scale drawing is 32 inches.

Using ratio and proportion, determine the width of the scale drawing of the floor.

actual length / scale length = actual width / scale width

36 feet / 9 inches = 28 feet / scale width

scale width = 28 feet (9 inches / 36 feet)

scale width = 7 inches

Perimeter is defined as distance around a two-dimensional shape.

The perimeter of a rectangle can be calculated using the formula below.

P = 2(l + w)

where P = perimeter

l = length

w =width

Plug in the values of the dimension of the scale drawing and determine its perimeter.

P = 2(l + w)

P = 2(9 inches + 7 inches)

P = 32 inches

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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

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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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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If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.

The definition of the MoE, or margin of error, is

MoE = sigma ÷ sqrt(n)

The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.

The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.

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1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD

1b) The additional information required using ASA Congruency postulate  is BC ≅ QR

2a) The symbolic form of the congruent triangles is written as;

ΔABC ≅ ΔADC

2b) The congruence Postulate that is used is SAS Congruency postulate.

1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;

∠AOB ≅ ∠BOD

1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;

∠Q = ∠B

∠R = ∠C.

Therefore, the additional information is BC ≅ QR

2a) The symbolic form of the given congruent triangles is expressed as;

ΔABC ≅ ΔADC

2b) The congruence postulate that was used here is SAS Congruency postulate.

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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 common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

a.

common ratio r = a2/a1

= -3360/4480

= -0.75.

r = a3/a2

= 2520/-3360

= -0.75

b.

[tex]a_{n}[/tex] = a*r^(n-1)

here a = 4480 and r = -0.75.

= 4480(-0.75)^(20-1)

= 4480(-0.75)^19

= 4480*(-0.00422)

[tex]a_{20}[/tex] = -18.9056.

c.

[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))

= 4480*((1--0.75^4)/(1--0.75))

= 4480*((1-0.31640625)/(1--0.75))

= 4480*(0.68359375/1.75)

= 4480*0.390625

= 1750

Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

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Answer:

y=3x+1

Step-by-step explanation:

we know slope so just fill in the rest

y=3x

-2=3(-1)

-2=-3

We add 1 to make the equation true so the y intercept is 1

Hopes this helps please mark brainliest

Tower B is 14.9 miles away from the fire.

What is the law of sines?

According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.

Here,

According to the law of sines

BC/sin A = AC/sin B = AB/sin C

∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°

AB = 21 miles

So, BC = (AB/SinC)×SinA

BC = 14.9 miles

Hence, Tower B is 14.9 miles away from the fire.

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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: 1/4

Step-by-step explanation:

0.75 liters is the same as 750 grams.

So, the total mass of the mixture is [tex]300+150+750=1200[/tex] g.

This means the ratio is [tex]\frac{300}{1200}=\frac{1}{4}[/tex].

Answer:

Flour : total mass = 1 : 4

Step-by-step explanation:

Given ingredients for the cake:

First convert the mass of the water to the same SI units as the other ingredients.

1 liter = 1000 g

⇒ Water = 0.75 liters = 750 g

Total mass of the mixture:

= flour + sugar + water

= 300 g + 150 g + 750 g

= 1200 g

Therefore, the flour to total mass ratio is:

⇒ Flour : total mass = 300 : 1200 = 1 : 4

From the diagram, A is the major arc

                               B is the minor sector

                               C is the major segment.

What do you mean by major arc, minor sector, and a major segment of a circle?

      1. Major arc: A significant arc is one that is larger than 180 degrees in measure.

      2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.

The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.

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The simplification of the number by solving square root  5√18 is 15√2.

For the given number

= 5√18

Find the factors of 18 by prime factorization.

18 = 2 ×3 ×3

Put in the number.

=  5√2 ×3 ×3

Taking 3 out of root.

=  5×3√2

Further solving.

= 15√2

Thus, the simplification of the number by solving square root  5√18 is 15√2.

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Answer: is 16.6%

Step-by-step explanation: Use the rule of three (mathematic).

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 solution to the quotient for 2.0 and 4.0 is 0.50

From the question, the mathematical statement is given as

The quotient for 2.0 and 4.0

The quotient of numbers is their division

This in other words mean that:

The quotient for a and b is a/b

Using the above highlights as a guide, we have

The quotient for 2.0 and 4.0 to be 2.0/4.0

Evaluate the quotients

So, we have the following representation

The quotient for 2.0 and 4.0 to be 0.50

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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:

expanded: x^2+8x+15

Step-by-step explanation:

(x+3)(x+5)

x^2+5x+3x+15

The value of the correlation coefficient is 0.60.

There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.

R² is the coefficient of determination, which measures how much variation can be explained by the regression line.

This means that, the R² value of the data is 36%

R² = 36% = 0.36

Correlation coefficients measure the strength of relationships between variables in the form of square roots.

That is ; R = √R²

R = √0.36

Hence, the correlation Coefficient, R is 0.60

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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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